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TECHNICAL REPORT STANDARD TITLE PAGE

1. Report No.

85-74

2. Government Accession No. 3. Recipient's Cotalog No.

4. Title and Subtitle

High Dynamic GPS Receiver Validation Demonstration

Final Report

5. Report Date

October 31, 1985

6. Performing Organization Code

7. Author(s) william j. Hurd> joseph Ie statman, Victor

A. V-ilnrnf fpr

8. Performing Organization Report No,

9. Performing Organization Name and Address

JET PROPULSION LABORATORY

California Institute of Technology

4800 Oak Grove Drive

Pasadena, California 91109

10. Work Unit No.

11. Contract or Grant No.

NAS7-918

12. Sponsoring Agency Name and Address

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

Washington, D.C. 20546

13. Type of Report end Period Covered

JPL Publication

14. Sponsoring Agency Code

RE 182 PX-644-11-00-03-20

15. Supplementary Notes

16. Abstract

The Validation Demonstration establishes that the high dynamic Global Positioning

System (GPS) receiver concept developed at JPL meets the dynamic tracking requirements for range instrumentation of missiles and drones. It was demonstrated that'•

the receiver can track the pseudorange and pseudorange rate of vehicles with acceleration in excess of 100 g and jerk in excess of 100 g/s, dynamics ten times

more severe than specified for conventional High Dynamic GPS receivers. These

results -and analytic extensions to a complete system configuration establish that

all range instrumentation requirements can be met. The receiver can be implemented

in the 100 in. volume required by small missiles and drones, and is ideally suited

for transdigitizer or translator applications.

17. Key Words (Selected by Author(s)).

Aircraft Communications and Navigation

Electronics and Electrical Engineering

Navigation, Detection, and Countermeasures

(General)

Navigation and Guidance

18. Distribution Statement

Unclassified - Unlimited

19. Security Clossif. (of this report)

Unclassified

20. Security Clcnilf. (of thl» page)

Unclassified

211 Ne. of Pagei

216

32, Price

JPL 0184 R9IB3
JPL PUBLICATION 85-74

High Dynamic GPS Receiver

Validation Demonstration

Final Report

William J. Hurd

Joseph I. Statman

Victor A. Vilnrotter

October 31, 1985

Prepared for

United States Air Force Systems Command

Armament Division

Through an agreement with

National Aeronautics and Space Administration

by

Jet Propulsion Laboratory

California Institute of Technology

Pasadena, California
The research described in this publication was carried out by the Jet Propulsion

Laboratory, California Institute of Technology, and was sponsored by the United

States Air Force Systems Command, Armament Division, through an agreement

with the National Aeronautics and Space Administration.

Reference herein to any specific commercial.product, process, or service by

trade name, trademark, manufacturer, or otherwise, does not constitute or imply

its endorsement by the United States Government or the Jet Propulsion

Laboratory, California Institute of Technology. .
ABSTRACT

The Validation Demonstration establishes that the high dynamic Global

Positioning System (GPS) receiver concept developed at JPL meets the

dynamic tracking requirements for range instrumentation of missiles and

drones. It was demonstrated that the receiver can track the pseudorange

and pseudorange rate of vehicles with acceleration in excess of 100 g and

jerk in excess of 100 g/s, dynamics ten times more severe than specified

for conventional High Dynamic GPS receivers. These results and analytic

extensions to a complete system configuration establish that all range

instrumentation requirements can be met. The receiver can be implemented

in the 100 in.' volume required by small missiles and drones, and is

ideally suited for transdigitizer or translator applications.

iii
ACKNOWLEDGEMENTS

The authors thank the other JPL employees who contributed to the task,

including L. J. Beder for developing the FFT hardware and software, R.

Sydnor, W. P. Hubbard, T. McDade, J. Hops and B. Bronwein for hardware

development, B. K. Levitt, L. Swanson and Q. Vo for' analytic support, J. 0.

Lonborg for the packaging study, and Y. Castillo for typing this

manuscript. We also thank the Armament Division for supporting this work,

especially T. Hancock, N. Gilfand, Lt. J. Collins and Capt. W. Jolley. •

IV
CONTENTS

1. SUMMARY . 1-1

1.1 EXECUTIVE SUMMARY 1-1

1.2 OBJECTIVES AND APPROACH. ......... 1-2

1.3 RESULTS. . . 1-2

1.4 CONCLUSIONS AND RECOMMENDATIONS.. 1-3

2. PURPOSE AND SCOPE 2-1

2.1 PURPOSE 2-1

2.2 SCOPE. 2-1

3. INTRODUCTION 3-1

3.1 BACKGROUND AND RATIONALE FOR DEMONSTRATION 3-1

3.2 DEMONSTRATION DESCRIPTION 3-1

3.2.1 Hardware Configuration 3-2

3.2.2 Specified Objectives and Accomplishments . 3-2

4. SYSTEMS DESCRIPTION 4-1

4.1 FUNCTIONAL REQUIREMENTS 4-1

4.2 RECEIVER PRINCIPLES 4-2

4.3 SYSTEM DESIGN 4-3

4.3.1 System 4-3

4.3.2 Demonstration Receiver 4-3

4.3.3 Test Instrumentation Subsystem 4-6

4.3.4 Data Evaluation Subsystem 4-8

4.3.5 A Typical Test Sequence 4-9

4.4 SYSTEM INTEGRATION AND TESTING 4-10

4.4.1 Implementation 4-10

4.4.2 Test Plans and Procedures 4-11

4.4.3 Test Schedule 4-11

4.4.4 Equipment Performance 4-11

4.4.5 Measured Spectra 4-11

5. PERFORMANCE AND ERROR BUDGET 5-1

5.1 SINGLE CHANNEL PERFORMANCE 5-2

5.1.1 Receiver SNR Losses in Processing 5-2

5.1.2 Loss-of-Lock Threshold SNR . 5-3

5.1.3 Static Errors Due to Receiver Noise 5-4

5.1.4 Instrumentation Errors and Channel Bias 5-5

5.1.5 Total Static Pseudorange Error 5-5

5.1.6 Total Static Pseudorange Rate Error 5-5

5.1.7 Dynamic Tracking Errors 5-5

5.2 COMPLETE RECEIVER PERFORMANCE. . 5-7

5.2.1 Static Accuracies 5-7

5.2.2 Dynamic Accuracies 5-10

5.3 OTHER PERFORMANCE CHARACTERISTICS 5-11

5.3.1 Acquisition . .".' 5-11
Page

8.

5.4

5.3.4 Data Bit Detection

RECEIVER MODIFICATIONS AND ENHANCEMENTS

5.4.1 C/A Code Tracking

5.4.4 Threshold Extension by Combined P and C/A Code Tracking . . .

DEMONSTRATION TESTS AND RESULTS ....

6.1

6.2

6.3

6.4

6.5

SUMMARY OF TEST CONDITIONS

AMLE EVALUATION TESTS

TRACKING FILTER EVALUATION TESTS

PERFORMANCE UNDER HIGH DYNAMICS

PERFORMANCE AT LOW SNR

A CANDIDATE COMPLETE RECEIVER DESIGN AND MINIATURIZATION

7.1

7.2

7.3

OPEN

8.1

8.2

8.3

DESIGN TRADE-OFFS

CANDIDATE BLOCK DIAGRAM FOR COMPLETE RECEIVER

7.2.1. RF Modules

7.2.3 Signal Selector

7.2.8 Clock Module

PACKAGING, COMPONENT COUNT, SIZE AND POWER

QUESTIONS AND FUTURE WORK

HIGH DYNAMIC P CODE RECEIVERS

8.1.3 Tracking Capability and Oscillator Effects

COMBINED P AND C/A CODE TRACKING

ENHANCEMENTS FOR TRANSDIGITIZER RECEIVERS

5-13

5-14

5-14

5-15

5-15

5-15

5-15

5-16

5-17

5-17

6-1

6-1

6-2

6-2

6-3

6-3

6-3

6-4

6-5

6-5

6-6

7-1

7-2

7-3

7-4

7-4

7-4

7-4

7-6

7-6

7-6

7-6

7-7

7-7

7-8

7-11

8-1

8-1

8-1

8-1

8-2

8-2

8-2

8-2

8-3

8-3

8-3

vi
Page

8.3.3 Smoothing .......................... 8-4

8.3.4 Data Aiding ......................... 8-4

8.3*5 Fast Acquisition and Reacquisition .............. 8-4

8.4 MINIATURIZATION ........................... 8-5

9. REFERENCES ................................. 9-1

10. ABBREVIATIONS ............................... 10-1

APPENDIX A DEMONSTRATION

A. 1 GENERAL

A. 1.1

A. 1.2

A. 1.3

A. 1.4

A. 1.5

A. 1.6

A. 1.7

A. 1.8

A. 1.9

A. 1.10

A. 1.11

FUNCTIONAL REQUIREMENTS

DEMONSTRATION REQUIREMENTS

Facilities

A. 2 DEMONSTRATION SYSTEM REQUIREMENTS

A. 2.1

A.2.2

A. 2.2.1

A. 2. 2.1.

A. 2.2.1.

A. 2. 2.1.

A. 2. 2. 2

A.2.2. 2.

A.2.2. 2.

A. 2. 2. 2.

A. 2. 3

A.2.3.1

A. 2. 3. 2

A.2.3.3

A.2.4

A.2.4.1

A.2.4. 2

A.2.4. 3

. . A-1

. . A-1

. . A-1

. . A-1

. . A-2

. . A-2

. . A-2

. . A-2

. . A-2

. . A-2

. . A-2

. . A-2

. . A-2

. . A-3

. . A-3

. . A-3

. . A-3

. . A-4

. . A-4

. . A-5

. . A-5

. . A-5

. . A-5

. . A-6

. . A-6

. . A-6

. . A-6

. . A-7

. . A-7

. . A-7

. . A-7

. . A-7

A. 3 VALIDATION DEMONSTRATION TESTS ................. A-8

A. 3.1 Constant Velocity Tests ............... A-8

A. 3. 1.1 Objectives ...................... A-8

A. 3. 1.2 Test Description. . .............. . . . A-8

A. 3. 1.3 Anticipated Results ................. A-8

A. 3. 1.4 Success Criteria ................... A-9

A. 3. 2 Step Acceleration Tests ............... A-9

A.3.2.1 Objectives. . . ............ ....... A-9

A. 3. 2. 2 Test Description ................... A-9

vii
Page

A.3.2.3 Anticipated Results . A-9

A.3.2.4 Success Criteria - A-9

A.3.3 Circular Motion Tests . A-10

A.3.3.1 Objectives -. . . . A-10

A.3.3.2 Test Description - A-10

A.3.3.3 Anticipated Results -..,..... A-10

A.3.3.4 Success Criteria - A-10

A.4 CHANGES DURING IMPLEMENTATION A-10

APPENDIX B ANALYSES AND SIMULATIONS B-1

B.1 RECEIVER CONCEPT B-1

B.1.1 GPS Signal Characteristics B-2

B. 1.2 Maximum Likelihood Estimation for One Code B-2

B.1.3 Approximate ML Method for One Code B-3

B.1.4 Approximate ML Method Versus PLL Tracking B-3

B.1.5 Combined ML Estimation for Both Codes B-4

B.2 RECEIVER IMPLEMENTATION MODEL B-5

B.2.1 Prediction Removal B-5

B.2.2 AMLE Window . . . . B-7

B.2.3 Predict Addition Block B-7

B.2.1 Tracking Filter B-8

B.2.5 Predictor B-8

B.2.6 Bit Synchronization Tracker B-9

B.3 SNR ANALYSIS B-9

B.3.1 Input Signal to Noise Ratio B-9

B.3.2 Theoretical Performance of Approximate ML Estimator . B-10

B.3.2.1 Pseudorange Estimation at High SNR B-11

B.3.2.2 Pseudorange Rate at High SNR B-11

B.3.2.3 Low SNR Effects B-12

B.3.3 Processing Losses and SNR Corrections B-13

B.3.3.1 Transmitter Filter B-13

B.3.3.2 Correlation Loss B-13

B.3.3.3 A/D Conversion B-14

B.3.3.4 Sine Wave Reference Quantization B-14

B.3.3.5 FFT Filter Passband B-14

B.3.3.6 Dynamics Effects B-14

B.3.3.7 Miscellaneous Losses B-14

B.3.3.8 Processing Loss Summary . . . B-15

B.3.4 AMLE Performance Including Losses B-15

B.4 TRACKING FILTER B-16

B.4.1 State Model and Filter Formulations B-16

B.4.2 Response to Random Noise B-16

B.4.3 Response to Dynamics B-18

B.4.3.1 Second Order Fading Memory Filter B-19

B.4.3.2 Third Order Fading Memory Filter - B-19

B.4.3.3 Second Order Kalman Filter. . . . B-20

B.4.4 The Demonstration Tracking Filter B-20

B.4.5 Tracking Filter for a Complete Receiver B-21

B.5 SIMULATED DEMONSTRATION SYSTEM B-21

B.5.2 Simulation Description B-21

viii
Page

B.5.3 Simulation Operation and Results ....... B-23•-.

B.6 FREQUENCY LOCKED LOOP ... B-21

APPENDIX C DETAILED TEST RESULTS C-1

C.1 TEST CONDITIONS C-1

C.1.1 Simulated Trajectories C-1 .

C.1.2 SNR Conditions C-3

C.1.3 AMLE Configuration C-3

C.2 STATISTICAL SIGNIFICANCE. . C-3

C.3 APPROXIMATE MAXIMUM LIKELIHOOD ESTIMATION EVALUATION -C-5

C.3.1 Measurement of Discrete AMLE Function ......... C-6

C.3.2 Effect of Code Adjustment . C-7

C.3.3 Evaluation of Original Interpolation Formulas C-8

C.3.4 Evaluation of Upgraded Interpolation Formulas .... C-9

C.3.5 AMLE Pseudorange Bias Versus SNR and NCO C-9

C.I TRACKING FILTER EVALUATION. . ..... C-10.

C.1.1 Second Order Fading Memory Filter . . C-10

C.I.2 Third Order Fading Memory Filter. C-11

C.1.3 'Second Order Kalman Filter C-12

C.5 TRACKING UNDER HIGH DYNAMIC CONDITIONS C-13

C.5.1 Constant Velocity Tests . C-11

C.5.2 Step Acceleration Tests C-16

C.5.3 Circular Motion Tests C-19

C.6 PERFORMANCE AT LOW SNR. . . C-22

FIGURES

1-1 Pseudorange Error Versus SNR for 50 g, 10 g/s, Circular Motion 1-1

3-1 Demonstration System Block Diagram. ..... ... 3-1

3-2 Demonstration System Photograph . 3-5

1-1 Demonstration System Interface Diagram 1-13

1-2 Demonstration Receiver Block Diagram. .... 1-11

1-3 Tracking Processor Functional Block Diagram 1-15

1-1 Demonstration Receiver RF Assembly 1-16

1-5 Test Instrumentation Subsystem Block Diagram 1-17

1-6 Test Instrumentation Subsystem - Frequency Synthesis Assembly ...... 1-18

1-7 TIS Signal Combiner and SNR Instrumentation 1-19

1-8 DES Flow Chart 1-20

1-9 The Alphanumeric Display 1-21

1-10 Real Time Graphic Display 1-22

1-11 Measured Spectra 10 MHz/div, 5 dB/div 1-23

5-1 Range Rate Errors,.with Dynamic Component Rempved, Versus SNR for

50 g, 10 g/s, Circular Motion . 5-18

5-2 Maximum Jerk Versus"SNR Threshold for Various Tracking Methods 5-19

6-1 Transient Responses to 50 g Step Acceleration, SNR = 3.1 dB-Hz 6-7

6-2 Transient Responses to 50 g, 10 g/s, Circular Motion, SNR = 33 dB-Hz. . . 6-8

6-3 Random Errors Versus Velocity for Constant Velocity Tests . . . . . . . . 6-9

6-1 Random Errors.Versus Acceleration for Step Acceleration, Tests 6-10

6-5 Peak Transient Errors Versus Acceleration for Step Acceleration

Tests . . 6-11

ix
6-6 Random Errors Versus Acceleration for Circular Motion Tests 6-12

6-7 RMS Tracking Errors Versus Acceleration for Circular Motion Tests .... 6-13

6-8 Pseudorange RMS Error Versus SNR for Circular Motion. 6-1 ^

6-9 Pseudorange RMS Error With and Without Dynamic Component. 6-15

7-1 GPS Receiver Functional Block Diagram 7-13

7-2 RF Module 7-14

7-3 Analog to Digital Converter Module 7-15

7-U Signal Selector 7-16

7-5 Clock Module 7-17

7-6 Receiver Packaging Concept 7-18

7-7 Packaging Concept for Tracking Processors ... 7-19

A-1 Anticipated Performance A-12

B-1 Receiver Model. B-27

B-2 Outlier Probability as a Function of SNR B-28

B-3 Second Order Fading Memory Filter - Noise Response B-29

B-4 Third Order Fading Memory Filter - Noise Response B-30

B-5 Second Order Kalman Filter - Noise Response B-31

B-6 Third Order Fading Memory Filter - Transient Response to Step

Acceleration B-32

B-7 Second Order Fading Memory Filter - Transient Response to Step

Acceleration. B-33

B-8 Second Order Fading Memory Filter - Response to Sinusoidal Motion .... B-31*

B-9 Second Order Fading Memory Filter - Transient Response B-35

B-10 Second Order Fading Memory Filter - Response to Constant Acceleration

and Sinusoids B-36

B-11 Third Order Fading Memory Filter - Transient Response B-37

B-12 Third Order Fading Memory Filter - Response to Sinusoids B-38

B-13 Second Order Kalman Filter - Transient Response ............. B-39

B-14 Second Order Kalman Filter - Response to Constant Acceleration

and Sinusoids B-40

B-15 Third Order Fading Memory Filter - Noise Reduction Factors B-41

B-16 Simulation Output (Circular Motion, 8 s Period, 50 g Acceleration). . . . B-42

B-17 Demonstration Receiver - Tracking Model B-43

B-18 PLL and FLL Functional Block Diagrams B-U3

B-19 Discriminator Characteristics B-43

B-20 Maximum Allowed Input Dynamics for FLLs and PLLs Versus Loop Bandwidth. . B-M

C-1 Simulated Trajectories C-25

C-2 AMLE Response Versus Pseudorange. C-26

C-3 AMLE Response Versus Velocity C-27

C-*» AMLE Amplitude Versus Velocity C-28

C-5 Errors Due to AMLE Interpolation C-29

C-6 AMLE Biases with Upgraded Interpolation Formulas C-30

C-7 Example of Second Order Fading Memory Filter Performance. ... C-31

C-8 Variation of AMLE Peak Coordinates - Second Order Fading Memory

Filter C-32

C-9 Dynamic Lag Errors, Second Order Fading Memory Filter C-33

C-10 Second Order Fading Memory Filter, RMS Noise Before and After

Filtering C-34

C-11 Example of Third Order Fading Memory Filter Performance C-35

C-12 Variation of AMLE Peak Coordinates - Third Order Fading Memory

Filter C-36
C-13 Dynamic Lag Errors, Third Order Fading Memory Filter C-37

C-14 Third Order Fading Memory Filter - RMS Noise Before and After

Filtering C-38

C-15 Example of Second Order Kalman Filter Performance C-39

C-16 Variation of AMLE Peak Coordinates - Second Order Kalman Filter C-UO

C-17 Dynamic Lag Errors - Second Order Kalman Filter C-41

C-18 Second Order Kalman Filter - RMS Noise Before and After Filtering .... C-M2

C-19 Tracking Errors - Circular Motion 150 g, 157 g/s, 34 dB-Hz C-43

C-20 Variation of AMLE Peak Coordinates - Circular Motion 150 g, 157 g/s ... C-44

TABLES

5-1 Receiver SNR Loss Summary 5-3

5-2 Dynamic Errors at 50 g and 50 g/s Maneuvers 5-6

5-3 Static Position Accuracy (HDOP=1.5, VDOP=2.5) 5-8

5-4 Static Absolute Pseudorange Accuracy 5-8

5-5 Static Differential Pseudorange Accuracy 5-9

5-6 Static Velocity Accuracy 5-9

5-7 HDIS and Demonstration Receiver Worst Case Dynamics 5-10

5-8 Dynamic Component of Accuracy ,• 5-11

5-9 Time-To-First-Fix Budget 5-12

5-10 Reacquisition Conditions 5-13

5-11 Reacquisition Time Budget 5-14

7-1 Summary of New 1C Development 7-8

7-2 Volume and Power Estimates. 7-12

B.3-1 Processing Losses Affecting AMLE B-15

C-1 Range Rate Interpolation Formulas Evaluation C-8

C-2 Pseudorange Interpolation Formulas Evaluation C-9

C-3 Constant Velocity Evaluation, High SNR C-14

C-4 Constant Velocity Evaluation, Medium SNR C-15

C-5 Constant Velocity Evaluation, Low SNR ..... C-15

C-6 Step-Acceleration Evaluation, High SNR C-17

C-7 Step-Acceleration Evaluation, Medium SNR C-18

C-8 Step-Acceleration Evaluation, Low SNR C-19

C-9 Circular Motion Evaluation, High SNR C-20

C-10 Circular Motion Evaluation, Medium SNR . . C-21

C-11 Circular Motion Evaluation, Low SNR C-21

C-12 Extended SNR, Circular Motion, 8 s, 50 g C-23

C-13 Extended SNR, Circular Motion, 8 s, 3 g C-24

xi
CHAPTER 1

SUMMARY

1.1 EXECUTIVE SUMMARY

This Validation Demonstration conclusively establishes that the high

dynamic Global Positioning System (GPS) receiver concept developed by JPL

meets the dynamic tracking requirements for range instrumentation of high

dynami c missiles and drones. Analysis indicates that all range

instrumentation requirements can be met, but only the pseudorange tracking

capability was demonstrated. It is recommended that a fully functional

receiver be developed using the high dynamic tracking concept.

It was demonstrated that the receiver accurately tracks pseudorange

and pseudorange rate with acceleration and jerk in excess of 100 g and 1QO

g/s, respectivelyi which constitute dynamics ten times more severe than

specified for conventional GPS High Dynamic Instrumentation Set (HDIS)

receivers [1]. Analysis shows that, at the same time, the receiver position

accuracy can meet the HDIS specifications. Accuracy is limited by the GPS

Space and Control Segments and by propagation effects, not by the receiver

or by vehicle dynamics. This is all accomplished without external aiding

by an inertial navigation unit.

The receiver can be implemented in the stated volume goal of 100 in.3

for missiles and small-scale drones. The design is almost entirely

digital, and is suitable for miniaturization by use of Very Large Scale

Integration (VLSI) Circuits. Still smaller volume appears feasible, but

detailed investigation was outside of the scope of study.

The receiver is ideally suited for transdigitizer or translator

applications. In these applications, the signal from an instrumented

vehicle is relayed to a remotely located processing receiver. The key

feature of the new receiver is that high dynamic vehicles can be tracked

without inertial aiding, which would be unavailable in typical systems.

1-1
1.2 OBJECTIVES AND APPROACH

The general objective of this Validation Demonstration is to establish

that the new receiver concept meets the high dynamic, low volume

requirements for range instrumentation of missiles and drones.

The approach was first to develop and publish a High Dynamic GPS

Receiver Validation Demonstration Plan [2]. This Plan, approved by

Armament Division, presented objectives, concepts, functional requirements

including tests and success criteria, a description of the receiver and the

entire Demonstration System, anticipated performance and error budget, and

a task schedule. The Plan was implemented by developing the receiver and

test instrumentation, conducting the experimental tests and supporting

analyses and simulations, and writing this Final Report. To minimize cost,

the Demonstration Receiver has only one channel, capable of tracking one

simulated satellite in pseudorange and range rate. This is sufficient to

validate the high dynamic and low SNR tracking capability. Feasibility to

meet the volume goal was established by performing a strawman electronic

and packaging design of a complete receiver and estimating the volume and

power.

The Plan established the specific objectives of the Demonstration.

Armament Division stated a volume requirement of 100 in.3 for final

implementation, but did not require specific accuracy, dynamics or SNR

threshold. These latter requirements were based on the overall GPS

accuracy and SNR, and on envisioned dynamics. The required rms pseudorange

accuracy was 17 m with acceleration of 50 g and jerk of 50 g/s, at an input

SNR of 31 dB-Hz. Late in the Demonstration, Armament Division issued

specifications for HDIS receivers for aircraft dynamics. Although these

requirements do not apply to the Demonstration Receiver, and the HDIS

operates at much lower dynamics, the Demonstration Receiver has comparable

accuracy. An informal goal was established to compare the performance of

the new high dynamic receiver to the HDIS specifications.

1.3 RESULTS

The receiver performance exceeds all Demonstration requirements and

meets the key HDIS requirements. Performanc e was determined

experimentally, by analysis, and by simulation, with close agreement.

Extensive experimental tests and simulations were conducted with

dynamics consisting of circular motion with acceleration of 50 g and jerk

of HO g/s. Pseudorange accuracy is O.U m rms at the nominal SNR of 38 dBHz, 0.6 m rms at 34 dB-Hz, and 1.2 m rms at the HDIS threshold

specification SNR of 31 dB-Hz. This is better than the Plan specification

of 2 m rms at 3^ dB-Hz, and is close to the HDIS low dynamics specification

of 1 m at 31 dB-Hz. Loss of lock threshold is 28 dB-Hz at these dynamics,

which is 3 dB better than the HDIS low dynamic coherent tracking

specification. Accuracy versus SNR is shown in Figure 1-1 for the stated

dynamics. Experimenta l data, simulation results and theoretical

performance are shown to agree within approximately 1 dB in SNR at SNRs

1-2
below 40 dB-Hz. Instrumentation accuracy of 0.15 m rms dominates at higher

SNRs, but meets the HDIS specification of 0.15 m.

The receiver operates accurately at accelerations up to 150 g and jerk

up to 150 g/s. At 100 g and 80 g/s, performance versus SNR is within 1 dB

of performanc e at 50 g and 40 g/s. Accuracy is maintained with

instantaneous acceleration steps of up to 150 g. Peak transient errors are

less than 0.004 m per g of step acceleration, with transient times of

approximately 0.14 s.

Total position accuracy was determined for the receiver operating with

the GPS Space and Control Segments and accounting for propagation effects.

While under dynamics exceeding 50 g and 50 g/s, the receiver accuracy is

essentially the same as the HDIS static accuracy specification. This is

true whether the receiver is measuring either absolute or relative

position.

Elimination of carrier phase tracking is the key concept which enables

the receiver to operate at extremely high dynamics. Therefore, receiver

velocity accuracy is not as good as the HDIS specifications, because the

most accurate velocity estimation depends on tracking carrier phase.

Software modifications could be made to enable carrier phase tracking when

under lower dynamics, thus meeting the HDIS velocity specifications.

Current range rate accuracy is 0.8 m/s at 31 dB-Hz SNR, plus 0.2 m/s for

each 1 g/s of jerk.

The receiver can meet all other key performance specifications of the

HDIS, with further development. These include acquisition or time to first

fix, reacquisition, parameter update rate, data accuracy, data bit

synchronization and data detection. Improvements can also be made in SNR

threshold. Fast acquisition for transdigitizer applications can be

incorporated without changing the basic receiver architecture.

1.4 CONCLUSIONS AND RECOMMENDATIONS

The receiver can meet all performance requirements now envisioned for

range instrumentation of high dynamic aircraft, missiles and drones.

Implementation in a volume of 100 in.3 or less is feasible. The receiver

can be implemented to operate either on the vehicles or as a transdigitizer

or translator receiver.

It is recommended that a fully functional, rack mounted receiver be

developed and tested. Preliminary investigations indicate that the HDIS

now being procured could be modified to include the high dynamic tracking

concepts. This approach appears to be cost effective and to maximize

commonality of range equipment. It is recommended that JPL develop a fully

functional high dynamic receiver, using a government furnished HDIS.

1-3
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CHAPTER 2

PURPOSE AND SCOPE

2.1 PURPOSE

The purposes of this final report are to conclusively show that the

receiver concept examined in GPS High Dynamic Receiver Validation

Demonstration can meet the key requirements for high dynamic range

instrumentation receivers, and to document the work for technology

transfer. This report fulfills deliverable item g of Task Order RE182, Amendment 320, "GPS Receiver for High Dynamic and Low Volume

Applications" [3], sponsored by the U.S. Air Force Systems Command,

Armament Division.

2.2 SCOPE

This report fully documents the objectives, concepts, equipment,

tests, results and conclusions of the GPS High Dynamic Receiver Validation

Demonstration. It describes the receiver, the instrumentation, the

demonstration, and the receiver performance, and how the receiver

performance was determined analytically, by simulation, and experimentally.

A miniaturized design of a complete receiver is presented and its size,

volume and power estimated.

Design trades affecting performance, comparisons to other types of

receivers, and methods for improving performance are included. The report

completely describes the receiver functionally and mathematically, but

schematics and software listings are not included.

2-1
CHAPTER 3

INTRODUCTION

3.1 BACKGROUND AND RATIONALE FOR DEMONSTRATION

The U.S. Air Force Armament Division, GPS Range Applications Joint

Program Office (RAJPO), is responsible for development of GPS receivers to

satisfy Department of Defense range instrumentation requirements.

A new receiver development program has been initiated for range

applications, because range requirements are significantly different from

those satisfied by the family of receivers under development by the GPS

Joint Program Office (JPO). Early in the program, RAJPO concluded that all

requirements for manned aircraft and for ground applications, but hot for

high dynamic missiles were within the current capability of industry.

Therefore, the main RAJPO activity has been to specify and procure the

aircraft and manpack receivers. In May, 1985, Interstate Electronics

Corporation was selected to develop these receivers. " ;

In late 1982, the Jet Propulsion Laboratory'presented to RAJPO a

concept for a receiver to satisfy the requirements for high dynamic

missiles, without requiring inertial aiding. This concept was

insufficiently developed and therefore too risky to include in the above

procurement. Development and demonstration were required. This Validation

Demonstration task began in May 1983 to establish the capability of the

JPL-proposed receiver to meet the high dynamic requirements.

3.2 DEMONSTRATION DESCRIPTION

The primary physical elements of the Demonstration are the receiver,

the Test Instrumentation Subsystem, and the Data Evaluation Subsystem,

shown in block diagram form in Figure 3-1. Other key elements of the task

are the Demonstration Plan [2], analyses and simulations of the receiver

performance, a minimization study, and this Final Report.

3-1
3.2.1 Hardware Configuration

The hardware elements of the demonstration were built in breadboard

form, so as to demonstrate the concept at minimum cost. A photograph of

the Receiver and the Test Instrumentation Subsystem is shown in Figure 3-2.

3.2.2 Specified Objectives And Accomplishments

Seven specific objectives were set forth in the Demonstration Plan, as

key steps validating the receiver concept. These objectives are repeated

here, with brief statements as to their accomplishments.

The first objective was to provide a Demonstration System

operating at JPL consisting of a receiver breadboard capable of tracking a

simulated signal from one satellite, and instrumentation for generation of

test signals, for control and display, and for data recording for post-test

evaluation. This was accomplished by designing and building a single

channel receiver breadboard, a Test Instrumentation Subsystem with a signal

simulator, and a Data Evaluation Subsystem with analysis software, all of

which comprised a Demonstration System sufficient to validate the receiver

concept.

Second was to determine the pseudorange and range rate accuracy of

the system with low receiver dynamics, and to demonstrate that this

accuracy is consistent with GPS system specifications for receivers.

This was accomplished by a series of low velocity tests. At an SNR of 34

dB-Hz, the rms pseudorange and range rate errors were 0.6 m rms and 0.4

m/s rms. The pseudorange error is very small compared to the overall GPS

system accuracy of approximately 15 m.

Third was to demonstrate the ability to track at velocities up to 3300

m/s and at accelerations up to 50 g with pseudorange error due to

dynamics of less than 15 m, and to determine the accuracy under

various dynamics. This was accomplished by high dynamic tests at constant

velocity, with step acceleration, and with simulated circular motion

trajectories. The rms pseudorange errors due to dynamics were under 0.3 o

under all conditions including velocities up to 10,000 m/s, acceleration up

to 150 g, and jerk up to 157 g/s.

Fourth was to demonstrate a breadboard design which is capable

of miniaturized implementation using technology that is within the stateof-the-art. The receiver is inherently suitable for miniaturization

because the design is mostly digital, and thus implementable via

VLSI and dense packaging. The RF circuitry in the breadboard consists

of a single mixing to baseband with no intermediate frequency (IF). Final

implementation would be much simpler than traditional GPS receivers, even

if one IF stage is added in final mechanization.

Fifth was to perform a design of an integrated circuit capable of

performing the key special purpose high speed signal processing

functions within the receiver. Fabrication and testing of this circuit

were specifically stated to be outside the scope of the demonstration. The

3-2
chip chosen to study was the 11-lag correlator. The breadboard correlator

was built using an architecture which enabled the basic operations to be

performed at 10.23 MHz, rather than the 20.46 MHz that would have been

necessary in a more straightforward design. This speed and the complexity

of the circuitry are both well within the state-of-the art for CMOS VLSI.

Further design was not deemed to be appropriate at this time.

Sixth was to perform a preliminary hardware design of a complete

receiver using the demonstrated concepts, to estimate the size, weight

and power consumption of a miniaturized implementation of this

design, and to determine the feasibility of meeting the key missile

application volume requirement of approximately 100 in.J. This

miniaturization study was performed. The volume goal is achievable, as

detailed in Chapter 7.

Seventh was to provide a final report covering all work in

sufficient detail and in appropriate forma t for transfer of the

demonstrated techniques and technology. This document fulfills this

objective.

Additional objectives were informally added as the Demonstration

progressed. These included more complete characterization of the receiver

performance by analysis, simulation and testing, enhancement of the

receiver performance especially in the area of threshold signal-to-noise

ratio, and comparison of the receiver to other possible implementations and

to the procurement specification for the High Dynamic Instrumentation Set

[1]. These goals were accomplished, and the comparisons given in Chapter 5

show that the receiver concept can meet all HDIS specifications, while also

having the ability to operate with dynamics 10 times more severe than

specified for the HDIS, which uses inertial aiding.

3-3
OPERATOR

TEST

INSTRUMENTATION

SUBSYSTEM

(TIS)

DEMONSTRATION

RECEIVER

MODEM

OR Sin.

DISKETTES

OPERATOR

DATA

EVALUATION

SUBSYSTEM

(DES)

PRINTER

Figure 3-1. Demonstration System Block Diagram

3-1
ORIGINAL PAGE IS

OF POOR QUALITY

TEST

INSTRUMENTATION

SUBSYSTEM SUBSYSTEM

SPECTRUM

ANALYZER

NOISE

GENERATORR. F.

ASSEMBLY

NOISE

METERS

TIMING AND

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Figure 3-2. Demonstration System Photograph

3-5
CHAPTER 4

SYSTEM DESCRIPTION

This chapter describes the Demonstration System in detail. Section

4.1 outlines the functional requirements as given by the Demonstration Plan

[2]. Section 4.2 briefly explains the receiver principles. The elements

of the Demonstration system, the Test Instrumentation Subsystem (TIS), the

Demonstration Receiver, and the Data Evaluation Subsystem (DES) are

described in Section 4.3. Finally, Section 4.4 highlights system

integration and testing.

4.1 FUNCTIONAL REQUIREMENTS

The functional requirements of the Validation Demonstration are based on

those given in the Demonstration Plan. Appendix A lists the original

requirements, and modifications, in detail. The following is a summary of

key requirements.

The Demonstration was required to be built, installed and tested at

JPL. It consists of the Demonstration Receiver, a Test Instrumentation

Subsystem (TIS) and a Data Evaluation Subsystem (DES). Real time displays

and post-processing of recorded data are sufficient for the evaluation of

system performance.

The system demonstrates the capability of the receiver to track a

simulated GPS L1 signal under high receiver dynamics and at low SNR.

Receiver functions not demonstrated include the low noise front end,

acquisition, data bit synchronization, data detection, tracking of actual

satellites, tracking of the C/A code, tracking of the L2 carrier, tracking

of multiple satellites, solution for position and velocity in three

4-1
dimensions, and external interfaces. These functions are not necessary to

validate the new high dynamic tracking concept.

Performance requirements, all of which were exceeded, are summarized.

The pseudorange error requirement was less than 2.0 m rms when under

constant velocity of less than 3300 m/s relative to the satellite, with

receiver P-code SNR of 3*1 dB-Hz at the input to the receiver. (This SNR was

chosen because it is exceeded with minimum satellite signal levels, an

antenna gain of -6 dB and total system noise figure of 3.5 dB.) The

required maximum pseudorange lag error due to receiver dynamics is less

than 15 m with pseudorange profile corresponding to radial acceleration of

50 g peak, and under step acceleration of 50 g.

The receiver is tested under various conditions of dynamics and signal

to noise ratio which might be encountered by a receiver on a high dynamic

vehicle. Constant velocity, step acceleration and circular motion are

simulated at high, medium and low SNR. High SNR conditions test

instrumentation accuracy and dynamic limits. Medium SNR tests normal

operating conditions. Low SNR evaluates the performance limitations under

adverse conditions.

4.2 RECEIVER PRINCIPLES

The main new concept demonstrated here is the method of estimating the

pseudorange and range rate of the receiver with respect to the satellites.

This is accomplished in a quasi-open loop, approximately maximum likelihood

(AMLE) manner, rather than by tracking with phase and delay locked loops,

as in other receivers. This approach enhances the ability to maintain

tracking under high receiver dynamics, and naturally leads to an all

digital implementation suitable for miniaturization. A second feature of

the receiver is the use of a high update rate tracking filter, which is

necessary for high dynamic tracking. This type of filter is within the

capability of current microprocessors.

Appendix B gives a detailed description and analysis of the AMLE

concept. Basically, the receiver estimates pseudorange by using a bank of

11 correlators with delay or lag spacing of one-half a P-code chip

(approximately 14.7 m). The range rate estimate, which is related to the

estimate of Doppler shift, is derived from a bank of 50 Hz wide filters

generated by a EFT of the cross correlation between the received baseband

signal and a locally generated P-code. Frequency and range feedback are

provided by the tracking filter to center the range of the AMLE at the

predicted frequency and delay, but the accuracy of this feedback does not

affect estimation error as long as the feedback is within the correlator

and FFT range. Thus the estimation technique is termed quasi-open loop.

4-2
4.3 SYSTEM DESIGN

4.3.1 System

The Demonstration System consists of three functional blocks. The Test

Instrumentation Subsystem (TIS) generates a test signal with the simulated

dynamics and SNR. The Demonstration Receiver tracks this signal and reports

results back to the TIS for recording and display. The Data Evaluation

Subsystem (DES) post-processes the recorded data.

The system configuration is shown in Figure 3-1» while the main

interfaces are shown in Figure 4-1. This section presents the assembly

level designs of the subsystems, designed to meet the above requirements.

4.3.2 Demonstration Receiver

A block diagram of the Demonstration Receiver is shown in Figure 4-2.

The principal assemblies are: front end assembly, analog to digital

converters, correlation assembly, signal processing assembly, code

generator and timing assembly. A functional block diagram of the tracking

processor, i.e., the digital portion of the Demonstration Receiver is shown

in Figure 4-3.

4.3.2.1 Front End Assembly

The front end assembly accepts the simulated satellite signal and

noise from the TIS, and a fixed 20.46 MHz reference frequency from a

synthesizer. It multiplies the 20.46 MHz signal by 77 to generate a

nominal L1 reference. It amplifies the input signal and demodulates it to

baseband in two phase-quadrature channels, using that L1 reference signal.

It then low pass filters the baseband signals, amplifies them, and outputs

these analog signals to the analog to digital converter assembly. Note that

the front end amplifier is not the low noise amplifier that is anticipated

for a final receiver, as this is not necessary to demonstrate the high

dynamic capability. The front end assembly is presented in Figure 4-4.

4.3.2.2 Analog To Digital Converter Assembly

The analog to digital converters accept baseband analog signals from

the front end assembly, and a clock signal from the timing assembly. They

perform 3-bit analog-to-digital conversion and output the digital baseband

to the correlation assembly. The sampling rate is twice the nominal P code

chip rate. The implementation uses two evaluation boards with TRW TDC1029

converters. Although these are 6-bit converters, only 3 bits are used so

that the effective resolution is 3 bits.

4.3.2.3 Correlation Assembly

The correlation assembly accepts the digital baseband signal from the

analog to digital converters, clock and timing signals from the timing

assembly, a code signal from the code generator, and a digital frequency

control signal from the signal processing assembly. Each data bit time is

4-3
divided into 32 subintervals called correlation intervals. The correlation

assembly performs its processing functions over each correlation interval

and outputs correlation data for each interval to the signal processing

assembly. A complex signal is formed at the frequency specified by the

frequency control signal. The baseband input signal, considered a complex

number, is multiplied by this frequency reference signal to remove the

predicted doppler frequency. The amplitude quantization of the frequency

reference is 3-level and of the baseband signal is 3-bit. The product

signal is cross-correlated with 11 lags of the code signal input. At the

end of each correlation interval, the correlation values are output to the

signal processing assembly.

Functionally, the correlators need to operate at the sampling

frequency of 20.46 MHz. The implementation accomplishes this with logic

clocked at the 10.23 MHz rate of the reference code. The sampled data are

demultiplexed into two paths, denoted "even" and "odd", and separate

correlations are performed at 10.23 MHz. Finally the results are combined

in a particular way to reproduce the 11 complex correlation values. This

design is better suited to low power CMOS VLSI implementation.

4.3*2.4 Signal Processing Assembly

The signal processing assembly accepts correlation data from the

correlation assembly, clock and timing signals from the timing assembly,

and initialization data from the T1S. It performs several major functions:

acquisition of pseudorange and range rate, synchronization to the bit times

of the data modulation, Fast Fourier Transformation (FFT) of the

correlation data, formation of raw estimates of pseudorange and range rate

from the FFT outputs, smoothing of the raw estimates in a tracking filter,

control of the code generator, and output of frequency values to the

correlator assembly. The signal processing assembly outputs smoothed values

of estimated pseudorange and range rate to the TIS, frequency data based on

the smoothed range rate to the correlation assembly, and code phase control

data based on the smoothed pseudorange to the code generator.

Synchronization to the data bit times is accomplished by

initialization from the TIS. Code Acquisition is accomplished by searching

over 1023 chips of the code. In an independent receiver, these functions

would be accomplished by detecting the received energy over different

candidate time intervals and for different pseudoranges and range rates,

using the same basic detection algorithms as for parameter estimation

described below. The demonstration receiver does not implement these

functions because they are not required to validate the dynamic and noise

performance of the receiver concept. It is noted, however, that acquisition

and bit synchronization affects only software in the signal processing

assembly, and not the hardware.

The correlation data are buffered over the 32 correlation intervals

corresponding to one data bit time. Double buffering is done so that one

buffer can be loaded while previous data are processed. The correlations

are then Fourier transformed, one lag at a time, using a softwareimplemented FFT. The detected energy is calculated for each FFT frequency

4-4
and for each correlation lag, and the maximum value and its lag and

frequency are noted. An interpolation algorithm is then used to estimate

the raw values of pseudorange and range rate for that bit time from the

maximum value of detected energy and from values in adjacent frequencies

and lags.

The tracking filter operates on the raw estimates to form smoothed

estimates of pseudorange and range rate. The operator can select a seconder third-order filter, with various parameters.

The tracking filter outputs are used to predict the pseudorange and

range rate for the next measurement time, which is three data bit times

ahead of the last data used. The predicted range rate is used to control

the frequency input to the correlator so that the residual frequency (after

cross correlation) is within the range of the FFT. The predicted

pseudorange is used to control the code phase output from the code

generator so that the residual delay is within the range of the correlator.

The signal processing assembly functions are performed by two

processors. A Texas Instruments TMS32010 inputs the correlation values,

performs the FFTs, and detects the maximum energy. An Intel 8086 with an

8087 floating point coprocessor computes the raw estimates, updates the

tracking filter, and controls the hardware. The correlation data is stored

in a double buffer over a data bit time, so while the correlator fills the

first buffer, one correlation subinterval at a time, the TMS32010 performs

FFTs on data from the second buffer, one code lag at a time. The results of

the TMS32010 computations are transmitted to the 8086 through a First In

First Out (FIFO) buffer.

4.3.2.5 Code Generator Assembly

The code generator assembly accepts clock and timing inputs from the

timing assembly and code phase control inputs from the signal processing

assembly. It generates a pseudorandom code clocked at the nominal P code

chip rate of 10.23 MHz. The code is a short-period, simulated P code, for

implementation simplicity. The code phase is controlled by inputs from the

signal processing assembly. Although the predicted values of pseudorange

are inherently updated only once per data bit time, the code phase is

changed during a data bit time in order to compensate for range rate.

Updating of the code phase once each correlation time is sufficient. This

is accomplished by using the code phase and its rate of change once each

data bit time.

4.3.2.6 Timing Assembly

The timing assembly accepts a 20.46 MHz clock from a local oscillator

(frequency synthesizer). This is multiplied by 77 to generate the nominal

L1 frequency, and the resulting signal is output to the front end. The

timing assembly also generates buffered clock outputs at the sampling

frequency and at the P code frequency, and outputs them to the other

assemblies as required. It generates and outputs all required timing

4-5
signals, including correlation interval timing. It generates and outputs

reference epoch signals at 1 pps, and resets all timing signals upon

command. It also generates a reset signal and a frequency update timing

signal for the TIS.

4.3.3 Test Instrumentation Subsystem

The TIS generates test signals and inputs them to the receiver,

initializes the receiver and supplies it with a frequency reference, and

displays and records the test signal parameters and the results of the

receiver measurements. A block diagram is shown in Figure 4-5. The

principal assemblies are the TIS computer, the test signal frequency

synthesis assembly, the code generator assembly, the random noise

generator, the signal combiner assembly and the signal to noise ratio

instrumentation.

4.3.3.1 TIS Computer

The TIS computer is a microprocessor based computer with keyboard,

floppy discs, printer, displays and parallel input and output ports. To

control the test signal, it accepts control inputs via the keyboard, and

timing inputs from the receiver timing assembly. It controls both the

frequency synthesis and code generator assemblies. To control the receiver,

it accepts initial values of pseudorange and range rate, and initializes

the receiver via a parallel port. Tracking results from the receiver are

accepted via a parallel port, recorded on floppy discs, and presented on

alphanumeric and graphic displays.

4.3.3.2 Test Signal Frequency Synthesis Assembly

The test signal frequency synthesis assembly accepts frequency control

inputs from the TIS computer, timing information and reset signal from the

receiver timing assembly, and a frequency reference input. It switches

frequency phase continuously upon command and under timing control,

generates phase coherent P code clock and L1 frequency signals, and outputs

these signals to the code generator assembly and the signal combiner.

Control and accuracy of these signals is such that the pseudorange

simulated is known to within 0.2 m at all times when a test is in progress.

The frequency update rate is four per data bit time, so as to simulate

changing doppler frequency due to acceleration during a bit time.

Figure 4-6 illustrates the TIS frequency synthesis assembly. The

input signals are a fixed 19 MHz and a programmed 1.3 MHz. These are mixed

and divided by 14 to improve phase stability by a factor of 14. The

resulting signal, at approximately 1.046 MHz (programmed), is mixed against

the fixed 19 MHz to obtain a phase stable, programmed, 20.46 MHz. This

signal is used as the P code times-2 clock, and is multiplied by 77 to

obtain the phase coherent, programmed, L1 carrier signal.

4-6
4.3.3.3 Code Generator Assembly

The code generator assembly accepts the P code clock from the

frequency synthesis assembly, and control signals from the computer. It

generates a phase controlled, simulated P code and a simulated 50 Hz data

pattern, sums these two signals modulo-2, and outputs this data-modulated P

code signal to the signal combiner assembly. The assembly is similar to the

receiver code generator assembly, except that the receiver code generator

does not generate data modulation, but is required to change phase on

command.

4.3.3.4 Random Noise Generator

The random noise generator generates bandpass random noise in the L1

band and outputs it to the signal combiner assembly. It consists of three

stages of high gain L-band amplifiers, separated by bandpass filters. The

noise generator is packaged in a separate chassis with its own power

supplies, so as to eliminate cross-coupling of the signal into the high

gain noise generator amplifiers.

4.3.3.5 Signal Combiner Assembly

The signal combiner assembly accepts the L1 carrier signal from the

test signal frequency synthesis assembly, the data-modulated P code signal

from the code generator, the L1-band random noise from the noise generator,

and manual signal level controls. It biphase modulates the carrier with the

data and code, sums the signal and noise, filters the summed signal and

noise in a filter simulating the satellite transmitter passband, and

outputs the filtered signal to the receiver. The filtered noise and the

filtered signal are available to the SNR instrumentation.

4.3.3.6 SNR Instrumentation

The SNR Instrumentation measures the test generator signal level,

noise level and SNR. The SNR for each test is computed using equation

(4-1), with measurements made with the set-up shown in Figure 4-7*

SNR (dB-Hz) = Ps - PN + 10 log BN + C - ATT (4-1)

where

PS = Signal power (dB)

PN = Noise power (dB)

BN = Equivalent noise bandwidth (Hz)

C = Correction factor (dB)

ATT = External attenuation (dB)

PS and PN are the signal and noise power as measured by the power

meters. The signal is band limited by a 37 MHz filter that simulates the

4-7
filter used by the GPS transmitter. The noise is band limited by two

47 MHz filters, with a combined noise bandwidth of BN. BN was evaluated by

integrating the noise transfer function observed on a spectrum analyzer

resulting in BH = 43 MHz. The correction factor C includes all the

mismatches between devices, cable losses, and unbalanced power dividers.

It was evaluated by measuring separately the signal and noise powers at the

output of the TIS, with a result of C = 6.0 dB. Note that if we assume

perfect line matching, no cable losses, no splitter losses, and perfect

attenuators, then C = 10 dB - 4 dB = 6 dB, agreeing with the measurement.

The attenuators included in the ATT attenuator were individually calibrated

and were within 0.2 dB of their nominal values.

The overall accuracy of SNR calibration is estimated to meet the

functional requirement [2] of ±. 1.0 dB.

4.3*4 Data Evaluation Subsystem

The data evaluation subsystem (DES) consists of operator controlled

software on a VAX 11/780. Figure 4-8 shows that the operator controls the

selection of a sequence of operations on a corresponding sequence of data

types. As the figure depicts, the operator can select from several

operations on each data type. The operator is notified if an illegal

operation is encountered.

4.3.4.1 DES Data Types

In the first step of DES operation, the program reads the TIS outputs,

reconstructs the simulated trajectory, and generates four basic data types

for further processing. These four data types are described below.

Raw AMLE errors are defined as the differences between measurements

at the output of the AMLE and simulated pseudorange, range rate and

acceleration. Neither the measurements nor the simulated data are directly

affected by the tracking filter. AMLE errors are dominated by random

effects: simulated input noise, quantization and roundoff errors, and

approximations inherent in the implementation.

Total tracking errors are defined as the differences between the

measurements at the output of the tracking filter and the simulated

pseudorange, range rate, and acceleration. Tracking errors include all

receiver effects. At high SNH, tracking errors are dominated by the

transient or steady state error of the tracking filter, and by

instrumentation errors. Filtered noise errors are defined as the

differences between the measurements at the output of the tracking filter

and the simulated pseudorange, range rate, and acceleration, passed through

an identical tracking filter. This removes all modelled dynamics effects.

At low SNR, the filtered noise errors represent raw AMLE errors, smoothed

by the tracking filter. At high SNR, the filtered noise errors are

dominated by instrumentation errors.

Monitor data are a set of diagnostic data used mainly in the analysis

of test failures. These include the peak power detected by the AMLE, the

4-8
location of the peak power, the feedback to the NCO and code generators,

and any adjustments to the data bit syncronization pointer.

4.3.4.2 DBS Processing

The DES performs summaries on the above defined data types. Often

utilized summaries are:

1. Time summary. Time summary data consists of plots of the

simulated pseudorange, range rate and acceleration, and of

appropriate errors (raw noise, filtered noise, or total tracking

errors) as a function of time. These plots are the primary tools

in the diagnosis of test success or failure. Under operator

control, the DES can overlay data corresponding to repeats of the

same simulated inputs to emphasize transient errors.

2. Bin distribution. Bin distribution summaries describe the

location of the AMLE maximum detected energy in range and

frequency, as a function of time. These summaries provide a

measure of how many range and frequency bins are used, as a

function of dynamics. They also indicate when the maximum

detected energy occurs in an incorrect or outlying bin, due to

low SNR.

3. AMLE bias. These summaries measure the effec t of the

approximation formulas used for range and frequency

interpolation. The summaries consist of plots of average

pseudorange and range rate errors vs. simulated pseudorange and

range rate where the simulated variables are modulo the

corresponding bin size. The measurement biases are the

differences between the average measurements and the simulated

values, as a function of pseudorange and range rate (modulo bin

size).

4. Statistical summary. Statistical summaries consist of the sample

means and sample variances for specified errors. Statistics are

computed for pseudorange, range rate, and acceleration.

5. FFT and Fourier analysis. Some of the error signals (e.g. the

AMLE bias) are analyzed to determine the dominant Fourier

coefficients. This is a way to characterize AMLE bias.

4.3.5 A Typical Test Sequence

A typical test consisted of four steps: first the operator commanded

the TIS with the desired test parameters, then the test was executed and

data stored, then the data was transferred to the VAX, and finally the

performance evaluation was conducted by the DES.

The TIS set up was via an interactive menu. The operator set the

following parameters:

4-9
1. Test identification: test name, operator, location.

2. Trajectory type: constant velocity, circular motion, or

acceleration. The operator also selected the velocity,

acceleration and period that specified the trajectory.

3. SNR parameters: measured signal and noise power, and the

value of the fixed attenuator.

4. Type of tracking filter and tracking filter parameters.

5. Displays: control of graphic and alphanumeric real time

displays.

6. Miscellaneous parameters: type of AMLE interpolation

formulas, ON/OFF control for AMLE feedback, method of code

acquisition, etc.

Once the TIS was set up, relevant parameters were sent to the Demonstration

Receiver, the test was conducted and results were stored in the TIS memory.

Then the data were sent to the VAX either via modem or through 8 in.

diskettes that served as intermediate storage. Finally, the DBS generated

the required performance evaluation summaries. All the data were saved on

9 track magnetic tapes for later processing.

4.4 SYSTEM INTEGRATION AND TESTING

4.4.1 Implementation

The demonstration system was built in two 19 in. instrumentation

racks, seen in Figure 3-2, clearly separating the TIS from the Receiver.

The TIS rack includes a computer assembly, a digital assembly, an RF

assembly, a noise generator, and SNR instrumentation. The computer, housed

in a MULTIBUS chassis, was based on an Intel 86/14 CPU board and included

memory, disk controller, real-time clock, and serial and parallel

interfaces. It also included a PROTEON PRO-80 synthesizer that under

computer control generated the frequencies simulating Doppler effects. The

digital assembly (mainly code generator and timing signals) was built on a

single prototyping board in a separate chassis. The RF assembly performed

the frequency synthesis and the signal combing functions. The noise

generator was built from a series of high gain amplifiers and bandpass

filters. The SNR instrumentation consisted of two power meters that

measured the signal and noise powers separately. The noise power was

nominally fixed, but varied with ambient temperature. The signal power was

controlled by fixed and variable attenuators on the front of the RF

assembly.

The main components in the Demonstration Receiver rack are the

MULTIBUS chassis, correlator assembly, FFT assembly, and RF assembly. The

computer was identical to that used in the TIS. The correlator assembly

consisted of four prototyping cards: two correlator cards, a code generator

4-10
and timing card, and two A/D modules. The correlator resided on two cards,

separating the correlation of the even samples from that of the odd

samples, allowing 10.23 MHz hardware to operate on a 20.46 signal. The FFT

assembly used a TMS320 Evaluation Module to perform the needed FFTs, and

included all the buffering to the correlators and to the FFT. The RF

assembly included the L1 frequency generator, the I-Q mixers and the

baseband analog circuitry.

During the testing two displays were utilized. The alphanumeric

display shown in Figure 4-9 displayed the simulated data and the tracking

error with and without filter smoothing. The graphic display shown in

Figure 4-10 displayed simulated data and tracking data, under operator

control. In the figure, the display shows the simulated velocity and the

position tracking error for a circular motion test. This particular real

time graphic display presents the simulated velocity and the position

error. The simulated velocity scale is ± 1400 m/s while the pseudorange

error scale is ± 24 m.

4.4.2 Test Plans And Procedures

A Test Plan and Procedures document was issued approximately three

months prior to testing, as a JPL Interoffice Memorandum (IOM) [4]. It

defines the required tests during the integration phase, i.e. tests that

validate the subsystems, the subsystem interfaces and the complete system.

It also identifies the Validation Demonstration tests in detail, including

types of dynamics, SNR conditions, test logs, and supplemental tests.

4.4.3 Test Schedule

The originally planned Validation Demonstation tests started at the

end of November 1984 and were concluded by the end of December 1984.

Additional tests were conducted through June 1985 to verify new

interpolation formulas, to evaluate the outlier detection performance and

the resulting SNR threshold, and to identify the performance improvement

achieved by narrowing the AMLE window.

4.4.4 Equipment Performance

During the Validation Demonstration there were no equipment failures.

The operation was automated so that a sequence of tests, each test with

different dynamics but with the same SNR, could be conducted without

operator intervention between tests. The size of the sequence was limited

only by the disk storage on the VAX disk, typically permitting 100 minutes

of testing.

4.4.5 Measured Spectra

During system integration, the frequency spectra of the generated

signal and noise were recorded. Figure 4-11a shows the noise spectrum. The

4-11
passband is defined by two 3-pole, 47 MHz, Chebychev filters. Figure 4-11b

shows the spectrum of the L1 signal, a (sin(x)/x)2 type spectrum with

nulls separated by 20.46 MHz. Figures 4-11 c and 4-11d show the combined

signal and noise at C/NQ of 70 dB-Hz and 80 dB-Hz. (The nominal SNR for a

0 dB antenna is approximately 40 dB-Hz, at which level the spectrum appears

to contain only noise.)

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H-23
CHAPTER 5

PERFORMANCE AND ERROR BUDGET

This chapter presents performance predictions and error budgets for

both the Demonstration Receiver and for a completely functional receiver

which could be developed using the principles and concepts demonstrated.

The critical and unique performance characteristics have been established

by analysis, simulation, and demonstration. These include all pseudorange

and range rate errors due to receiver noise, dynamics, and all effects

characteristic of the receiver.

Errors which depend on GPS system effects outside of the receiver are

included for the sake of completeness. Data for these effects are taken

from the recent Armament Division procurement specification for high

dynamic (HDIS) receivers [1]. Performance of the Demonstration Receiver is

compared to the HDIS specification, and it is shown that all important and

applicable specifications are met even at the much higher dynamics where

the Demonstration Receiver operates. This is true even though the receiver

was not designed to these requirements.

Performance characteristics important to a receiver implementation but

outside of the scope of the Demonstration are discussed in 5.3. These

characteristics were determined by analysis. The characteristics include

acquisition, reacquisition, data bit synchronization, data bit detection,

parameter update rates, and data accuracy.

Performance estimates are included for some modified receiver

configurations which were not tested. These configurations include C/A

code tracking, combined P and C/A code tracking, and phase locked tracking

under conditions of SNR and dynamics which permit phase locking.

5-1
Performance predictions for these cases, made by analysis and simulation,

are presented in 5.4.

5.1 SINGLE CHANNEL PERFORMANCE

This section presents the pseudorange and range rate measurement

performance for a single channel receiver alone, excluding errors due to

the GPS Space and Control Segments. Performance is characterized in terms

of the input signal to noise ratio and dynamics, the receiver processing

losses, the approximate maximum likelihood estimator (AMLE) performance,

and the tracking filter performance. The performance was determined by

measurement, analysis, and simulation.

Error budgets are presented for the processing losses in the receiver,

and for pseudorange and range rate errors, under both static and dynamic

conditions. The analyses and simulation results which justify the error

budgets are presented in Appendix B. The experimental results are presented

in Chapter 6 and Appendix C.

5.1.1 Receiver SNR Losses in Processing

Table 5-1 presents a summary of the SNR losses in the receiver, as

detailed in Appendix B. These losses represent all losses from ideal

theoretical performance due to receiver effects and transmitter bandwidth.

The total SNR loss is 1.5 dB ± 1.0 dB.

5-2
Table 5-1. Receiver SNR Loss Summary

Effect i Loss (dB)

Transmitter filter (gain due to definition of carrier ! -0.3 ± 0.1

power )

Correlation loss due to bandwidth in receiver

Analog to digital conversion, 3 bit

Reference sine wave 3-level quantization

FFT filter loss, offset from center frequency

Dynamics losses, 50 g maximum acceleration and

50 g/s maximum jerk

Miscellaneous

Total SNR losses

0.5 ±

0.3 ±

o.n ±

0.3 ±

0.3 ±

0.0 ±

1.5 ±

0.1

0.1

0.1

0.1

0.2

0.3

1.0

5.1.2 Loss-of-Lock Threshold SNR

Loss-of-lock occurs when the error in either pseudorange or range

rate, at the feedback inputs to the AMLE, is so large that the actual input

values are outside of the range of the AMLE. This occurs either at very

low SNRs, or with very high dynamics, or at a combination thereof. When

under the required dynamics, loss-of-lock occurs at SNRs that are well

below the linear region of the AMLE, because occasional large errors at the

AMLE output are averaged out by the tracking filter, just as a phase locked

loop averages out large errors at the phase detector output. The loss-oflock thresholds realized by the receiver are significantly better than the

34 dB-Hz specified in the Demonstration Plan [2], because the Plan

neglected this smoothing effect.

Loss-of-lock thresholds for various dynamics have been determined

experimentally, analytically, and by simulation* The threshold SNR for

dynamics up to 50 g acceleration and 50 g/s jerk is 28 dB-Hz. Methods of

improving threshold are discussed in 5.4.

5-3
To compare the loss-of-lock threshold to the HDIS specification, one

needs to know the total system noise figure of the receiver. This total

noise figure includes all noise sources through the output of the receiver

front end, including antenna input noise, cable losses, pre-selection

filter losses, and amplifier noise. A total noise figure of 3.5 dB is

practical, as suggested in the specification. This corresponds to a noise

spectral density of -174 dBm/Hz. For the signal level of -142 dBm specified

for the lowest signal strength satellite, the SNR is 31 dB-Hz. , Thus the

receiver threshold of 28 dB-Hz is 3 dB better than that requirement, even

when under accelerations of up to 50 g.

5.1.3 Static Errors Due To Receiver Noise

The static errors due to receiver noise are determined by the input

SNR less the processing losses, the AMLE performance, and the tracking

filter noise reduction.

The AMLE is analyzed in B.3. The performance is approximately linear

in SNR in the normal range of C/NQ from approximately 32.5 dB-Hz to 40 dBHz. Below 32.5 dB-Hz, performance degrades due to thresholding; above 40

dB-Hz, instrumentation errors become significant. In the linear region,

the AMLE rms pseudorange error is

oT(AMLE) =87.1(C/N0r°'5 (m) (5-1 )

and the rms range rate error is

°-r(AMLE) = 31.KC/N0 )-°' 5 (m/s) (5-2)

The tracking filter reduces the rms pseudorange and range rate errors,

as analyzed in B.4. In the AMLE linear region, the pseudorange error is

reduced by a factor of 3«5, and the range rate error is reduced by a factor

of 1.2. The resulting rms error at the filter output is

<JT=24.9 (C/N0) -°'5 (m) (5-3)

and the rms range rate error is

t = 25.9(C/N0)-°'5 (m/s) (5-4)

At low SNRs, noise sometimes causes pseudorange and range rate

estimation errors larger than would be expected from the above linear

theory. These large errors are called outliers, and a theory including

5-4
outlier effects is developed in B.3. Outlier effects become significant

at SNRs below approximately 32.5 dB-Hz. Loss-of-lock threshold, discussed

in 5.1.2, occurs when there are so many outliers that the large tracking

filter output error causes the signal to be outside the range of the AMLE.

This occurs at approximately 28 dB-Hz.

5.1.4 Instrumentation Errors and Channel Bias

The implementation of the receiver generates instrumentation errors

which are not accounted for by SNR effects or by dynamics. These effects

are most apparent at high SNRs. The high SNR tests were specified in the

Plan specifically to measure these effects. The rms pseudorange bias ranges

from 0.09 m at low dymamics to 0.15 m at high dynamics, and the higher 0.15

m figure is assumed for the overall error budget. The rms range rate

instrumentation effect is 0.13 m/s, and is essentially independent of

dynamics. Note that the 0.15 m rms error meets the HDIS procurement

specification of 0.5 ft (0.15 m).

5.1.5 Total Static Pseudorange Error

Static pseudorange error is all receiver-induced pseudorange error

except that due to dynamic lag in the tracking filter. It includes errors

due to receiver noise, processing losses and channel bias. The static error

indirectly depends on dynamics because the processing losses depend on

dynamics. Figure 1-1 presents the total rms of all random pseudorange

errors in the receiver, for dynamics up to 50 g acceleration and 50 g/s

jerk.

The total error is close to the HDIS P code specification of 3.2 ft

(1.0 m) at the required threshold SNR of 31 dB-Hz even though the

Demonstration Receiver operates at much higher dynamics, and therefore uses

an averaging time of only approximately 0.14 s, compared to the 1 s assumed

in the HDIS specification.

5.1.6 Total Static Pseudorange Rate Error

Figure 5-1 presents the total static pseudorange rate error for all

receiver effects, for dynamics up to 50 g acceleration and 50 g/s jerk.

The range rate errors for this receiver do not compare to the delta

pseudorange specifications for the HDIS because the HDIS specification

requires phase coherent carrier tracking. Section 5.4.3 discusses how

this receiver can accomplish phase coherent tracking and meet this

specification at appropriate dynamics, if desired.

5.1.7 Dynamic Tracking Errors

The tracking filter selected for the Demonstration is a third order

filter, so the dynamic tracking errors in both pseudorange and range rate

are determined primarily by jerk. For steady state jerk, i.e., for jerk

which is constant for a time long compared to the filter time constant of

approximately 0.14 s, the lag errors are

5-5
Pseudorange error = 0.00136 j (m)

Range rate error = 0.197 j (m/s)

(5-5)

(5-6)

where j ia jerk in g/s.

For a receiver in circular motion, or turning with a constant radial

jerk, the lag errors in pseudorange and range rate are approximately

proportional to jerk. The maximum errors are again given by equations

(5-5) and (5-6).

Transient errors due to step acceleration are proportional to the size

of the step, and have peak errors of approximately 0.0039 m/g in

pseudorange and 0.48 (m/s)/g in range rate. Transient errors due to very

high jerk for a short length of time are approximately the same as errors

due to step acceleration of an amount equal to the jerk magnitude

multiplied by the duration of the jerk. This approximation holds when the

duration of the jerk is comparable to or less than the filter time constant

of 0.14 s, with lower transient errors resulting for longer jerk at lesser

magnitude.

Tracking errors for 50 g and 50 g/s maneuvers are summarized in Table

5-2. These errors are much lower than those specified for the HDIS at much

lower dynamics, even for the inertially aided HDIS.

Table 5-2. Dynamic Errors at 50 g and 50 g/s Maneuvers

Condition

Steady state error

due to 50 g/s jerk

Peak error in 50 g,

50 g/s circular motion

Peak transient error

due to 50 g step accel

Pseudorange Error

(m)

0.068

0.068

0.196

Range Rate Error

(m/s)

9.83

9.74

24.0

Since the dynamic pseudorange error is very small even at 50 g/s jerk,

it may appear that the filter time constant could be lengthened to reduce

random errors and threshold SNR while retaining an acceptable dynamic

performance error. In fact this cannot be done because the filter time

constant is limited by the frequency range of the FFT and by the range rate

5-6
prediction error fed back to the AMLE. This prediction error exceeds the

range rate tracking error by approximately a factor of 2 for step

acceleration. With a 100 g step acceleration, the peak range rate

prediction error is 90 m/s (with peak tracking error of 48 m/s), compared

to a maximum FFT range of 160 m/s.

5.2 COMPLETE RECEIVER PERFORMANCE

This section presents the overall accuracies achievable with a

complete high dynamic receiver. The overall accuracies include effects of

the Space and Control Segments, with the same assumptions as to the error"

components as presented in the HDIS specification. The results in this

section are presented in ft and ft/a to allow easy comparison to the HDIS

specification.

5.2.1 Static Accuracies

The static accuracy is evaluated at 38 dB-Hz and at 31 dB-Hz. As shown

in B.3, the loss-of-lock condition defined for the HDIS P code L1 signal,

-142 dBm, corresponds to 31 dB-Hz with a total system noise figure of 3.5

dB. The following results present the HDIS specifications parenthetically

next to the performance of the Demonstration Receiver.

5.2.1.1 Position Static Accuracy

Static position accuracy is not dominated by receiver noise or channel

bias in either the Demonstration Receiver or the HDIS. Rather, in the

absolute mode, accuracy is dominated by the Space and Control segment

errors. In the differential mode, accuracy is dominated by multipath.

Table 5-3 presents the static component of the position accuracy, in

the absolute and differential tracking modes. The errors for the

Demonstration Receiver are identical to those of the HDIS specification.

5-7
Table 5-3 - Static Position Accuracy .

(HDOP=1.5, VDOP=2.5)

Parameter H

Horizontal

Vertical

I rms Position Error (ft) !

I Absolute ! Differential !

I 38 dB-Hz ! 31 dB-Hz ! 38 dB-Hz ! 31 dB-Hz !

21 (21)

35 (35)

23 (23)

38 (38)

6 (6)

11 (11)

6 (6)

13 (13)

( ) - HDIS specification

Table 5-4 presents the error budget for static pseudorange accuracy,

or User Equivalent Range Error (UERE), for tracking in the absolute mode.

The UERE is identical to the rms pseudorange error used in the previous

text. The Demonstration Receiver, as designed for extreme dynamics, is

within 0.2 ft of the HDIS specification. The specification is met if the

receiver tracking filter is modified for the HDIS maximum dynamics.

Table 5-4 - Static Absolute Pseudorange Accuracy

Parameter

! Error Budget (ft) !

+«__________-____————_—_+

I 38 dB-Hz ! 31 dB-Hz !

Space Segment

Control Segment

User Segment

Ionospheric delay

Tropospheric delay

Receiver noise,

quantization, and biases

Multipath

UERE (rms)

10

8.6

1.3

1.3

1.2

4.0

14.0

(10)

(8.6)

(1.3)

(1.3)

(0.8)

(4.0)

(13.9)

10

8.6

5.3

1.3

4.0

4.0

15.4

(10)

(8.6)

(5.3)

(1.3)

(3.2)

(4.0)

(15.2)

( ) - HDIS specification

5-8
Table 5-5 presents the static pseudorange accuracy or UERE budget for

tracking in the differential mode. In the differential mode, the processing

cancels the effects of the Space and Control Segments as well as some of

the ionospheric and tropospheric delays. As in the case of absolute mode

accuracy, the Demonstration Receiver, as designed for extreme dynamics, is

within 0.4 ft of the HDIS specification. The specification is met if the

receiver tracking filter is modified for the HDIS maximum dynamics.

Table 5-5 - Static Differential Pseudorange Accuracy

Parameter H

'

Ionospheric/Troposphere delay

Channel bias

Receiver noise

Multipath

UERE (rms)

38

0.5

0.5

1.2

4.0

4.2

Error Budget

dB-Hz ! 31

(0.5)

(0.5)

(0.8)

(4.0)

(4.2)

0.5

0.5

4.0

4.0

5.7

(ft) I

dB-Hz !

(0.5)

(0.5)

(3.2)

(4.0)

(5.3)

( ) - HDIS specification

In summary, the static position accuracy of the Demonstration Receiver

is essentially identical to that specified for the HDIS.

5.2.1.2 Velocity Static Accuracy

The Demonstration Receiver, as designed for extreme dynamics, does

not perform the phase coherent tracking required of the HDIS. Therefore,

the velocity static accuracy is not directly comparable to that of the

HDIS. Table 5-6 presents the horizontal and vertical velocity errors.

Table 5-6 - Static Velocity Accuracy

!

I

Horizontal !

Vertical !

rms position error (ft/s)

38 dB-Hz !

1.7 (0.6) !

2.9 (1.0) !

31 dB-Hz

3.7 (0.7)

6.1 (1.1)

( ) - HDIS specification

5-9
5.2.2 Dynamic Accuracies

The dynamic environment of the HDIS, defined in Table XI of attachment

5 of [1], is repeated in Table 5-7. The conditions for the aided HDIS

correspond to acceleration of 10.4 g and jerk of 10.4 g/s for 0.1 s. In

contrast, the Demonstration Receiver operates with acceleration in excess

of 100 g and jerk in excess of 100 g/s, for any duration consistent with

maximum velocity and acceleration.

Table 5-7 - HDIS and Demonstration Receiver Worst Case Dynamics

! Parameter

1

! Velocity (ft/s)

! Acceleration (ft/s2)

! Jerk (f/s3)

! HDIS (aided)

! 5000

1 330 for 10 s

I 330 for 0.1 s

! HDIS (unaided) |

I !

! 580 I

! 130 I

! 130 for 0.1 s !

'Demonstration!

j Receiver i

I > 32,000 I

! > 3,200 !

! > 3,200 I

As shown in B.4, if all the receiver channels use the same tracking

filter, the worst case tracking error of the receiver is identical to that

exhibited by a single channel when the jerk is in the direction between the

receiver and the tracked satellite. Since we assume that in the

implemented Demonstration Receiver all channels use identical steady state

gain tracking filters, the effect of GDOP can be ignored.

The third order tracking filter used in the Demonstration Receiver has

zero pseudorange and range rate tracking errors for any constant velocity

or constant acceleration. The errors in a 10.4 g, 10.4 g/s circular

motion are 0.045 ft and 6.6 ft/s for position and velocity, respectively.

This position accuracy is significantly better than the HDIS specification,

even for the aided HDIS receiver. The velocity accuracy is better than that

of the unaided HDIS but not as good as that of the aided HDIS. This is due

to the noncoherent nature of the tracking.

Table 5-8 presents the dynamic error specifications for the HDIS, and

the dynamic errors generated by the Demonstration Receiver at much higher

dynamics.

5-10
Table 5-8 - Dynamic Component of Accuracy

! Parameter I Position Error (ft) I Velocity Error (ft/s) !

HDIS - average under

dynamics of Table 5-7

- aided

- unaided

Demonstration Receiver

constant velocity

constant accel.

100 g/s jerk

50g,50 g/s circular!

1.0

7.6

0.

0.

0.42

0.21

1.0

13.5

0.

0.

63.

32.

5.3 OTHER PERFORMANCE'CHARACTERISTICS

This section discusses some performance characteristics of interest

that could be achieved with the Demonstration Receiver concept, but were

not demonstrated. Rationale for the performance predictions is included.

5.3.1 Acquisition

The Demonstration Receiver can be especially powerful in fast

acquisition applications because of the wide search capability of the AMLE

window. All HDIS requirements can be easily met. Also, the techniques

could be extended to meet the extremely fast acquisition time which might

be required for a transdigitizer receiver.

During initial acquisition, data

overcome the problem of having data

detection time, the detection interval

each possible time delay is examined

least one of these detection intervals

number of input data points in the

reducing the correlation interval to

resulting frequency range of the FFT

± 980 ft/s at L1.

bit synchronization is unknown. To

transitions occur during the FFT

is reduced to one half bit time, and

over two consecutive intervals. At

will always be transition free. The

FFT could be maintained at 32 by

one half of the normal length. The

is ±. 1600 Hz, which corresponds to

In the pseudorange domain, the AMLE window, using 11 correlators

separated by one-half P-code chip, can detect pseudorange uncertainties of

± 250 ft. All this detection is accomplished in a single data bit time,

i.e., 20 ms.

5-11
The HDIS specifications for Time-To-First-Fix (TTFF) are given in

Table I, Attachment 5 of the HDIS specification. The specified SNR, 38 dBHz, is high enough so that the false detection rate is very low, and

detection over one pair of 10 ms intervals, or a single bit time, is

sufficient. The worst case specified velocity uncertainty is within the

uncertainty of the AMLE window, so no search in frequency is required.

Because of the 10 minute uncertainty in user clock, the acquisition

must start with a full search over the 1023 chips of the C/A code,

including recovery of the data bit boundary (bit synch, see 5.3.3). Then,

the 50 Hz data stream is detected, and finally, P code acquisition is

obtained.

The budget for the Demonstration Receiver TTFF is given in Table 5-9.

The total acquisition time is 62 s, or approximately half of the HDIS

specification of 120 s.

Table 5-9 - Time-To-First-Fix Budget

Step

H

Search set up

Search C/A code (1023 chips)

Identification of bit synch, positioning of the code

Preparation for data recovery

Recovery of a data frame (1500 bits)

Verification of data

Transfer to P-code lock, confirmation

Tracking filter transient time (0.14 s time constant)

Duration !

bits 1 sec !

2

1023

500

2

1500

2

50

14

0.04

20.46

10.00

0.04

30.00

0.04

1.00

0.28

! Total ! 3093 ! 61.86 !

The search time, 20.46 s, is based on moving the window in steps of

one chip, and using one bit time in each step to compute the FFTs for the

two 10 ms intervals. This results in each point appearing at least four

times within the AMLE window. The repeat appearances can be used to

accommodate lower SNRs than the specified 38 dB-Hz by adding the FFT

outputs noncoherently, e.g., an approximate 6 dB improvement is obtained by

the four repeats. An additional 3 dB improvement could be achieved by

detecting over 2 bit times, increasing the TTFF by 20.26 s.

5-12
5.3*2 Reacquisition

The unaided HOIS specification requires that under the conditions

given by Table 5-10, reacquisition shall be established within 2 s. This

section shows that the reacquisition time for the proposed receiver is

0.5 s.

Table 5-10 - Reacquisition Conditions

! Parameter I

C/NQ at input to preamplifier

Duration of signal loss

Position uncertainty

Velocity uncertainty

Acceleration uncertainty

units I

dB-Hz

s

ft

ft/s

ft/32

unaided

38

10

1000

200

20

aided !

38

60

200

3.5

0.003

Because the velocity window for 20 ms integration is ± 490 ft/s, no

velocity search is required. The pseudorange uncertainty is the position

uncertainty added to the effect of an unknown receiver oscillator frequency

offset. As an example, a frequency offset of 1 part in 109 causes 1 ft of

pseudorange drift per second of signal loss, or 10 ft and 60 ft for signal

outages of 10 s and 60 s specified for the unaided and aided HOIS,

respectively. With an AMLE window of ± 250 ft, the pseudorange search over

the total maximum uncertainty of 1060 ft can be completed in five data bit

times.

We assume that the receiver is tracking the P-code, and the

reacquisition is performed without returning to C/A code. As presented in

Table 5-11, the total reacquisition time is 0.5 s, well under the HOIS

specification of 2 s.

5-13
Table 5-11 - Reacquisition Time Budget

Step f Duration ! +_______+___—_+

! bits ! sec !

Search set up

Search P code (1060 ft

Re- position P-code

Confirm reacquisition

uncertainty)

Tracking filter transient time (0.14 s time constant)

2

5

2

2

14

0.04

0.10

0.04

0.04

0.28

! Total ! 25 ! 0.50 !

5.3.3 Data Bit Synchronization

Data bit synchronization can easily be obtained in software once

acquisition is accomplished. Bit synchronization is quantized to the

nearest correlation time, so there are only 32 possible synch phases.

Synch is obtained by finding the phase which maximizes the value of the

AMLE detection function. This can be done analogously to data bit

synchronization such as in a transition tracking bit synchronizer [5,6].

At C/NQ = 38 dB-Hz, a data bit sync loop bandwidth of 0.5 Hz will

achieve an rms timing error of one-quarter of a correlation interval, which

is sufficient to obtain sync to the nearest correlation interval.

Conservatively, loop lock will occur within five inverse loop bandwidths,

or 10 s.

5.3.4 Data Bit Detection

The receiver can also perform data bit detection in software. This

capability is inherent since the FFT measures carrier phase. Data bits are

detected differentially by observing when the measured phase in one bit

time differs from the phase in the previous bit by more than 90 degrees.

The phase in the early bit time must be extrapolated ahead one bit time to

compensate for range rate and for the feedback frequency at the AMLE input.

Data detection will not be possible at very high dynamics, when the phase

extrapolation process breaks down. This dynamic limit has not been

established, but is comparable to the dynamic limit for a receiver using

phase coherent tracking.

5-14
5.3.5 Parameter Update Rates

The inherent update rate of the Demonstration Receiver is 50 times per

second, or once every data bit time. This rate is higher than the 10 times

per second update rate specified for the HDIS (Table XIII, Attachment 5,

[1]). In fact, the receiver implementation can be simplified if the signal

channels continue to be updated at 50 times per second, while a flash

solution for time and position is computed at a lower rate, reducing the

computational requirements. '

5.3.6 Data Accuracy

The Demonstration Receiver computes or has otherwise available all of

the output data items specified for the HDIS (Table XIII, Attachment 5,

[1]), except for the Inertial Referenc e Unit (IRU ) status. The

Demonstration Receiver does not require an IRU even for tracking under very

high dynamics; nevertheless, an IRU can be integrated with the receiver if

so desired.

The accuracies specified for the UERE and position are met, as

discussed in 5.2. The accuracy of GPS system time, 100 ns, is equivalent to

a position error of 100 ft and is met under all the specified conditions.

The velocity accuracy of the Demonstration Receiver is better than

that specified for the unaided HDIS but not as good as that of the aided

HDIS. This is because the receiver uses noncoherent tracking rather than

the HDIS phase locked loop tracking.

Data resolution specified for the HDIS can easily be met.

5.4 RECEIVER MODIFICATIONS AND ENHANCEMENTS

This section discusses some modifications and enhancements which can

be incorporated into the receiver. These include C/A code tracking, phase

coherent (PLL) tracking, and threshold enhancement by combined P and C/A

code tracking.

5.U.1 C/A Code Tracking

Implementation of the receiver would require the addition of C/A code

tracking capability for acquisition. In some applications, notably with

translators or transdlgitizers, only C/A tracking might be used.

Capability for both P and C/A code can be implemented with only minor

changes in digital logic and the addition of a C/A code generator. It is

not necessary to add a second IP-baseband channel with restricted

bandwidth, new A/D converters, or a new sampling clock. The existing

correlators can be run at the existing clock rate, but with increased lag

spacing via digital delays.

5-15
There is a performance advantage to processing the C/A code with the

existing sampling rate. For acquisition, the lag spacing can be one-half

chip. After acquisition, the lag spacing can be reduced to one-quarter

chip or less. This reduces the rms pseudorange error, as shown in Appendix

B.3.

One quarter chip spacing gains root 2 in rms error over the normal

half chip spacing. Assuming this one-quarter chip lag spacing, the rms

pseudorange error above threshold would be

CTT(C/A) * "7 (CC/A/N0)-0

-

5

 (»)

where CC/A is the received C/A code power. At a C/A code SNR of 34 dB-Hz,

the rms pseudorange error would be 3.5 m.

For a C/A code only receiver, such as for a transdigitizer, the

sampling rate and processing rate would be reduced to 2.046 MHz, and onehalf chip lag spacing would be used. The rms error would be root 2 greater

than above.

5.4.2 Threshold SNR Versus Dynamics

Threshold SNR depends on the design point maximum dynamics and on the

parameters of the tracking system. The frequency tracking in the

Demonstration Receiver is equivalent to a second order frequency locked

loop (FLL). Achievable threshold varies in approximate inverse proportion

to the square root of maximum jerk. Thus threshold can be reduced to

approximately 18 dB-Hz if the system is designed for 1 g/s maximum jerk.

This threshold is better than the non-coherent tracking threshold required

for the HDIS at low dynamics.

Threshold extension is achieved by increasing the AMLE estimation time

and the tracking filter time constant. Since the coherent-integration

(FFT) time in the AMLE cannot be longer than one data bit time, the

estimation time is increased by accumulating energy over several bit times,

for each correlation lag and frequency.

Tracking at dynamic s in excess of those demonstrated can be

accomplished at the cost of SNR threshold, by decreasing the detection time

and the filter time constant, and increasing the filter update rate.

Tracking with jerk in excess of 500 g/s is possible with a threshold of

approximately 31 dB-Hz.

Figure 5-2 shows the maximum jerk versus threshold SNR for the

demonstrated FLL tracking technique, with modified detection times and

tracking filter time constants. Also shown are maximum jerk versus

threshold for phase locked loop tracking, discussed in 5.4.3, and for

threshold extension by combined P and C/A code tracking, Section 5.4.4.

In Figure 5-2, the curve for the Demonstration Receiver FLL is based

upon the demonstrated tracking capability at 100 g/s jerk and a SNR of

28 dB-Hz. Actual performance is not a smooth curve, because integration

5-16
time can be varied only in multiples or factors of the data bit time.

5.4.3 Phase Coherent Tracking and Threshold

Because the FFTs in the AMLE inherently measure carrier phase, phase

coherent carrier tracking can be implemented by changing the tracking loop

filter software. Coherent tracking is optimized by the FFT signal

processing, because the integration times are matched to the data bit

times. Effectively, the loop is an optimum Costas loop with arctangenttype phase detection.

Phase coherent tracking is limited by the phase lag error due to

dynamics and by the rms phase error due to noise in the loop bandwidth. At

10 g/s jerk, a third order loop with a loop bandwidth, BL, of 15 to 20 Hz

can achieve satisfactory dynamic phase error. Larger loop bandwidths are

not feasible without decreasing the phase detector measurement time to less

than one bit time, thus increasing threshold. Tracking threshold occurs

with a loop SNR of approximately 15 dB. Allowing 1.5 dB processing losses,

as for the non-coherent tracking, the threshold C/Nn is approximately 28

dB-Hz. Maximum jerk versus threshold is shown in Figure 5-2. Capability

to track jerk varies as Bj^, or as the cube root of threshold C/NQ, since

the PLL is assumed to be third order. The estimated accuracy of the curve

is ± 2dB at C/NQ = 28 dB-Hz. Performance is worse than shown at low SNRs

due to squaring loss, which has not been accounted for.

An adaptive receiver would be desirable. Such a receiver could

monitor both dynamics and SNR and select appropriate tracking. Coherent

tracking could be used at low and moderate dynamics and with SNRs above 28

dB-Hz. Non-coherent tracking with the demonstrated filter time constants

would be used for high dynamics. Non-coherent tracking with a longer time

constant would be used at low dynamics and low SNR, to extend SNR

threshold.

5.4.4 Threshold Extension by Combined P and C/A Code Tracking

Since the P and C/A code signals are carrier-phase coherent with a

known 90 degree phase difference, tracking threshold can be Improved by

phase coherently combining the P code and C/A code signals. Since the L1,

C/A code signal is 3 dB stronger than the P code signal, the potential

threshold improvement is 4.77 dB in terms of P code power [71.

Threshold improvement can be achieved both with frequency tracking, as

in the high dynamic demonstration, and tracking carrier phase with a PLL.

Phase detection of both signals must be relative to the same local

oscillator. The AMLE implementation with the FFT is ideal.

Tracking capability (maximum jerk) is shown in Figure 5-2 for combined

P and C/A code tracking both with PLLs and with FLLs. At a P code SNR of

23 dB-Hz, maximum jerk of 10 g/s can be tracked non-coherently. At very

low dynamics, non-coherent FLL tracking is possible with a P code SNR of

approximately 13 dB-Hz.

5-17
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5-19
CHAPTER 6

DEMONSTRATION TESTS AND RESULTS

The Demonstration tests are divided into four categories: AMLE

evaluation, tracking filter evaluation, tracking under high dynamic

conditions, and performance at low SNR. This chapter presents the

experimental performance and compares it to the performance predicted by

analysis and simulation.

The results of the Validation Demonstration tests meet or exceed all

the performance requirements of the Plan (Appendix A) and are in close

agreement with system analysis and simulations (Appendix B). Details of the

test results are presented in Appendix C.

6.1 SUMMARY OF TEST CONDITIONS

In the Demonstration tests, the Test Instrumentation Subsystem (TIS)

generated three types of simulated trajectories: constant velocity, step

acceleration, and circular motion. For simplicity, the simulated variables

(pseudorange, range rate and acceleration) are with respect to a GPS

satellite rather than relative to Earth. In the worst case, the satelliteEarth motion may add 750 m/s and 0.1 g to the range rate and acceleration,

respectively.

In step acceleration tests, constant positive and negative

accelerations are applied for 6 s intervals, separated by intervals of high

range rate and no acceleration. For example, in a 50 g test the peak range

rate and acceleration are ± 1470 m/s and ± 190 m/s*, respectively. In

circular motion tests, the pseudorange is sinusoidal, simulating the

component of circular motion in the receiver-satellite direction. The

amplitude of the waveform is selected to correspond to the specified

acceleration and period. In constant velocity tests, the range rate is

6-1
constant for the duration of the test. Note that short intervals of

constant velocity are part of the step acceleration tests.

Tests were conducted at three SNR levels - high (60 dB-Hz), medium (UO

dB-Hz) and low (3^ dB-Hz), for each type of trajectory and with different

magnitudes of dynamics. The high SNR level tested instrumentation effects

and the signal level dynamic range of the receiver. Medium SNR tests

simulated the nominal conditions with minimum specified satellite signal

level, 3.5 dB receiver noise figure, and a 0 dBi antenna. The low SNR is

the SNR that occurs with a -6 dBi antenna gain, which is common with

missile antennas. Still lower SNRs were used to determine the minimum or

threshold SNR for satisfactory tracking.

6.2 AMLE EVALUATION TESTS

The AMLE evaluation tests measured the errors in pseudorange and range

rate estimation caused by the Demonstration Receiver implementation. The

tests confirmed the detailed structure of the AMLE function over the

discrete set of points where it is evaluated, and bounded the bias error in

fine estimation caused by the interpolation formulas. Averaged over

pseudorange and range rate, the pseudorange and range rate estimation bias

errors were 0.5 m and 0.1 m/s rms, respectively. After the end of the

planned tests, new interpolation formulas were introduced which reduced the

bias errors to less than 0.1 m and 0.1 m/s, respectively. Details of the

AMLE evaluation tests are presented in Appendix C.

6.3 TRACKING FILTER EVALUATION TESTS

The pseudorange and range rate estimates generated by the AMLE are

passed through a tracking filter achieving three objectives: smoothing of

measurement noise, estimation of receiver state (pseudorange, range rate

and acceleration), and prediction of pseudorange and range rate to position

the AMLE window. Various filters were compared by analysis, simulation, and

experiment to select a filter for the Demonstration Receiver. Filter

selection and mechanization for a complete receiver are outside the scope

of the testing.

Filter selection is driven by three criteria. First, the filter must

be computationally efficient to allow a 50 times per second update rate.

Second, the filter must estimate the state and provide predictions to the

AMLE under the required high dynamics. Third, the filter must reduce the

pseudorange noise by as much as possible consistent with the above.

Three classes of filters were evaluated: second- and third-order

fading memory filters, and a second-order Kalman filter. All filters had

fixed gains to minimize the computational complexity; in particular, the

Kalman filter used steady state gains obtained by various assumptions on

process noise and measurement noise. In each class, 12 to 15 filters were

tested, with different filter parameters, i.e. filter time constant and

weighting for the fading memory filters, and standard deviation of process

6-2
and measurement noise for the Kalman filter. The tests were 50 g, 1470 m/s

step acceleration trajectories, with high, medium, and low SNR.

Details of the filter analysis and simulations are given in B.4.

Experimental results, presented in Appendix C, agreed with the analysis and

simulations in all cases. The filter selected for the rest of the

Demonstration was a third-order fading memory filter, with a time constant

of 0.14 s.

6.3.1 Transient Response

Figures 6-1 and 6-2 show the transient responses to 50 g step

acceleration and 50 g circular motion. The figures were generated by

overlaying repetitions of the indicated trajectories: 8 repetitions for

step acceleration and 30 repetitions for circular motion. In the step

acceleration tests, during the constant acceleration intervals, the dynamic

components of the pseudorange and range rate errors are zero after the

transient decays, as expected for a third order filter. The step

acceleration causes a range rate transient with a peak of 24 m/s, which

decays to a negligible value within twice the filter time constant, or

0.28 s. There is no significant pseudorange transient. In the circular

motion testf the pseudorange and range rate errors have sinusoidal

components with magnitudes that are proportional to the maximum jerk. For

the test of Figure 6-2, the maximum Jerk is approximately 40 g/s and the

peak errors due to dynamics are 0.06 m and 8 m/s, respectively.

6.3.2 Noise Response

The noise response of the filter is best evaluated by tests at low

SNR, since instrumentation effects dominate at high SNR. As shown in 6.4,

the dynamics of the test have a negligible effect on noise performance as

long as the dynamic component of the error is removed from the tracking

results. At 34 dB-Hz, the pseudorange and range rate estimates generated by

the AMLE have standard deviations of 1.7 m and 0.6 m/s respectively. The

tracking filter reduces these by a factor of 3.5 for pseudorange and a

factor of 1.2 for range rate, resulting in standard deviations of 0.6 m and

0.4 m/s for filtered pseudorange and range rate, respectively.

6.4 PERFORMANCE UNDER HIGH DYNAMICS

Performance as a function of dynamics and SNR is evaluated by using

simulated constant velocity, step acceleration, and circular motion

trajectories, under various SNR conditions. The tracking errors have

dynamic components that are introduced by the tracking filter lags, and

random components that are caused by thermal noise and instrumentation

effects. The random errors are approximately independent of receiver

dynamics. This is only an approximation because the nonlinearity of the

AMLE operation and the nature of some instrumentation effects introduce

some dependence on receiver dynamics. Nevertheless, as the tests

demonstrated, performance under high dynamics can be approximated by

6-3
evaluating these two error components separately.

To separate the dynamic error from the random error, the DES uses two

error measures, as defined in Chapter 4. The "total tracking error" is the

tracking result minus the simulated trajectory. These errors include both

the random and dynamic components. The "filtered output noise" is the

tracking result minus a filtered version of the simulated trajectory (i.e.,

passed through a tracking filter identical to that used in the

Demonstration Receiver). Thus "output noise" error, at SNRs below 50 dB-Hz,

is dominated by thermal noise. Instrumentation errors dominate at SNRs

above 50 dB-Hz.

6.4.1 Constant Velocity Tests

Tests were conducted at constant velocities up to 10,000 m/s. The

results showed that there is only minimal degradation at the high

velocities. Figure 6-3 shows the rms pseudorange and range rate errors

under high, medium, and low SNR, as a function of velocity. The figure

presents both the unfiltered and filtered output noise where the unfiltered

noise is at the AMLE output and the filtered noise is at the output of the

tracking filter. Note that for the constant velocity test, the dynamic

components of pseudorange and range rate are zero, hence the total tracking

error is identical to the filtered output noise. At low SNR, 34 dB-Hz, the

rms pseudorange and range rate errors are under 0.8 m and 0.6 m/s,

respectively. The dynamic components of the errors are zero, thus the

errors are due only to thermal noise and instrumentation effects.

As Figure 6-3 shows, there is a slight increase in the various error

components as the velocity increases above 300 m/s. This is caused by

coupling between instrumentation and dynamics effects. The main cause of

degradation is the method by which the local code generator is corrected to

account for dynamics. A detailed explanation is presented in Appendix B.

At very low velocities, there is also a slight increase in rms error.

This is caused by the original AMLE interpolation formulas. As discussed in

Appendix C, this bias was later removed using better interpolation

formulas, but only after the completion of the illustrated tests.

Tests at velocities that were approximate multiples of 1800 m/s showed

a high rate of false detections and loss-of-lock regardless of the SNR.

There were no similar problems at other velocities (e.g. 3000 m/s and 10000

m/s) and there is no analysis or simulation that explains the problem. The

problem is believed to be in the instrumentation and not fundamental to the

design. This area is targeted for further investigation.

6-4
6.4.2 Step Acceleration Tests

The step acceleration tests were conducted with step accelerations of

up to 100 g. The transient response for a 50 g step acceleration test is

shown in Figure 6-1. Figure 6-4 presents the rms pseudorange and range rate

errors with the transient removed, at various SNRs and accelerations. At

low SNR, the random errors are Independent of the acceleration and are

under 0.7 m and 0.6 m/s for pseudorange and range rate, respectively.

The theoretical peak transient errors for a 100 g step acceleration

are 0.39 m and 48 m/s for pseudorange and range rate, respectively. Figure

6-5 presents the measured peak transient errors as functions of dynamics

and SNR. The pseudorange transient error is comparable to the ambient noise

and cannot be accurately measured. The peak transient range rate error for

a 100 g step in acceleration is 48 m/s and is proportional to the

acceleration, as expected for a linear filter. These results agree with the

analysis and simulations.

The maximum magnitude of the step acceleration, for reliable tracking,

is determined by the size of the AMLE prediction error compared to the

width of the FFT filter bank. For the Demonstration Receiver, the

prediction peak error under 100 g step acceleration is approximately

100 m/s, or 500 Hz. This error is close to the limits of the AMLE window,

± 800 Hz, allowing perhaps a maximum step acceleration of 150 g. Note that

as the prediction error increases, there is a reduction in SNR due to the

1600 Hz lowpass filtering caused by integration over the correlation time.

Higher dynamics can be accomodated if a different tracking filter is used,

or if the range of the FFT is increased by using shorter correlation

intervals and more points in the transform.

6.4.3 Circular Motion Tests

Circular motion tests were conducted for various accelerations and

jerks and for low, medium, and high SNR. Circular motion corresponds to

sinusoidal motion in pseudorange. The period of the sinusoids were 8 s,

resulting in peak jerks of ir/4 times the peak accelerations, in consistent

units.

Figure 6-6 presents random pseudorange and range rate errors as

functions of dynamics and SNR. The output noise is independent of the

dynamics and depends mainly on the SNR. At low SNR, the rms pseudorange and

range rate errors at the output of the tracking filter are under 0.6 m and

0.5 m/s, respectively.

The theoretical rms dynamic errors for the 100 g, 80 g/s, circular

motion trajectory are 0.08 m and 11.3 m/s for pseudorange and range rate,

respectively. Figure 6-7 shows the total measured total tracking error as a

function of dynamics and SNR. The dynamic component of the pseudorange

error is negligible compared to the random effects. For range rate, the

dynamic component dominates the rms error, and is proportional to

acceleration.

6-5
The prediction errors for circular motion tests are proportional to

jerk. Successful tests were conducted up to 150 g, 157 g/s circular motion,

and operation may be acceptable for jerk of up to 250 g/s. If even higher

dynamics are needed, receiver processing (tracking filter and length of

correlation interval) can be changed to accommodate the dynamics at a cost

in SNR threshold, as discussed in 5.4.2.

6.5 PERFORMANCE AT LOW SNR

Low SNR tests were conducted to determine the performance of the

receiver as a function of the SNR, and to determine the minimum acceptable

SNR, or tracking threshold, as a function of dynamics. The tests

demonstrated that the receiver can track reliably down to 28 dB-Hz, almost

independent of the test dynamics.

Circular motion tests were used to determine low SNR performance.

Figure 1-1 shows the agreement between the analysis, simulation, and

experimental results for a 50 g, 10 g/s, circular motion trajectory. For

SNRs between 32 dB-Hz and 50 dB-Hz, the mean square pseudorange error is

inversely proportional to SNR. At lower SNRs, many false detections (or

outliers) occur, causing large increases in error as the SNR decreases. For

SNRs over 50 dB-Hz, instrumentation errors dominate. These errors are not

included in the theoretical model or in the simulation, causing the

observed discrepancy between simulations and experimental results.

Figure 6-8 shows the tracking errors for different dynamics:

accelerations of 3 g» 50 g, 100 g and 150 g. The dynamics have little or no

effect on the loss of lock threshold, and only minor effect on the rms

pseudorange error due to random noise. The minor increase in pseudorange

error at high dynamics is due to changes in the carrier frequency over the

measurement time and to instrumentation effects, both in the TIS and in the

Demonstration Receiver, as explained in Appendix B.

Figure 6-9 demonstrates that the removal of the dynamic component of

the tracking error has only a minimal effect on the pseudorange error, even

at dynamics as high as 50 g, 10 g/s, circular motion. This is because the

rms dynamic component at such dynamics is less than 0.05 m, which is

negligible compared to random noise and instrumentation errors.

6-6
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6-15
CHAPTER 7

A CANDIDATE COMPLETE RECEIVER DESIGN AND MINIATURIZATION

This chapter presents a preliminary design of a candidate complete low

volume, high dynamic, GPS receiver, with estimates of size and power. This

work was completed and reported orally and in viewgraph form in early 198U,

and represents the knowledge at that time. This report specifically does

not take into account the recent Armament Division solicitation and

specifications for GPS receivers [1], or the resulting selected receiver

designs.

Section 7*1 lists major trade-offs in the design of a complete

miniaturized receiver. Section 7.2 describes the block diagram design of a

GPS receiver consisting of single or dual L-band antennas, RF and digitizer

circuits, five signal processors, a navigation and control unit (NCU), and

host interface via a 1553 bus. The design emphasizes digital technology and

minimizes the analog sections, thus lending itself to miniaturization.

Section 7.3 shows that by using advanced technologies such as CMOS

processors, gate array and custom VLSI, leadless chip carriers, and twosided substrate boards, the receiver can be packaged in a small volume. To

illustrate this an example is shown of the receiver packaged in a section

of an air-to-air missile, using approximately 100 cubic inches of space.

The power estimate for the receiver is approximately 80 W. This

estimate is believed to be conservative. More study is needed to refine

the power estimate and its accuracy, and to determine whether the heat

generated in the receiver can be dissipated in the thermodynamic

environment of specific missiles. This work is outside of the current

scope.

7-1
7.1 DESIGN TRADE-OFFS

There are several design trade-offs that have significant effects on

the volume, power and cost of the GPS receiver. A full analysis of the cost

effectiveness of each trade-off is beyond the scope of this report. The

following is a qualitative summary of the relevant trade-offs.

The receiver can operate with a single antenna or with multiple

antennas. Additional antennas enhance the operation of the receiver during

partial masking of GPS satellites. On an aircraft, antennas may be placed

on the top and bottom surfaces, or on the wing tips, so that GPS signals

can be received even during banking or rolling. The additional masking

immunity has to be weighted against the added hardware and software costs.

There are risks associated with adaptive selection of the "right" antenna

by the receiver, and in the synchronization of switching between antennas.

In our design we elected to use one antenna.

)

The GPS receiver uses the L2 band signal to calibrate ionospheric

delay, thus improving real time accuracy. In range applications, the

receiver might perform ionospheric calibration by receiving data from a

host vehicle or a control center, or by operating in a differential GPS

mode. Furthermore, it may be acceptable to operate with degraded accuracy

during-real time operation (satisfying the range safety requirements), but

achieve full accuracy during post-test analysis when the ionospheric

calibration data is added. In our design, we elected to use L2 so that

self-contained real time accuracy is maintained.

A factor contributing to the size of the receiver is the presence of

L1 and L2 bandpass filters in the front of the RF section. These filters

reject out-of-band interference and reduce the risk of pre-amplifier

saturation. To achieve low receiver noise temperature, the filters are

typically built as tuned cavities with significant volume. In a range

missile application it may be acceptable to ignore interference signals,

and build the receiver without the bandpass filters. In our design we

conservatively elected to include the bandpass filters.

The number of signal processing channels depends on the receiver

application. A high dynamic receiver needs four channels to continuously

track the four satellites used in the Time-Space-Position Information

(TSPI) solution. A fifth channel can be used to search and acquire more

satellites, to solve for the ionosphereic calibration based on L1-L2

measurements, and to serve as backup during masking. If size and power are

not a limitation (such as for a transdigitizer receiver), enough channels

can be provided to track all the visible satellites. However, if size and

power are at premium, the receiver can be built with only one or two

channels with reduced dynamic performanc e and SNR threshold. We

conservatively selected a full five channel receiver.

There are variations in the structure of the signal processor channel.

The demonstration system uses an 11-lag correlator, a FFT processor, and an

8086 CPU as key components. The span of the correlator is important during

acquisition, but can be reduced during tracking, so a different span can be

7-2
used In the final receiver. Doppler frequency detection is performed in a

TMS32010 processor using 64-point complex FFTs. If the number of lags and

the number of frequencies is reduced, the size and complexity of the

interface between the correlators and the FPT processor is reduced, and the

processing may be performed by a Discrete Fourier Transform (DFT). In other

alternatives, the functions performed by the 8086 might be performed in an

8-bit processor, or the 8086 and TMS32010 functions might be combined in

the TMS32010 or an upgraded chip, reducing both size and complexity. We

conservatively elected to use the signal processor configuration of the

Demonstration Receiver.

There are two schemes to compensate for pseudorange variations during

Integration time. In the Demonstration, the local code is delayed or

advanced when the accumulated pseudorange is an integer number of

correlator lags. An alternate approach is to re-clock the received signal

at a rate that depends on pseudorange variation. This approach requires

more circuitry but improves the threshold. We selected the "code control"

method of the Demonstration Receiver in our design.

The TSPI solution can be performed in two ways. One method is to

combine all raw pseudorange and range rate data and all orbit data in a

single tracking filter residing in the Navigation and Control Unit (NCU).

Another method is to smooth the raw pseudorange and range rate in the

signal processing channel, and then combine the smoothed results and the

orbit data in a NCU TSPI solution, distributing the processing load. We

selected the second approach in our design.

7.2 CANDIDATE BLOCK DIAGRAM FOR COMPLETE RECEIVER

A candidate top level functional design of a high dynamic receiver is

shown in Figure 7-1. The design shown is for a single antenna, five

channel, L1 and L2 band, P and C/A code receiver.

The signal from the antenna is amplified, demodulated to in-phase and

quadrature baseband components, and digitized in four analog to digital

converters. There is only one signal channel for each of L1 and L2 up to

this point, not one channel for each satellite. The local oscillators and

the sampling clocks are derived in open-loop fashion from a single fixed

frequency oscillator, the local oscillators being at the nominal L1 and L2

center frequencies and the sampling clock at twice the P code chip rate.

This is a significant simplification over receivers which demodulate the

signals from each satellite separately in phase-locked loop channels

requiring seperate frequency-controlled oscillators. The receiver has only

one oscillator and one frequency generator.

Both P and C/A code signals are recovered through the same baseband

circuitry and A/D converters. The outputs of the analog to digital

converters are input to five identical tracking processors (TPs), one for

each channel. These units implement the approximate ML estimation of the

pseudorange and range rate to the satellites. In the implementation shown,

the tracking processors also perform the tracking filter function, that is,

7-3
they filter the raw estimates to reduce random noise effects. The smoothed

estimates of pseudorange and range rate are output to the NCU, which

converts them to position, velocity, and clock offset.

The NCU interfaces to a system input-output interface unit, which in

turn interfaces to the outside world. The NCU, accepts initialization and

control from the I/O interface unit, and tracking filter outputs from the

tracking processors . It performs all necessary ephemeris, clock and

propagation calculations, based either on data received from the I/O

interface unit or on data extracted from the satellite data signals. Using

this data and the tracking filter output data, it calculates receiver

position and velocity, and outputs them to the I/O interface unit along

with status information. It also controls the tracking processors, and

provides them with pseudorange and range rate estimates during acquisition

and reacquisition.

If the implementation is such that all smoothing is done in the NCU,

this unit outputs pseudorange and range rate estimates to the tracking

processors at all times.

7.2.1 RF Modules

Figure 7-2 describes the structure of a RF module. The signal from the

L-band antenna is split into L1 and L2 paths,, and then band-limited by a

narrow bandpass filter (approximately 30 MHz) to reject interference. The

filtered signal is split into in-phase and quadrature (I and Q) components,

then mixed down to baseband. After the mixers, the signals are filtered by

10 MHz lowpass filters. Each RF module produces four analog baseband

signals: L1-I, L1-Q, L2-I, and L2-Q.

7.2.2 Analog-to-Digital Converter Module

The Analog-to-Digital Converter (ADC) module described by Figure 7-3

consists of four ADC circuits, one for each incoming signal. The ADCs

sample at twice the frequency of the P-code ( 20.46 MHz) and output three

bits for each sample of the analog signal.

7.2.3 Signal Selector

The signal selector (Figure 7-4) allows the connection of the,ADC

outputs to the tracking processors. Logically, the signal selector is a

switch box with two inputs from LI and L2, and five outputs to the tracking

processors. Each switched.output signal is 6-bits wide: 3 bits I, 3 bits

Q. The signal selector is controlled from the tracking processors with L1-

L2 selection independent for each channel. When expanding the design to

two antennas, the signal selector becomes a larger switch with four inputs

and five outputs, with independent antenna selection for each channel to

optimize SNR performance.

7.2.4 Tracking Processor Unit

There are five identical tracking processors, one for each channel.

7-4
Each unit accepts the signal from one pair of ADCs via the signal selector,

implements the approximate ML estimation of raw pseudorange and range rate,

smooths the raw estimates in a tracking filter, and outputs the smoothed

estimates to the NCU.

A functional block diagram of the tracking processor is shown in

Figure 4-3. The main elements of this unit are the numerically controlled

oscillator (NCO), the complex multiplier, the code generator, the

correlator, the FFT buffer, the FFT processor and a microprocessor to

extract pseudorange and range rate estimates from the FFT outputs and

implement the tracking filter.

The first step in the processing is to translate the frequency of the

received signal by the previous best estimate of carrier frequency, so that

the residual frequency (to be estimated by the FFT) is near zero. This is

accomplished by the sine cosine generator and the complex multiplier. The

sine-cosine generator generates sine and cosine functions at the current

best estimate of carrier frequency, using the tracking filter frequency

estimate, or, during acquisition, an input from the NCU. The complex

multiplier digitally multiplies the signal input by the cosine and sine

functions, considered as a complex numbers, thus accomplishing the

frequency translation. The sine and cosine functions are quantized to 3

levels for implementation simplicity, with an SNR loss of only 0.4 dB.

The output of the complex mixer is cross-correlated with eleven lags

of the code. The FFT integration interval, equal to the data bit time T, is

divided into K subintervals of length T/K, with K chosen to be 32. These

subintervals are called correlation intervals. The correlations for each

lag are sums over the correlation intervals of the products of the code

lags multiplied by the complex mixer output. One effect of the summing is

to low pass filter the product signals with a low pass filter of bandwidth

K/(2T), which is negligible when the frequency error is small.

The correlator results for each lag are input to the FFT buffer at the

end of the correlation interval. These correlation values are then output

to the FFT processor one lag at a time. In other words, the buffer can be

viewed as a matrix which is filled by the row and emptied by the column.

The FFT buffer outputs are input to the FFT processor. This circuit

computes a FFT for each correlation lag, using data from the K correlation

intervals. A straightforward FFT over T seconds with K input points results

in computing the energy in K filters, each of bandwidth 1/T Hz, spaced 1/T

Hz apart. Since the gain responses of these filters cross over at the -4 dB

points, causing significant degradation when the actual received frequency

is at or near one of these crossover points, additional computations are

made to compute the response of additional filters, centered at the

crossover points of the original filters. This is done by appending K

zeros to the K data points and doing a 2K-point FFT.

There is also a complication because the time delay is not constant

over the integration time. At high velocity, the delay can change by

several lags in one integration time. To account for this, the code

7-5
generator lag is updated each correlation time, rather than each

integration time. The average rate of change of code phase is analogous to

the code oscillator offset frequency in a code locked loop.

The remaining functions are implemented in the TP microprocessor. The

energy outputs of the FFTs are maximized over time lag and frequency to

find the correlator time lag and the FFT frequency closest to the actual

delay and frequency. The approximate ML estimates are then calculated by

interpolation using two adjacent lags and two adjacent frequencies, and

output to the tracking filter. The tracking filter is a fixed gain filter

operating at an update rate of 50 per second.

7.2.5 Navigation and Control Unit

The NCU computes receiver position and velocity from the tracking

filter outputs and from the satellite ephemerides, clock offsets, and

propagation corrections. In some applications, such as short time-offlight missiles, the satellite data could be input to the receiver from a

host vehicle. These data could also be extracted from the received

satellite signals by the tracking processors, but this extraction might not

be reliable under extreme conditions of high acceleration and low SNR. The

needed data could also be obtained using the receiver, itself in an

initialization mode prior to launch.

The NCU also interfaces to the receiver input-output interface unit,

which communicates with the outside world. It determines which satellites

are to be tracked, initializes and controls the tracking processors,

performs acquisition in conjunction with the tracking processors, and

maintains data bit synchronization. All of these are software implemented

functions.

7.2.6 Input-Output Interface

The Input-Output Interface unit interfaces between the NCU and the

host system. The 1553 bus was selected for this design because it is a

standard bus for aircraft. It is a bi-directional high-speed serial bus and

is used to interface between the receiver and the host vehicle.

7.2.7 Voltage Regulating Module

The voltage regulating module converts the host vehicle's supply

voltage to those required by the receiver, at the correct power. It also

includes a backup battery for data storage.

7.2.8 Clock Module

The clock module, Figure 7-5, uses a crystal as a frequency reference

to create the needed clocks. As an example, using a crystal at the P-code

frequency, two multipliers create the L1 and L2 frequencies from which one

can derive all the other required frequencies.

7-6
7.3 PACKAGING, COMPONENT COUNT, SIZE AND POWER

This section discusses severed advanced technologies that contribute

to the packaging of the proposed receiver, proposes implementations of

various receiver modules, defines the new integrated circuits that need to

be developed, and estimates total volume and power.

7.3.1 Technology Review

The recent advances in electronic technology allow for building

smaller and denser components both in the digital and analog sections of

the receiver.

One of the most power consuming parts in the circuit is the

microprocessor (CPU). Recently, Harris introduced a CMOS version of the

8086 processor. CMOS technology reduces power consumption, while the 8086

provides a 16-bit processing capability. Other companies are (and will be)

offering similar products.

Many of the 16-bit processors currently available have coprocessors

that perform high speed floating point arithmetic. These allow the high

update rate for tracking filters, orbit determination, and TSPI solutions.

Examples are the Intel 8087 and National's floating point unit.

Only a few years ago, the high cost of development restricted VLSI to

products that were manufactured in large volume (e.g. 100,000 or more

chips). Today, Gate Array and Semi-Custom technologies reduce the prices

substantially. The development of a gate array, with 2500-1000 gates, may

cost under $100K and be more cost effective than Medium Scale

Integration/Small Scall Integration (MSI/SSI) circuits for production of as

few as 100 to 1000 units.

Many new ICs are offered in Ceramic Leadless Carrier Chip (CLCC)

packages in addition to the standard dual-in-line package (DIP). The new

package offers reduced area and volume. Typical volume improvement is 8:1

over DIPs and 2:1 over Ceramic Flatpacks. In addition, the CLCC package

allows for better thermal management. In surface mounting, the CLCC uses

more area than silicon dice, but is easier to mount and replace.

Hybrid technology combines several components on a single substrate,

where the interconnection patterns are photo-etched. The components can be

complex (e.g. VLSI dice) or simple (e.g., resistors, transistors). This

technology allows for mixing of digital and analog components, in.a manner

similar to a printed circuit board.

The dense packaging of RF circuits is facilitated using micro-strip

circuits. These are hybrid circuits using microwave components, such as

power-splitters, filters, amplifiers, and mixers.

Monolithic Microwave Integrated Circuits (MMIC) are the analog

equivalent of MSI/SSI. A typical MMIC replaces a whole microstrip on a

7-7
single die of silicon or GaAs. The technology is new but not beyond the

current state-of-the-art.

7*3*2 Module-by-Module Design And Estimates

The following are implementation schemes for each of the functional

blocks described in Section 7*2. The implementation uses components that

are either available now or in the near future. The component selection is

tentative and depends heavily on the selected microprocessors and VLSI

components. Table 7-1 summarizes the new VLSI circuits that need

development.

Table 7-1

Summary of New 1C Development

! Function

Routing of a signal from ADCs to TPs

Code generator, mixer, computer

interface

Controls for the FFT buffer

Correlator

•

Tracking processor interface to the

NCU

Interface inside the Tracking Processor

.

NCU interface to 1553

Interfaces inside NCU, NCU to signal

selector and tracking processors

Digital divider chains

'

Total

Module

Signal

Selector

Tracking

Processor

Tracking

Processor

Tracking

Processor

'

Tracking

Processor

Tracking

Processor

I/O interface

NCU

Clock

Number

1

1

1

1

1

1

1

1

1

9

7-8
In each module the design includes major components and also some

discrete components for biasing, surge protection, etc. The

microprocessors selected are in the Intel 8086 family. Similar designs can

be made with National Semiconductor (NSC) 32016 or Motorola's MC68020.

Gate arrays have 2500 to 8000 equivalent gates per device and are available

from companies such as Hughes, Harris, Motorola, LSI systems, and NSC. The

memory components used in the rest of the discussion are NSC's 8Kx8 static

CMOS RAM NMC6164 and Advanced Micro Devices' 64Kx8 EPROM AM67512. We

assume each new VLSI chip to be CMOS and to consume 0.25W.

7.3.2.1 RF Module

The RF module is estimated to consume 10 W. The input stages are

tuned cavity bandpass filters to minimize the noise temperature. The rest

of the circuit can be mounted on a microstrip: the intermediate bandpass

filters are side-coupled L-band photo-etched filters and take approximately

2 in.2 for each, the lowpass filters are discrete component LC filters,

requiring approximately 1 in.2 each.

7.3.2.2 ADC Module

Each ADC module uses four 6-bit ADC chips (Analog Devices AD9000), a

voltage reference, two operational amplifiers, and the associated resistors

and capacitors. The total power for each module is estimated to be 5 W.

For the two-antenna receiver, the reference circuitry need not be

duplicated in the second ADC module.

7.3.2.3 Signal Selector

The signal selector has two 6-bit inputs, five 6-bit outputs, a 5-bit

control word (1 bit per tracking processor), and power connections. It can

be implemented using a single gate array, consuming 0.25W.

7.3.2.4 Signal Processor

The signal processor is implemented as follows:

1. The correlator uses one semi-custom VLSI chip or 1 to 2 gate

arrays. Cell count indicates that, even using an 8000-gate

device, two gate arrays may be needed. They would be

identical.

2. The FFT buffer uses three chips. The memory portion uses two

RAM devices to implement 16-bit access, while the control

portion uses a single gate array chip. The total memory size

is H to 8 Kbytes.

3. The FFT uses one processor and two ROM chips. The processor

is the Texas Instruments TMS32010, used in the Validation

Demonstration.

7-9
4. The NCO is a single chip, Stanford Telecommunication Inc. ST1172. This is a CMOS device that is used in the Validation

Demonstration.

5. The code generator uses a single gate array device. It

creates the P-code and C/A codes and, under computer control,

advances or retards them to compensate for Doppler shift.

The code generator also controls the location of the bit

synchronization pulse. The mixer is part of the code

generator gate array.

6. The computer consists of a CMOS CPU (Harris 80C86), two chips

of program memory, (128 KBytes), four chips of data memory

(32 KBytes) and two gate array chips. One gate array is

dedicated to the interface to the NCU, while the other

performs all the interfaces inside the signal processor. It

may be possible to combine the two gate arrays into a single

chip.

The tracking processor uses a total of 18 to 20 chips, mostly CMOS.

The total estimated power is 5 W.

7.3.2.5 NCU

The NCU consists of a CPU (Intel 80286), a floating point coprocessor,

two chips of program memory (128 Kbytes), eight chips of data memory (6k

KBytes), and one gate array chip, for a total of 13 chips. The gate array

chip performs all the interfaces within the NCU and between the NCU and the

tracking processors and signal selector. The estimated NCU power

consumption is 5 W.

7.3.2.6 I/O Interface

The 1553 I/O interface can be implemented with commercial hybrid

components and a single gate array chip. For example, ILC Data Device

Corporation manufactures a DDC65122 that, with the addition of two line

transformers (DDC25679)» provides a complete 1553 interface. The volume

for the three components is 1.22 in. 3 and the required power, for 25% duty

cycle, is 7 W. The gate array chip performs all the interface functions

between the NCU and the DDC65122.

7.3.2.7 Power Distribution Module

To obtain high efficiency, a switching power supply must be used. It

is projected that 80% efficiency can be achieved.

7.3.2.8 Clock Module

The clock module consists of analog and digital sections. The analog

sections are on a microstrip and consist of five frequency multiplying

circuits. Each circuit has an amplifier, a frequency multiplier, and a

7-10
band pass filter, and takes approximately 2 to 3 in.2. The digital section

consists of a single gate array circuit chip.

7.3.3 Packaging, Volume and Power

This section illustrates the packaging of the receiver in a section of

an air-to-air missile. As shown in Figures 7-6 and 7-7, the components are

mounted on circular plates, (substrates). The plates can be single- or

dual-sided, depending on the thermal environment. At the edge of each

plate, space is provided for an interconnection harness. Each plate has 17

to 19 in.2 of usable area and can contain, for example, 20 44-pin VLSI

packages.

The RF module can be packaged on two single-sided plates. The ADC

modules and the signal selector occupy one single-sided plate. Three

double-sided plates are used for the five tracking processors, the NCU, and

the I/O interface. The clock module occupies a single-sided plate.

We assume that each plate occupies 10 in.3 (i.e., a cylinder of 5 in.

in diameter and 0.5 in. height). Then all the electronics discussed above

requires 70 in.3. Adding 30 in.3 for the power distribution module, the

total volume is approximately 100 in.3. The heights of the individual

plates may be adjusted to provide better heat distribution or easier

access.

The power dissipation is estimated as follows. Each of the tracking

processors consumes approximately 5 W. The NCU also consumes approximately

5 W. Adding the power used by the other modules and considering the

efficiency of the powe r distribution module , the total power is

approximately 80 W. Table 7-2 summarizes the volume and power estimates.

There is concern about dissipation of the estimated power in the

limited volume, and in the missile environment. To refine the estimates

would require:

1. Definition of the thermal environment, e.g., missile skin

temperature, duration of operation etc.

2. Definition of the specific components to be used, rather

than using assumptions such as 250 mW per gate array chip.

This will affect the number of components as well as power.

3. Refined power estimates for the microstrip circuits in the RF

and clock modules.

This work is outside of the scope of the present task.

7-11
Table 7-2

Volume and Power Estimates

Module

HF

ADC and signal selector

Tracking processors (5)

NCU and I/O interface

Clock

Power Distribution

Total

Volume ! Power

(in.3) ! (W)

20

10

25

5

10

30

100

!

! 10 I

! 10

I

25

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7-14
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7-15
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7-16
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7-17
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7-19
CHAPTER 8

OPEN QUESTIONS AND FUTURE WORK

The Demonstation has not answered all questions about GPS receivers,

and, indeed, has generated new ideas for potential improvements. This

chapter briefly discusses some open questions and suggestions for answering

them. The issues are categorized as applicable to a high dynamic P code

receiver, to an optimized P and C/A code receiver, to a transdigitizer

receiver, and to a miniaturized receiver.

8.1 HIGH DYNAMIC P CODE RECEIVERS

The Demonstration Receiver tracks only on the P code, although the C/A

code would be used for acquisition in an implemented receiver. This

section discusses potential improvements which can be realized while

tracking P code only.

8.1.1 Critical Velocity Problem in Demonstration Receiver

The Demonstration Receiver has higher errors and higher SNR threshold

when the pseudorange rate is approximately 1800 m/s, and at multiples of

this rate. There is no problem at other rates tested, up to the maximum

test rate of 10,000 m/s. Analysis and simulations did not reveal the same

behavior. Therefore, the behavior is believed to be caused by an

instrumentation effect peculiar to the hardware. The problem could be

either in the Receiver or in the TIS. The problem is not believed to be

fundamental to the receiver design, but it should be resolved.

8.1.2 AMLE Parameter Optimization

The AMLE in the Receiver maximizes over nine correlator lags and 64

frequencies. Higher jerk or step acceleration can be tracked if the

frequency range is widened. The penalty in performance is that threshold

SNR would Increase slightly, because there would be more places for

outliers to occur. On the other hand, some reduction in threshold SNR can

be achieved by reducing the number of correlator lags, with three lags

probably being sufficient after acquisition. The number of frequencies can

also be reduced when the maximum dynamics are less. These trades should be

investigated by simulations. Experimental verification with reduced number

of correlator lags would be easy to do with the Demonstration Receiver, but

changes in the frequency domain would be more complex. Increasing the

range in the frequency domain would require more points in the FFT.

8-1
8.1.3 Tracking Capability and Oscillator Effects

Further refinement of the tracking filter is desirable. Also, the

performance should be determined for trajectories with different dynamics,

and for the situation in which oscillator frequency offsets occur due to

acceleration. These oscillator frequency offsets appear to the receiver as

changes in velocity. Thus a step acceleration would cause the signal

processing to see what appears to be simultaneous steps in frequency and

acceleration. For an oscillator sensitivity of 2 x 10~9/gf a 100 g step

acceleration would cause a maximum frequency:shift of 315 Hz, which is well

.within the range of the FFT in the AMLE, so no problem is anticipated.

Performance should be verified both by simulations and by receiver tests.

8.1.4 Phase Coherent and Adaptive Tracking

As discussed in 5.4.3, the Receiver is inherently capable of phase

coherent tracking when dynamics permit. Various phase locked loops should

be compared analytically and by simulation, and dynamics capabilities

determined. Stability is a concern, because of the transport delay in the

AMLE, loop filter calculations and NCO, and because the desired loop

bandwidth for high dynamic tracking is not very small compared to the loop

filter update rate of 50/s. One way to add coherent tracking without

sacrificing maximum dynamics would be to adaptively switch between

frequency and phase tracking, depending on dynamics and SNR.

8.1.5 Parallel FLL and PLL Tracking, and Smoothing

High dynamic FLL tracking and phase coherent tracking could be

conducted in parallel. The receiver would operate as demonstrated to

achieve high dynamics and low SNR threshold capability. In parallel with

this, the receiver would track carrier phase in software, without feedback.

The velocity measurement capability of a PLL would be achieved without the

loss of lock problems. Loss of phase lock would occur under some

conditions, but would cause only a temporary loss of accuracy in measuring

velocity and acceleration. Tracking would continue with the FLL.

A further refinement could be accomplished by using a Kalman or other

type of smoothing filter. A smoothing filter uses data acquired up to the

present time to estimate parameters for an earlier time. Smoothing filters

are better than standard tracking filters both in their errors due to

random noise and in dynamic response. Improvements of 6 dB or more are

possible [8]. This benefit could probably be realized with a delay of

approximately 0.5 s. There is some cost in complexity. Considerable

analysis and simulation is required to determine feasibility, cost and

benefits. '

8.2 COMBINED P AND C/A CODE TRACKING

Combined P and C/A code tracking, discussed in 5.4.4, has the

potential to reduce tracking SNR threshold by 4.8 dB relative to the

received P code power, or relative to the total received L1 power. This

can be accomplished either for the demonstrated FLL tracking, or using PLL

8-2
tracking. What is necessary is to correlate the received signal against

the P and C/A codes simultaneously, and to combine these correlations in

the proper phase. Separate correlators are required for the two codes, or

else a more complicated correlator is required that can process both codes

simultaneously with proper carrier phase. Performance should be

established by simulation. Verification with actual satellite signals is

desirable.

8.3 ENHANCEMENTS FOR TRANSDIGITIZEK RECEIVERS

The following potential enhancements are particularly applicable to

transdigitizer or translator receivers.

8.3*1 Optimum C/A Code Pseudorange Estimation

The performance of the AMLE or of a delay locked loop can be improved

by reducing the correlator lag spacing. This is mentioned in 5.4.1, and

the expression for rms pseudorange error in Appendix B includes this

effect. The rms pseudorange error is proportional to the square root of

the lag spacing, when the lag spacing is not too small, when the SNR is

sufficiently high, and when the received signal is not bandlimited.

The key requirement appears to be received signal. Suppose the C/A

signal were received with a 10 MHz bandwidth and sampled at 20.46 MHz, as

in the Demonstration Receiver. Using a lag spacing of one sampling time

results in 20 correlator lags per chip. There is a potential gain of root

10 over a typical two lag per chip implementation. Since the theoretical

rms pseudorange error at an input SNR of 32.5 dB-Hz is less than one lag

spacing, it appears likely that most of this theoretical improvement could

be realized. This gain is most likely realizable in a receiver which uses

only the C/A code but is not bandwidth limited. In a translator or

transdigitizer receiver, the bandwidt h is limited. Analysis and

simulations are in order to see how much improvement can be realized.

8.3.2 Code Locking and Restricted Sampling Rates

The main concern addressed here is that the sampling rate of a

transdigitizer might not be compatible with the Demonstration Receiver, and

that the Receiver sampling rate might not be compatible with the HDIS

sampling rate. This would complicate possible modifications to the HDIS to

include the high dynamic tracking capability. These concerns are

unwarranted.

The Demonstration Receiver does not code delay lock in the usual

sense. Instead, code delay for each data bit time is quantized to the lag

spacing. In delay locked loop implementations, code phase is maintained as

close as possible to the received code phase.

As implemented, operation of'the Demonstration Receiver depends on

having the sampling rate be twice the nominal chip rate. Other digital

receivers typically offset the sampling rate from twice the chip rate.

What is important here is that there is no fundamental reason why the high

8-3
dynamic tracking concepts cannot be used with other sampling rates and with

the usual type of code locking. The cost would be in required correlator

speed, since the half speed correlation technique used in the Receiver

would not be applicable. It is likely that there would be a reduction in

instrumental pseudorange bias. Thus the high dynamic concepts could be

incorporated using the sampling rate of the HDIS and a matche d

transdigitizer.

8.3.3 Smoothing

Kalman, or other least squared estimator, smoothing would be ideal for

use in a transdigitizer receiver. The delay of under 1 s would be

acceptable. The added computational complexity could be tolerated, because

size and production cost are not critical. Both real time and delayed

solutions could be provided. Smoothing could be used either with phase

locked or frequency locked tracking, or with both. It would also be

possible to use a different time constant for the delayed solution than for

the real time tracking, or to use an adaptive smoother. It may be, possible

for the near real time smoother solution for a C/A code transdigitizer

receiver to be comparable in accuracy to a P code receiver. This deserves

serious investigation.

8.3.4 Data Aiding

A PLL transdigitizer should have the capability of using data aiding

from a local reference receiver. However, it is desirable that the

receiver also be capable of achieving good performance without this aiding.

This would probably improve reliability and operability. One of the

inherent disadvantages of data aiding is the delay or transport lag

introduced, which reduces the dynamic tracking capability of a PLL. Use

of the frequency locked high dynamic tracking concepts for real time

tracking, and phase locked tracking with data aiding and smoothing, may be

ideal.

8.3.5 Fast Acquisition and Reacquisition

Fast acquisition and reacquisition are required in a high dynamic

transdigitizer receiver. One of the key advantages of using a

transdigitizer receiver rather than a receiver on a vehicle is that it is

much more feasible to achieve fast acquisition in a ground based receiver.

The Demonstration Receiver concept is ideal for fast acquisition. The

multiple lag correlator and the FFT are inherent to the architecture. More

correlator lags and more FFT frequencies need to be implemented. Fastest

acquisition is obtained by correlating against all lags of the C/A code

simultaneously, and performing all FFTs in real time. Since acquisition

ideally should be possible at all SNRs at which tracking is possible, an

integration time of 0.1s to 0.2 s is desirable. Complete acquisition could

be accomplished in under 0.5 s.

The above completely parallel acquisition is probably unnecessary.

Searching of approximately one-tenth of the delay-frequency bins in

8-1}
parallel would result in acquisition time of 1 s to 2 s. Since the same

FFT computations are required regardless of the order of bin searching, it

is hardware-efficient to build a limited number of correlator lags and to

do the FFTs for all of these lags in parallel. Computation of all required

FFTs is feasible with current technology. Possible approaches are special

purpose logic, parallel signal processing microprocessors, or array

processors. The challenges are in determining realistic requirements, and

then in meeting them at low cost.

8.4 MINIATURIZATION

The packaging study of Chapter 7 accomplished its goal of establishing

the feasiblity of a 100 in.3 high dynamic receiver. Determining the

minimum possible size was outside of scope. Also, significant technology

advances have occurred since the packaging study was conducted. Finally,

there is a program to develop 6 in.^ receivers, sponsored by the Defense

Advanced Research Projects Agency (DARPA). The DARPA receivers have either

single or multiple channels, include front ends, control, display and

batteries, and have power consumption consistent with the volume. A very

rough estimate is that a high dynamic receiver would be 1.2 to four times

more complicated than the DARPA receivers, depending on the number of

channels in both receivers, and could be implemented in a corresponding

volume of 7 in.3 to 25 inA Acquisition would be faster than required for

the HDIS, but not extremely fast as for a transdigitizer receiver.

Reacquisition would be very fast.

8-5
CHAPTER 9

REFERENCES

1. System Specification for Global Positioning System (GPS) High Dynamics

Instrumentation Set (Medium Volume), type A, YISP-83-14, USAF Armament

Division, Deputy for Range Systems, Eglin AFB, FL, 20 July 198U.

2. Hurd, William J., "High Dynamic GPS Receiver Validation Demonstration

Plan," JPL D-1181, Jet Propulsion Laboratory, Pasadena, California,

Nov. 30, 1983. (JPL internal document.)

3. Contract NAS7-918, Task Order RE-182, Amendment No. 320, "GPS Receiver

for High Dynamic and Low Volume Applications."

4. Hurd, William J., "GPS Receiver Test Plans and Procedures, Final

version," JPL Interoffice Memorandum 331-84-277A, August 3, 1984. (JPL

internal document.)

5. Hurd, William J. and Anderson, T. 0., "Digital Transition Tracking

Symbol Synchronizer for Low SNR Coded Systems," IEEE Trans, on Comm.

Vol. COM-18, April 1970.

6. Holmes, J.K., "Coherent Spread Spectrum Systems," John Wiley & Sons,

1982.

7. Hurd, William J., "High Dynamic, Low Volume GPS Receiver," NTC 83, San

Francisco, November 1983.

8. Pomalaza-Raez, C.A., and Hurd, W.J., "Improved Carrier Tracking by

Smoothing Estimators," IEEE Trans, on Aerospace and Electronic

Systems, September 1985.

9. Spilker, J.J., "GPS Signal Structure and Performance Characteristics,"

J. Inst. Navigation, Vol. 25., No. 2, Summer 1978.

9-1
10. Wozencraft, J.M. and Jacobs, I.M., "Principles of Communication

Engineering,n John Wiley & Sons, New York.

11. Hurd, W.J., and Statman, J.J., "High Dynamic GPS Unaided Pseudorange

Tracking Demonstration," IEEE International Telesystems Conference,

Las Vegas, 1984.

12. Ekstrand, B., "Analytic Steady-State Solution for a Tracking Kalman

Filter," IEEE Transactions on Aerospace and Electronic Systems,

November 1983, pp. 815-819.

13. Statman, J. I., "Fading Memory Filter as a Special Case of Kalman

Filter," JPL Interoffice Memorandum 331-85.5-10, July 17, 1985. (JPL

internal document.)

14. Statman, J. I., "Position Error Caused by Unmodeled Dynamics," JPL

Interoffice Memorandum 331-85.5-41, July 17, 1985. (JPL internal

document.)

9-2
CHAPTER 10

ABBREVIATIONS

ADC(A/D) - Analog to Digital Converter

AMLE - Approximate Maximum Likelihood Estimator

BPF - Bandpass Filter

C/A-code - Coarse/Acquisition Code (also known as SPS)

CLCC - Ceramic Leadless Chip Carrier

CM - Circular Motion (simulated trajectory)

CMOS - Complementary Metal Oxide Semicopduetor

CPU - Central Processing Unit :

CV - Constant Velocity (simulated trajectory)

DARPA - Defense Advanced Research Projects Agency

DBS - Data Evaluation Subsystem

DFT - Discrete Fourier Transform

DIP - Dual In-line Package

EPROM - Erasable Programmable Read Only Memory

FIFO - First In First Out (Buffer)

10-1
FFT - Fast Fourier Transform

FLL - Frequency-Locked Loop

g - Gravity-induced acceleration (approximately 9.8

GDOP - Geometric Dilution Of Precision

GPS - Global Positioning System

HDIS - High Dynamics Instrumentation Set

HDOP - Horizontal Dilution Of Precision

I - In-phase signal

1C - Integrated Circuit

IF - Intermediate Frequency

I/O - Input/Output

I-Q - In phase - Quadrature signals

IRU - Inertial Reference Unit

JPL - Jet Propulsion Laboratory

JPO - (GPS) Joint Program Office

L1 - L-band frequency (1575.42 MHz)

L2 - L-band frequency (1226.7 MHz)

LDIS - Low Dynamics Instrumentation Set

LPF - Lowpass Filter

MLE - Maximum Likelihood Estimator

MMIC - Monolithic Microwave Integrated Circuit

MSI - Medium Scale Integration

NCO - Numerically Controlled Oscillator

NCU - Navigation and Control Unit

NSC - National Semiconductors Corp.

P-code - Precision'Code (also known as PPS)

10-2
PLL - Phase-Locked Loop

PPS - Precision Positioning Service (P-code)

Q - Quadrature signal

RAJPO - (GPS) Range Applications Joint Program Office

RAM - Random Access Memory

RMS - Root Mean Square

ROM - Read Only Memory

RF - Radio Frequency

s - seconds

SA - Step Acceleration (simulated trajectory)

SNR - Signal to Noise Ratio

SPS - Standard Positioning Service (C/A-code)

SSI - Small Scale Integration

TIS - Test Instrumentation Subsystem

TP - Tracking Processor

TSPI - Time, Space, Position Information

TTFF - Time To First Fix

UERE - User Equivalent Range Error

VDOP - Vertical Dilution Of Precision

VLSI - Very Large Scale Integration

10-3
APPENDIX A

DEMONSTRATION FUNCTIONAL REQUIREMENTS

The functional requirements on the Validation Demonstration were given

in.the Demonstration Plan [2]. This appendix presents the requirements from

the Plan, with subsequent changes indicated by an asterisk in parentheses,

(*). The deviation from the original requirements are summarized in

Section A.4. The functional requirements are presented in terms of

requirements on the Demonstration itself, on the Demonstration System, and

on the Demonstration Tests. Requirements are presented on a functional

level rather than at the design level.

A.1 GENERAL DEMONSTRATION REQUIREMENTS

A.1.1 Location

The Demonstration System will be installed and the Validation

Demonstration conducted at JPL.

A.1.2 System Configuration

The system shall be configured so as to clearly distinguish between

the receiver being tested and the test and control instrumentation.

The functions of each unit shall be identified, and the interfaces

shall be clearly defined. The hardware configuration of the receiver shall

be such as to allow identification of the relationship between areas of the

breadboard receiver and areas of a miniaturized implementation.

A-1
A.1.3 Real Time Displays

Real time displays will be provided during all performance tests

showing, as a minimum, the pseudorange of the simulated input signal and

the pseudorange estimated by the receiver. There is a design goal to

provide a real time comparison of these data if this can be done within

schedule and budget.

A. 1.4 Data Recording

Sufficient data shall be recorded during all tests to enable

statistical post-test analysis to determine performance.

A. 1.5 Data Analysis

Post-test data analysis shall be conducted of all test data sufficient

to determine the receiver performance.

A.1.6 Facilities

No facilities shall be required other than those available in a

typical electronics laboratory at JPL.

A. 1.7 Special Test Equipment

No test equipment shall be required that is not normally available at

JPL or is not identified as part of the Demonstration System.

A. 1.8 Data Processing Facilities

All data processing shall be done on computers which are part of the

Demonstration System, or 'on computers available at JPL. No special data

processing facilities shall be required.

A.1.9 Pre-Demonstration System Testing

The Demonstration System, including both the receiver and the test

instrumentation, shall undergo system tests according to documented test

procedures prior to start of the Validation Demonstration tests.

A.1.10 Test Conduct

All Validation Demonstration tests shall be conducted according to

documented test procedures.

A. 1.11 Documentation

The following documentation of the Demonstration is required:

1. As built engineering drawings,

A-2
2. Software requirements, design, acceptance test and operations

documents in JPL Interoffice Memorandum (IOM) form,

3, System Test Procedures, in JPL IOM form,

U, Validation Demonstration Test Procedures, in JPL IOM form,

and

5, Final Report, as a deliverable document.

A.2 DEMONSTRATION SYSTEM REQUIREMENTS

A.2.1 General Description

The Demonstration System shall consist of the Demonstration Receiver

to be tested, a Test Instrumentation Subsystem (TIS) and a Data Evaluation

Subsystem (DES). The Demonstration Receiver is to be evaluated as to its

capability to measure pseudorange and range rate under conditions

simulating receiver velocities to 3300 m/s (Mach 10) and accelerations to

50 g, and under various noise conditions.

The relative velocity between receiver and satellite is up to

4100 m/s, including the maximum satellite velocity relative to the surface

of the Earth of approximately 800 m/s, so both the receiver and the TIS

must accommodate this velocity. Satellite acceleration is negligible.

The TIS will not generate a signal with an actual P code, but instead

will use a short period pseudorandom sequence clocked at the P code chip

rate. The receiver will process signals with this simplified code and thus

will not be able to track actual GPS satellites. The actual L1 carrier

frequency will be generated, or else a carrier at another frequency but

with phase and frequency variations which would occur at the actual L1

frequency.

Only functions specified in this Plan are required to be demonstrated.

Receiver functions which are not required to be demonstrated include the

low noise front end, acquisition, data bit synchronization, data detection,

tracking of actual satellites, tracking of the C/A code, tracking of the L2

carrier, tracking of multiple satellites and solution for position and

velocity in three dimensions, and external interfaces. These functions are

not necessary to validate the new concept for high dynamic tracking

performance.

A.2.2 Interfaces

Interfaces are separated as to external interfaces, i.e., between the

system and the operator or external instruments, and internal interfaces,

i.e., between subsystems.

A.2.2.1 External Interfaces -

\

External interfaces to the Demonstration System are defined by

A-3
subsystem.

A.2.2.1.1 Receiver External Interfaces -

There are no interfaces from the Demonstration Receiver external to

the system.

A.2.2.1.2 TIS External Interfaces -

The Test Instrumentation Subsystem has the following interfaces

external to the system:

Inputs:

1. Test signal generation control

2. Test signal generation parameters (range versus time, SNR)

3. Receiver initialization and control

4. Frequency reference

5. Clock synchronization and reset

6. Measured SNR (if not automated)

7. Measured clock epoch offset (if not automated, *)

Outputs:

1. Test signal real time display

2. Test signal hard copy (»)

3. Test signal machine readable

H. Receiver output real time display

5. Receiver output hard copy (•)

6. Receiver output machine readable

7. Clock epoch comparison, real time, hard copy and machine

readable (•)

8. Measured SNR, real time, hard copy and machine readable

A-U
A.2.2.1.3 DBS External Interfaces -

The Data Evaluation Subsystem has the following interfaces external to

the system:

Inputs:

1. Control

Outputs:

1. Statistical performance evaluation of test data

A.2.2.2 Internal Interfaces -

Internal interfaces are defined by subsystem pairs.

A.2.2.2.1 Receiver - TIS Interfaces -

TIS to Receiver:

1. Test signal including random noise

2. Carrier frequency reference

3. Clock frequency reference

4. Clock reset signal (*)

5. Initial data bit synchronization (*)

6. Initial estimates of pseudorange and range rate

Receiver to TIS:

1. Estimated pseudorange, smoothed

2. Estimated range rate, smoothed

3. Estimated raw pseudorange

1. Estimated raw range rate

5. Measurement time tag

6. Receiver clock epoch (•)

A.2.2.2.2 Receiver - DBS Interfaces -

There are no interfaces between the Receiver and the Data Evaluation

Subsystem.

A-5
A.2.2.2.3 TIS - DBS Interfaces -

 ;

TIS to DBS:

1. Test signal machine readable

2. Receiver output machine readable

3* Measured SNR, machine readable

4. Measured clock epoch offset, machine readable (*)

DBS to TIS: None

A.2.3 Processing

Processing is defined by subsystem.

A.2.3.1 Receiver Processing -

The receiver accepts clock frequency, clock reset, and Initial data

bit synchronization signals from the TIS, generates all required timing

signals, time tags its output data, and provides an output clock epoch

signal. It accepts initial estimates of pseudorange and range rate, a

signal plus noise input and a carrier reference input from the TIS. It

demodulates the signal against the carrier reference, measures the

pseudorange and range rate each data bit time, smoothes the measured data,

and outputs the smoothed estimates of pseudorange and range rate.

Pseudorange is measured relative to the receiver internal clock, and the

output estimates are time tagged by that clock.

A.2.3.2 Test Instrumentation Subsystem Processing -

The Test Instrumentation Subsystem accepts the listed external inputs

and generates a test signal with the specified simulated pseudorange versus

time history and the specified signal to noise ratio. The test signal

consists of a simulated P code signal, biphase modulated by a pseudorandom

data bit pattern at 50 bps, with this signal modulated onto an actual or

simulated L1 frequency carrier. All components of the generated signal must

have phase variations corresponding to the simulated receiver dynamics. The

SNR of the output signal is measured and this value is output in real time,

in hard copy and in machine readable form, perhaps with operator

assistance. The test signal is output to the Receiver and the parameters of

the signal are output in machine readable form to the DBS and externally,

and selected simulated pseudorange and range rate data are output on a real

time display and in hard copy form.

The TIS generates phase coherent carrier and clock reference signals

and outputs them to the receiver. These signals are at fixed frequencies,

unaffected by the simulated signal. The frequencies of these signals are

controlled by external inputs. The purpose of generating these signals in

the TIS rather than Using a reference internal to the Receiver is so that

A-6
the frequency can be generated relative to the same primary standard as the

test signal, and so that the effects of frequency offsets can be evaluated.

The TIS also generates a clock reset signal and an initial data bit

synchronization signal and outputs these to the Receiver.

The TIS accepts all output data from the Receiver and outputs these in

machine readable form to the DBS and externally, and outputs selected data

on a real time display and in hard copy form. It also accepts the clock

epoch signal from the Receiver, compares this to its own clock epoch, and

outputs the difference, in real time, in hard copy and in machine readable

form, perhaps with operator assistance.

A.2.3.3 Data Analysis Subsystem Processing -

The Data Analysis Subsystem accepts time tagged simulated pseudorange

and range rate, time tagged smoothed and raw receiver estimates of

pseudorange and range rate, signal-to-noise ratio and clock epoch

comparison data from the TIS, performs statistical analyses on these data,

and outputs the results.

A.2.4 Performance Requirements

Performance requirements are defined by subsystem.

A.2.4.1 Receiver Performance -

The pseudorange error shall be less than 2.0 m rms when under constant

velocity of less than 3300 m/s relative to the satellite and with receiver

P code power to noise spectral density ratio of 34 dB-Hz at the input to

the Receiver. (This SNR will be exceeded with an antenna gain of -2 dB and

a receiver noise temperature of 300 K or with and antenna gain of -7 dB and

a receiver noise temperature of 100 K.)

The pseudorange lag error due to receiver dynamics shall be less than

15m with pseudorange profile corresponding to radial acceleration of 50 g

peak and jerk of 50 g/s peak, and under linear acceleration of 50 g. (*}

A.2.4.2 Test Instrumentation Subsystem Performance -

The simulated pseudorange versus time shall be controlled to within 10

m (goal 0.1 m) and known to within 1.0 m (goal 0.1 m). All components of

the simulated signal shall meet this requirement.

The signal-to-noise ratio shall be controlled to within 2 dB (goal 0.5

dB) and measured to within 1 dB (goal 0.5 dB).

The TIS shall not introduce errors in recording of receiver

pseudorange of more than 0.05 m and in range rate of more than 0.01 m/s.

A.2.4.3 Data Analysis Subsystem Performance -

The DBS shall not introduce errors in evaluation of pseudorange

A-7
performance of more than 0.05 m or in evaluation of range rate performance

of more than 0.01 m/s.

A.3 VALIDATION DEMONSTRATION TESTS

The specified validation demonstration tests are intended to test the

receiver under various conditions of dynamics and signal-to-noise ratio

which might be encountered by a receiver on a high dynamic vehicle.

Constant velocity, step acceleration and circular motion are simulated each

at high, medium and low signal-to-noise ratios. High SNR conditions test

instrumentation accuracy and dynamic limits. Medium SNR tests simulate

normal operating conditions. Low SNR tests evaluate the performance

limitations under adverse conditions. The velocities, accelerations and

SNRs specified here are subject to change due to the results of analysis or

earlier tests, or to simulate cases deemed to be of specific interest.

For each test iteration, the initial conditions of the case may be

achieved by any method convenient to the actual mechanization of the

Receiver and the TIS. The test iteration begins after the Receiver has

acquired tracking of the signal input at the specified velocity and SNR.

Signal to noise ratios are specified as the ratio of received P code

power to noise spectral density at the receiver input, in dB-Hz. The

selected SNRs are 60 dB-Hz, 40 dB-Hz and 34 dB-Hz for high, medium, and low

SNR, respectively. The high SNR corresponds to maximum GPS signal strength

and antenna gain, the medium SNR corresponds to the minimum specified GPS

signal, a 0 dB to -1 dB antenna gain, and a 100 K system temperature, and

the low SNR corresponds to minimum signal strength with a -6 dB to -7 dB

antenna gain, which might occur in bad circumstances.

A.3.1 Constant Velocity Tests

A.3.1.1 Objectives -

The objectives of these tests are to determine the performance of the

receiver as a function of signal-to-noise ratio when operating at constant

velocity, and to validate that the receiver achieves a pseuderange accuracy

of better than 2.0 m rms at a SNR of 34 dB-Hz and at velocities of up to

3300 m/s.

A.3.1.2 Test Description -

The receiver will be tested simulating constant velocity motion at 300

m/s, 1000 m/s and 3300 m/s at high, medium and low SNR. At 1000 m/s, data

will be taken at several additional SNRs sufficient to fully characterize

performance. Each test condition shall be simulated for approximately 10

minutes.

A.3.1.3 Anticipated Results -

The anticipated results for the constant velocity tests are shown in

A-8
Figure A-1. The dashed line indicates the calculation error for SNRs above

threshold, and the dots indicate anticipated data. At 3,1 dB-Hz and 10 dBHz, the results should be close to theoretical. At high SNR, the errors

will be greater than theoretical due to instrument accuracy. At very low

SNR, the errors will be lower than the dashed line due to thresholding.

A.3.1.1 Success Criteria -

The constant velocity tests are successful if the rms pseudorange

error is less than 2.0 m at a SNR of 31 dB-Hz at all velocities up to 3300

m/s.

A.3.2 Step Acceleration Tests

A.3.2.1 Objectives -

The objectives of the linear acceleration tests are to evaluate

performance under constant acceleration and at various SNRs, and to

validate that, the receiver will operate under constant acceleration of 50 g

with a pseudorange error due to acceleration of less than 15 m.

A.3.2.2 Test Description -

The receiver will undergo the following test at accelerations of

approximately 3 g, 10 g, 20 g, 30 g and 50 g and at low, medium and high

SNRs. The receiver will be operated simulating constant velocity in one

direction, then step to constant acceleration until reaching the same speed

but the opposite direction, then constant velocity, then constant

acceleration of the same magnitude but opposite sign as the previous

acceleration until the initial velocity is reached. For each chosen

acceleration, the duration of acceleration will be approximately 12 s and

the duration of constant velocity will be approximately 8 s so that each

cycle takes approximately 10 s. Figure A-1 shows the profiles of position,

velocity and acceleration for the 50 g step acceleration case. The velocity

will change from approximately -3000 m/s to +3000 m/s. The cycle will be

repeated approximately 15 times for each test. Additional cases may be

added to determine performance limitations. (*)

A.3.2.3 Anticipated Results

After being at zero acceleration 1 s or more, the range error due to

acceleration will be approximately zero. After a step of acceleration, the

range error will rise to its steady state value of approximately -0.2 m/g,

reaching 90 percent of the steady state value in approximately 0.6 s. When

the acceleration is stepped back to zero, the error will decay towards

zero, again with a 90 percent rise (fall) time of approximately 0.6 s.

There will be no overshoot.

A.3.2.1 Success Criteria -

The step acceleration tests are successful if at a constant

acceleration of 50 g, the rms pseudorange error near the end of the

A-9
intervals of constant acceleration, is less than 15m , 16 m and 17 m for

high, medium and low SNRs, respectively. If loss of lock occurs at low SNR,

the tests are successful if it is determined statistically that the rate of

loss of lock is less than once per 15 cycles of the test trajectory (once

per 360s of 50 g acceleration). (*)

A.3.3 Circular Motion Tests

A.3.3.1 Objectives -

The objectives of these tests are to evaluate the performance of a

receiver in turns at various speeds, radial accelerations and SNRs, and to

validate that the pseudorange error due to acceleration and jerk is less

than 15 m at high SNR and under acceleration of 50 g or jerk of 50 g/s.

A.3.3.2 Test Description -

The receiver will be operated with inputs simulating sinusoidal range

variations at peak accelerations of 10 g, 20 g and 50 g and at high, medium

and low SNRs. The period of the sinusoidal motion shall be such that the

angular velocity is unity and thus the maximum jerk is equal to the maximum

acceleration, in consistent units. Approximately 100 cycles will be made

for each test. Additional cases may be added to determine performance

limitations. («)

A.3.3.3 Anticipated Results -

The range error due to sinusoidal range changes at unity radian

frequency is also sinusoidal at unity radian frequency. The peak range

error is approximately 0.2 m for each g of peak acceleration, and the range

error lags the range input by approximately 15 degrees.

A.3.3.4 Success Criteria -

The tests are successful if for the 50 g acceleration test at high,

medium, and low SNRs, the rms pseudorange error is less than 15 m, 16 m,

and 17 m, respectively, at the phases of maximum error, averaged over 100

or more points. If loss of lock occurs at low SNR, the tests are successful

if it is determined statistically that the rate of loss of lock is less

than once per 100 full sinusoidal cycles at 50 g peak acceleration. (*)

A.4 CHANGES DURING IMPLEMENTATION

When comparing the original functional requirements to the resulting

Demonstration System implementation, it is observed that only minor

deviations occurred. None of these deviations interferred with the

demonstration objectives as stated in the plan. The deviations are in

these areas:

1. Hard copy outputs at the testing site

The test data was stored on magnetic media - first on 8"

A-10
floppy diskettes and then on 9-track magnetic tapes for

processing on a VAX computer. Separate printer outputs were not

created at the TIS.

2. Clock reset

At the beginning of each test, the receiver generated a reset

pulse for the timing circuits in the receiver and the TIS. This

performed clock reset and initial data bit synchronization

functions. This is a change from having an external common reset

signal.

3. Clock epoch comparison

Clock epoch signal, in the form of 50 pps pulses, were available

for observation. The receiver and TIS clocks were compared on a

logic analyzer and the continuous data bit synchronization was

verified. However, clock epoch data was not recorded on the

diskettes.

4. Requirements on pseudorange lag errors

The requirements for the lag errors in pseudorange assume a

second order fading memor y dynamic filter. During the

demonstration, a third order filter with better response was

used. Hence performance was much better than the original

requirements.

5. Test trajectories

Test trajectories were slightly modified. For example, circular

motion tests used radian frequency of 0.785 rather than unity;

this resulted in each cycle being an integer number of seconds.

A-11
10

RESULTS INDEPENDENT OF

VELOCITY, 300 TO 3300 m/s

g 1.0

o

C£

"O.lh ^x, -4

44m ^^

SNRi

.01

20 30 40 50 60

SNR (dB-Hz)

Figure A-l. Anticipated Performance

A-12
APPENDIX B

ANALYSIS AND SIMULATIONS

This appendix presents a summary of the analysis and simulation

performed for the GPS High Dynamic Receiver Validation Demonstration

program.

B.1 RECEIVER CONCEPT

The main new concept described here is in the method of estimating the

pseudorange and range rate of the receiver with respect to the satellites.

This is accomplished in a quasi-open loop, approximately maximum likelihood

(ML) manner rather than by tracking with phase and.delay Locked loops, as

in other receivers. This enhances the ability to maintain tracking under

high receiver dynamics, and naturally leads to an all digital

implementation suitable for miniaturization. A second feature of the

receiver is the use of a high update rate navigation or tracking filter,

which is necessary for high dynamic tracking and which is within the

capability of current microprocessor technology.

B-1
B.1.1 GPS Signal Characteristics

The GPS satellites transmit pseudonoise signals at two L-band

frequencies, denoted L1 and L2. Two different pseudonoise signals are used

on each satellite, a P code signal and a C/A code signal. The P code is a

long period pseudonoise sequence with a chip (clock) rate of 10.23 MHz, and

the C/A code is a period 1023 pseudonoise code clocked at 1.023 MHz. Both

codes are biphase modulated by binary data at 50 bps. The L1 carrier is

phase modulated by both pseudonoise signals, with the C/A code lagging the

P code by 90 degrees. The L2 carrier is modulated by either the P or the

C/A signal, but not both at the same time. The L1 carrier frequency is 154

times the P code chip rate, and the L2 carrier frequency is 120 times the P

code chip rate. All frequencies are phase coherent. On L1, the C/A signal

has twice the power of the P code signal. The carriers are completely

suppressed.

The L1 signal can be expressed as

AD(t)p(t) cos (U]Lt + 4^) + BD(t)c(t) sin (u^t + <|) ) (B.1.1)

where

A = P signal amplitude

B = C/A signal amplitude

D(t) = data signal at 50 bps

p(t) = P code signal

c(t) = C/A code signal

u>l = LI radian carrier frequency

<j>l = constant but random carrier phase.

This signal is filtered before transmission to restrict its bandwidth

to approximately 37 MHz. This effect is neglected in the estimation

process, but is considered as "correlation loss" in B.3-3.2.

B.1.2 Maximum Likelihood Estimation for One Code

A receiver observes a noise-corrupted, attenuated, doppler-shifted

version of the transmitted signal delayed by the propagation delay between

satellite and receiver. The receiver has a different clock than the

satellite, hence by observing the signal from one satellite only it cannot

tell the difference between the clock offset and the signal delay due to

range.

When only the P code signal is present, the received signal r(t) is

r(t) = AD(t-T)p(t-T) cos (u (t-t) +<(>) + n(t) (B.I.2)

B-2
where

A = amplitude of received L1,P signal

T = time delay plus clock offset, proportional to pseudorange

<j> = phase of received LI signal suppressed carrier

n(t) = white Gaussian noise

to = received radian carrier frequency

The transmitter filtering effects are ignored.

Now assume that the signal is observed over a period of time T, such

as one data bit time, during which all parameters A, D,T,U and 4>, are

constant. The parameters of interest for tracking are u> and T , and the

maximum likelihood estimates are the values of Tm and ton which maximize

2

o t

(t - im) e .

 n dt (B.I.3)

The value of D does not affect the magnitude of the complex integral.

The phase of the complex integral can be used to recover the modulation or

to perform phase tracking. The ML method for the P code signal is to

multiply the received signal by all possible delays of the P code, and then

for each of these products to measure the energy at all frequencies. The

values of time delay and frequency for which the energy is a maximum are

the maximum likelihood estimates of these parameters.

B.1.3 Approximate ML Method for One Code

In practice, one can not actually measure the energy at an Infinite

number of lags and at an infinite number of frequencies. But suppose that

the delay and frequency are known to be within some small intervals. It is

then practical with current technology to calculate the products for a set

of discretely spaced lags within the interval of possible time delays, and

for each lag to calculate the energy at a set of discretely spaced

frequencies using a Fast Fourier Transform (FFT). A receiver using this

estimation method is called an approximate maximum likelihood estimator

(AMLE) receiver.

B.1.M Approximate ML Method Versus PLL Tracking

Typical GPS receivers estimate time delay by tracking the P code in a

delay locked loop, using two lags of the code to generate an error signal.

This type of loop may lose lock when the time delay error exceeds

approximately one-half of the lag spacing. If N lags are used in the (AMLE)

method, good delay estimates can be obtained even as the tracking filter

B-3
pseudorange error approaches approximately N/2 lags. This improves the

ability to track when there are large errors due to vehicle dynamics.

In an analogous manner, the AMLE receiver can tolerate errors in

estimating carrier frequency of approximately one half of the frequency

span of the FFT. A phase locked loop implementation is similar to having

only one filter, and thus is much less tolerant to tracking errors due to

vehicle dynamics.

B.1.5 Combined ML Estimation for Both Codes

The L1 carrier is modulated by both the P code and the C/A code, and

the delays of both signals can be independently estimated by the method

presented above. This is not optimum, however, because the time delay,

frequency and phases of the two signals have known relationships. In

particular, the P and C/A signals have the same carrier frequency and the

same delay, and the C/A carrier phase lags the P carrier phase by 90

degrees. The overall maximum likelihood method is to choose the im and u>n

which maximize

J r(t) [p(t-Tm) + /2~c(t-Tm) eJ7r/Z | e " n dt (B.I.4)

The factor of the square root of two arises because the C/A signal

amplitude is that much higher than the P code signal amplitude.

Use of the overall maximum likelihood method would yield significant

protection against tracking failure under very weak signal conditions, and

would yield some improvement in random noise performance under normal SNR

conditions. Good performance depends on having a high enough SNR so that

the lag and the FFT filter which have maximum detected energy are the lag

and frequency closest or next-closest to the correct answers. Very low SNRs

can cause other lags and filters to have maximum energy. Simultaneous

detection of the P and C/A code signals increases the effective SNR by

about 4.8 dB over the P code only SNR, because the C/A code is twice as

strong as the P code. This would improve the threshold performance of the

receiver by almost 4.8 dB. Under normal SNR conditions, there would be only

a small improvement in random noise performance, because due to its wider

bandwidth the time delay estimation performance of the P code would

dominate.

Implementation cost and performance tradeoffs should be made for

a combined maximum likelihood receiver versus a receiver detecting the P

code and the C/A code signals independently.

B-4
B.2 RECEIVER IMPLEMENTATION MODEL

This section presents the mathematical model of the Demonstration

Receiver, based on the actual hardware and software implementation. The

theoretical background for this implementation is given in Appendix B.1, a

description of the software simulation in Appendix B.5, and more detail of

the hardware implementation is presented in Chapter 1.

The receiver model is illustrated in Figure B-1. The main functional

blocks are the predict removal block, AMLE window, predict addition block,

tracking filter, predictor, and bit synchronization tracker. All variables

in the figure are column vectors composed of pseudorange, range rate, and

acceleration. The variables are defined as

^ rji

X = (T,T,T) = simulated inputs

— . •• T

AX = (AT,AT,AT) = differential AMLE inputs

— T

AX = (AT ,AT ,AT ) = differential AMLE outputs

3- a a cl

— • •• T

X = (T ,T ,T ) = unfiltered state estimate

a a a a

— T X,. = (tf,if,if) = filtered state estimate

T

c = (T ,T ,T ) = AMLE predicts

r p p p

The formula s in the following sections are specific to the

Demonstration Receiver and may change in other implementations of the AMLE

concept. Examples of implementation dependent features are the spacing of

pseudorange lags and range rate bins, the method of code dithering, and the

loop delay caused by the pipelined implementation.

B.2.1 Prediction Removal

The prediction removal block, implemented in hardware and software,

centers the AMLE window at the predicted pseudorange and range rate. It

performs three functions: range rate predict removal, pseudorange predict

removal at the center of the bit-time, and stepping of pseudorange each

correlation time to compensate for range rate.

Code stepping is used to adjust the phase of the local code during a

bit time. In the Demonstration Receiver, the local code generator is

clocked at a fixed 20.16 MPPS rate. Since the change in received code

delay may be more than one correlator in one bit time, it is necessary to

adjust the phase of the local code each correlation interval. The

Demonstration Receiver measures the accumulated phase of the local code (or

the accumulated pseudorange) in two parts: the integer number of lags is

maintained in software, while the fractional part is stored in hardware,

B-5
represented by a 7-bit counter. The counter scaling is such that a full

count corresponds to one code lag, or 14.7 m. At the beginning of every

correlation interval the counter is incremented, by a step that is

proportional to the unquantized range rate predict. The counter value is

constant over a data bit time and is given by

= round k (B.2.1)

k = (128-T)(31'L) = 0.0056 counts/(m/s) .(B.2.2)

where

= code step for (n+l)th bit

T = data bit time (0.02 s)

L = distance corresponding to a lag (14.7 m)

Since pseudorange and range rate values are referenced to the data bit

center, the code stepping occurs in locations that are approximately

symmetrical with respect to this center. To accomplish this, the counter

setting at the center of the data bit, i.e., after the sixteenth

correlation interval, is forced to be 63, approximately half the full scale

of the counter. Note that code stepping does not occur until the change in

pseudorange over a bit time becomes approximately one lag. Thus, code

stepping begins to occur at a range rate of roughly 750 m/s, or mach 2.5.

The pseudorange predict at the center of each bit time is quantized to

an integer number of lags. This means that the hardware counter must have

the value 63 at these times. Thus the change in accumulated pseudorange

from the center of one bit time to the center of the next bit time must be

an integer number of lags. This is implemented in three parts: code

stepping over the first bit, code stepping over the second bit, and a phase

shift at the bit transition. The phase shift at the bit transition is

implemented as a one time increment of the code phase counter, given by:

where

= k, t - T - iSD + 16D

 l

 . (B.2.3)

2

D = code phase increment between the n and (n+1) bits

k2 = 128/L ^8.7 counts/m

B-6
To remove the range rate predict, the range rate predict is converted

to frequency and quantized to the nearest 50 Hz, with zero frequency

omitted. The incoming signal is mixed with a complex signal at this

quantized frequency.

B.2.2 AMLE Window

The AMLE window processing consists of three steps. First, every

1/1600 s, correlation values are computed for eleven code lags. Then, every

bit time, an FFT is computed for each lag and the peak FFT power over the

AMLE window is identified. Finally, interpolation formulas are applied to

estimate the location of the AMLE peak relative to the discrete points

where the AMLE is evaluated.

Correlation is performed by multiplying the noisy complex samples by

an unfiltered, shifted version of the code sequence, and summing. For each

lag, 32 complex zeroes are appended to the 32 complex correlation values

over the data bit time, and a 64-point complex FFT is performed. This

results in a 64 by 11 matrix of FFT power values. The matrix spans 1575 Hz

(63 multiplied by 25 Hz) in frequency, and 147 m (14.7 m multiplied by 10)

in pseudorange. The maximum of the discrete AMLE function is defined as the

largest number in the matrix, excluding the first and last lags. Once the

maximum is identified, fine pseudorange and range rate estimates are

obtained using one of the following interpolation formulas.

The interpolation formulas are divided into three categories based on

the assumed shape of the fitted function. The first category assumes that

the three input points, peak AMLE power or amplitude and two adjacent

points, are on an isosceles triangle. The formulas use two of the points to

determine the slope of the triangle's equal sides and the third to locate

the peak. The second group assumes that the points are on a parabola, solve

for the parabola coefficients, and estimate the location of the peak. The

third group uses the measured correlation function and the ratio of the two

points with the highest power (or amplitude) to compute the peak of the

function. Computation is by a second or third order polynomial. The TIS

operator controls the selection of the interpolation formulas. For most

Demonstration tests, the first group was used for delay and the second

group for frequency. After completion of the originally planned tests, it

was found that the third group is superior in bias, as shown in Appendix C.

B.2.3 Predict Addition Block

The predict addition block, implemented in software, adds the delta

pseudorange and range rate computed by the AMLE to the predicts:

T = T + AT

a p a

T = T + AT

a p a

V = T + AT

a p a

B-7
B.2.1 Tracking Filter

The tracking filter, implemented in software, is described in B.4. It

accepts pseudorange and range rate data, after predict addition, and

estimates filtered pseudorange, range rate, and for a third order filter,

acceleration. The tracking filter has the generic form

(B.2.4)

where the matrices A and B depend on the filter parameters.

B.2.5 Predictor

The predictor, implemented in software, generates pseudorange and

range rate predicts which are used to close the feedback loop. The

prediction consists of two steps: compensation for the loop delay, and

quantization of the predicts to discrete values.

As implemented, the forward data path has a delay of three data bit

times, i.e., 60 ms. The delay is caused by the pipelining of the processing

phases. Unquantized predicts, corrected for this delay, are given by

T*+3 = T* + 3TTJ + (9T2/2) tj (B.2.5)

(B.2.6)

T (B.2.7)

The quantized predicts are generated as follows. The pseudorange

predict is quantized to the nearest pseudorange lag, i.e., to the nearest

multiple of 14.7 m. The range rate predict is quantized to the nearest

multiple of 9.5 m/s (50 Hz). If the range rate predict is zero, a 50 Hz

offset is inserted. The following formulas summarize the prediction

quantization.

T = L • round (? /L) (B.2.8)

T = k • round* (7 /k) (B.2.9)

P P

B-8
where

L =* 14.7 m

k ^ 9.5 m/s

round* = "round to nearest non-zero value."

B.2.6 Bit Synchronization Tracker

The bit synchronization tracker updates the bit synchronization

pointer as needed. In the Demonstration Receiver, initial bit synch is

accomplished by initialization from the TIS. During tracking, bit synch is

adjusted, in units of 1/32 of a data bit time, by redefining the first

correlation interval in the data bit. Changes in bit synchronization occur

when the accumulated pseudorange is close to a multiple of 187 km, with an

initial offset of 93.5 km. Hysteresis was provided to avoid rapid switching

when the receiver stays close to a transition point. The change in

pseudorange that is equivalent to a unit change in bit synch can be

computed from

As = c/t ~ 187 km (B.2.10)

lOUU

where

^1600

 = frequency of correlation intervals (1600 Hz)

c = speed of light

As = change in pseudorange

When bit synch changes, additional operations must be performed to

align the correlation buffers over the data bit, and to adjust the

accumulated pseudorange. For example, residual accumulated pseudorange in

the center of the data bit time, as represented by the corresponding 7-bit

counter, must be set to 63*

B.3 SNR ANALYSIS

Performance analyses are presented in support of the performance and

error budget of Chapter 5.

B.3.1 Input Signal to Noise Ratio

The signal to noise ratio of interest for performance analysis is the

ratio of code power to noise spectral density at the output of the receiver

front end, i.e., at the input to the signal processing equipment. This SNR

is determined by the satellite, signal strength at the input to the antenna,

the antenna gain at the proper polarization, and the system noise figure.

The GPS signal strength is specified such that the power at the output of a

B-9
0 dBi antenna with right circular polarization (RCP) is at least -133 dBm

for L1, P code; -130 dBm for L1, C/A code; and -136 dBm for L2, either

code. This is met whenever the satellite elevation is over 5 degrees and

the atmospheric loss is less than 2 dB.

Receiving system noise is specified in terms of either system noise

figure, Fs(dB), or system noise temperature, Tg (Kelvins, K). Noise

temperature is the thermal noise generated in a resistor at temperature Tg.

System noise figure is the noise that the system would add to a resistor at

room temperature, 290 K. Thus

Fg = 10 Iog1() (1 + Tg/290) (B.3.1)

A total system noise figure of 3.5 dB is practical, and is the noise figure

specified for the HDIS procurement [1]. System noise figure includes

amplifier noise and noise added and losses caused by all other components,

such as cables and filters.

The 3«5 dB noise figure corresponds to a system temperature of 359K.

The resulting system noise spectral level is

N = 4k T (B.3.2)

0 s

where k is Boltzmann's constant. This results in

NQ = -173 dBm/Hz (B.3.3)

For antenna gain of G dB, the input SNR is

C/NQ (dB-Hz) = C (dBm)

+ G (dB)

- NQ (dBm/Hz) (B.3.4)

For a 3.5 dB noise figure and minimum specified L1, P-code signal strength,

this is G + 10 dB-Hz.

The HDIS procurement specification requires a loss of lock threshold

of -142 dBm on the weakest satellite, with a 3.5 dB system noise figure.

The -142 dBm signal corresponds to minimum satellite signal strength and a

-9 dBi antenna gain. Thus threshold SNR is specified indirectly: the

receiver must track for all SNRs exceeding 31 dB-Hz, measured at the point

in the system where system noise figure is specified to be 3.5 dB or less.

B.3.2 Theoretical Performance of Approximate ML Estimator

First, the performance of the approximate ML estimator is presented

assuming that the SNR is high enough that the errors in time delay and

frequency estimation are almost always small, i.e., the rms errors are

small compared to the time lag and FFT filter frequency spacings. Low SNR

performance is then presented, using outlier theory. Loss of lock

threshold depends on the tracking filter as well as the AMLE, and is

discussed in section B.3.5.

B-10
B.3.2.1 Pseudorange Estimation at High SNR

Suppose that the range rate or received frequency Is constant and

known. Then the ML method for pseudorange Is to measure the received

energy at all possible code delays, at the appropriate frequency. In the

approximate implementation, only a finite number of code delays can be

used. The pseudorange estimation error can then be calculated as a

function of the spacing between the code lags. There is also an effect due

to sampling and due to bandwidth limiting filtering before sampling. Here,

we ignore the bandwidth limitaion. We assume that there are N samples per

code chip, and that the pre-sampler filter integrates its input over the

time between samples. With these assumptions, it can be shown that the rms

error in pseudorange estimation is

OT = cTc(4NT)~°-5 (C/N0)~°'5 (B.3.5)

where

c = speed of light

N_ = noise spectral density

C = effective code power

T = integration time

T = chip time

N = number of lags per chip time

For N = 2, T = 20 ms and for the P code, this evaluates to

OT = 73.3 (C/NQ)~0'

5

 (B.3.6)

This result does not depend on the phasing between the code lags processed,

or on having the actual delay be constant over the integration interval.

Note that in this approximate calculation, the rms error goes to zero as

the lag spacing goes to zero. This is explained by the assumptions made in

the calculations not being valid as this occurs. For any fixed SNR, the

assumption that the rms delay error is small compared to the lag spacing

breaks down as the lag spacing is decreased.

The result can be compared to a coherent delay locked loop. For

example, it agrees with the result of Spilker [9], with N=1 corresponding

to a 1-Delta delay locked loop and T corresponding to 1/(2BL) where BL is

the bandwidth of the delay locked loop.

B.3.2.2 Pseudorange Rate at High SNR

Pseudorange rate estimates are made by estimating received carrier

frequency. Assuming perfect delay estimation, frequency estimation in the

AMLE is analogous to maximum likelihood reception of Frequency Position

Modulation. This is treated by Wozencraft and Jacobs [10, Chapter 8].

B-11
Transforming the notation of [10] to our notation, equation (8.1 |6a) of the

reference becomes

of = (c/2IIfL1) 6°'5 T'1'

5

 (C/N0 )~0-

5

 . (B.3.7)

where c is the speed of light and fL1 is the carrier frequency. Since this

equation is independent of Tc, it holds for both P and C/A codes. One

factor of T arises because frequency estimation inherently improves as

coherent measurement time increases. The remaining factor of T"" arises

because the signal energy in the measurement time is proportional to T.

For T = 20 ms,

a.. = 26.2 (C/NQ) °'5 (m/s) (B.3.8)

B.3.2.3 Low SNR Effects

At low SNR, nonlinear estimation is often accompanied by threshold

effects that may cause catastrophic deterioration in system performance.

The SNR at which rapid degradation begins to occur is generally referred

to as the threshold. In the AMLE, loss-of-lock typically occurs several dB

below threshold. Thresholding is caused by the appearance of large noise

spikes, which can result in pseudorange and range rate estimates that are

essentially independent of the actual parameters embedded in the received

signal.

The operation of the AMLE below threshold can be explained in terms of

the decision array generated by the FFT. Each element of the array

represents the energy of both signal and noise at a particular frequency

and delay. (In this domain, delay and frequency are proportional to

pseudorange and range rate, respectively.) The total number of coherenceareas, or "degrees of freedom" in the decision array is estimated to be 32

x 5 = 160 (32 independent time-samples derived from each waveform, over a

range of 9 delay-lags corresponding to 5 independent correlation

intervals). A coherence region that contains only noise can be modelled by

a Rayleigh random variable, while the coherence region containing the

signal is Rician. Since the AMLE selects the coordinates of the largest

element, the probability of correct decision, PC, is the probability that

the Rician random variable exceeds each of the 159 Rayleigh random

variables. Detection of a maximal coherence area corresponding to a

Rayleigh random variable is often called an

 n outlier n

. The probability

of choosing an outlier is qx= 1 - Pc. The variation of q with SNR is shown

in Figure B-2.

Conditioned on an outlier occurring,the variance of range and range

rate estimates can be obtained by treating them as continuous uniformly

B-12
distributed random variables over their domains. The conditional variance

in pseudorange estimation becomes (R2)/12, while in range rate it evaluates

to (V2)/12. (Here R = 29.1 x H is the total extent of range, and

V = 9.5 x 32 is the extent of range rate in an AMLE window.) The

estimation variance at any SNR can be represented as a linear combination

of outlier and non-outlier results. Using the high SNR results from B.3.2.1

and B.3.2.2, the following general expressions are obtained :

2

 = q(R2/12) + (1 - q)(cTc)

2

(4NT)"1(C/N()) * (B.3.9)

U-V

\

 2I1£L1 /

(

2

~— ) 6T"3 (C/Ng)'1 (B.3.10)

These expressions do not take into account the various processing

losses encountered in the receiver. The effect of these losses is the same

as a reduction in C/NQ of 1.5 dB, as per B.3.3 and B.3.U.

B.3.3 Processing Losses and SNR Corrections

The AMLE performance can be characterized in terms of the effective

C/NQ at its input. This effective SNR is the SNR at the output of the

receiver front end, including all system noise effects, minus losses in

signal processing. These losses include effects both ahead of and in the

AMLE. The effects are summarized in B.3.3.8 and are discussed individually

in the following paragraphs.

B.3.3.1 Transmitter Filter

The theoretical analyses assumed that the P code signal is not band

limited. The actual transmitted P code signal is bandlimited to 37 MHz, or

± 18.5 MHz about the carrier frequency. The transmitter filter reduces the

signal power by 0.3 dB. Since the specified power, C, is the power in the

37 MHz band, the signal power density within the band is 0.3 dB higher than

if the total power were not band limited. Since the power near the carrier

frequency dominates the solution, there is an effective gain of 0.3 dB ±

0.1 dB.

B.3.3.2 Correlation Loss

After being mixed to baseband, the signal is low pass filtered prior

to A/D conversion. This reduces the peak of the cross-correlation function

between the input signal and the local P code by 0.8 dB. The noise is

also affected, since the correlator noise is the product of the local P

code and the filtered receiver noise. The spectral density of this product

B-13
noise, at zero frequency, is 0.3 dB less than NQ, the receiver noise

density at zero frequency. The net effect is a reduction in effective SNR

by 0.5 dB ±. 0.1 dB.

B.3.3.3 A/D Conversion

The next loss is due to signal quantization. A three-bit analog to

digital converter is used. With optimum signal level, a 3-bit A/D

converter would have a loss of 0.2 dB. We conservatively estimate the

actual loss to be 0.3 dB±.0.1 dB, averaged over the likely range of input

signal levels.

B.3.3.4 Sine Wave Reference Quantization

The next loss is due to 3-level quantization of the reference sine

wave at the input to the digital complex multiplier. This loss is 0.4 dB,

since the total power in the three level signal excee.ds the power in the

fundamental frequency component by this amount. The tolerance is ± 0.1 dB.

B.3.3.5 FFT Filter Passband

There is a loss in SNR when the frequency of the signal at the input

to the FFT is not at the center frequency of one of the FFT filters. The

mechanization uses filters spaced by one-half of the filter bandwidth, with

responses crossing over at the -1 dB points. The maximum loss is 1 dB, and

the average loss is 0.3 dB ± 0.1 dB.

B.3.3.6 Dynamics Effects

There are also losses in SNR due to receiver dynamics. Acceleration

causes the signal bandwidth to expand, because the carrier after code

removal is effectively a chirped sinusoid. Jerk causes the reference

frequency fed back to the AMLE complex multiplier to be in error, which

means that the frequency at the correlator outputs is offset from zero.

This causes signal attenuation because the 1/1600 s correlation time

corresponds to a low pass filter. Each of these effects is approximately

0.3 dB maximum and 0.1 dB average with circular motion of 50 g maximum

acceleration and 50 g/s maximum jerk. Since jerk is the derivative of

acceleration, maximum acceleration occurs when the jerk is zero, and the

two losses are not both high at the same time. We conservatively assume an

average total loss of 0.3 dB±.0.1 dB. (The loss is approximately 1 dB at

maximum acceleration and jerk of 100 g and 100 g/s.)

B.3.3.7 Miscellaneous Losses

There may be miscellaneous losses which have not been accounted for,

and there may be errors in estimating the above losses. In the

Demonstration Plan [2], we assumed miscellaneous losses of 1.5 dB ± 1.5 dB,

and we also carried a correlation loss for transmitted waveform of 1 dB.

As a result of the simulations and demonstration tests, we now believe that

the Plan was overly conservative, and that all significant effects have now

been accounted for. We add an additional tolerance of ± 0.3 dB.

B-14
B.3.3.8 Processing Loss Summary

The total processing losses are summarized in Table B.3-1. The total

loss in effective SNR is 1.5 dB ±. 1.0 dB.

Table B.3-1 Processing Losses Affecting AMLE

Transmitter filter (gain due to definition of C) -0.3 dB ± 0.1 dB

Correlation loss due to bandwidth in receiver 0.5 dB ±. 0.1 dB

Analog to digital conversion, 3-bit 0.3 dB±.0.1 dB

Reference sine wave 3-level quantization 0.4 dB ± 0.1 dB

FFT filter loss, offset from center frequency 0.3 dB±.0.1 dB

Dynamics losses (50 g accel., 50 g/s jerk) 0.3 dB ± 0.2 dB

Miscellaneous 0.0 dB ± 0.3 dB

Total processing losses 1.5 dB ± 1.0 dB

B.3.4 AMLE PERFORMANCE INCLUDING LOSSES

The effect of processing losses on the rms pseudorange error is to

decrease the effective signal to noise ratio in the expression for rms

error. Let Fp be a processing loss factor which multiplies the SNR; this

factor is Fp = 0.708 for the nominal 1.5 dB processing loss. Then the rms

pseudorange estimate error in the high SNR region, including losses, is

0 (AMLE) = cT (4NT)~°'5 (F C/N.)~°*5

T

 ° P ° (B.3.11)

=87.1 (C/N0)-°'5 (m)

The rms pseudorange rate estimate in the high SNR region, including losses,

is

a.(AMLE) = (c/2HfT1) 6°'5 T~1>5 (F C/Nft)~°-5

T LI . p 0 (B.3.12)

=31.1 (C/N0)~°-5 (m/s)

The same loss factor applies in the low SNR region, with appropriate

modifications of equations (B.3.9) and B.3.10).

B-15
B.U TRACKING FILTER

The signal processing channels of the GPS receiver provide raw

estimates of pseudorange and range rate once every data bit time, or 20 ms.

A tracking filter is used to achieve three objectives: first, to derive the

system state from the observables (e.g. estimate platform acceleration),

second, to smooth the random noise effects, and third, to predict

pseudorange and range rate for the purpose of positioning the AMLE window.

In the following discussion, the noise response and the dynamic response of

various filters are presented, an optimal filter is selected for the single

tracking channel demonstration, and different forms of filter

implementation for the final receiver are discussed.

B.4.1 State Model and Filter Formulations

In the demonstration, two types of filters were considered: the fading

memory filter [11], and the Kalman filter [12]. The fading memory filter

weights each measurement by an exponentially decaying weight, based on the

filter time constant. The Kalman filter includes each measurement in the

state estimate, based on the modeled measurement noise and state (process)

noise. The fading memory filter can be expressed as a special case of a

general Kalman filter, by making particular assumptions on measurement and

process, noise [13].

As in many tracking applications, it is assumed that filter gains

reach steady state values. The use of steady state gains reduces the

computational load associated with filter updates and. removes potential

sources of numerical instability. Fading memory filter steady state gains

depend on the weighting matrix and on the filter time constant. Gains for

the second order filter are presented in [11]; similar expressions for a

third order filter were derived during the Demonstration. The Kalman filter

steady state gains depend on the measurement noise and process noise

covariance matrices. Formulas for the steady state gains of a second order

Kalman filter, derived by Ekstrand [12], were used in the Demonstration.

B.U.2 Response to Random Noise

The pseudorange,and range rate measurement noise in the following

discussion are modeled as independent white Gaussian random variables with

zero mean and covariance matrix R, with

(B.4.1)

where

a = standard deviation of pseudorange measurement

<j. = standard deviation of range rate measurement

X

B-16
A convenient way to compute the covariance of state estimate due to

measurement noise is to separately compute the covariance due to

pseudorange noise with standard deviation of 1 m, denoted E1, and due to

range rate noise with standard deviation of 1 m/s, denoted E2. These

matrices can be easily obtained because the tracking filters are

implemented with steady state gains. Then, because the filters are linear,

the covariance of the state estimate, E, is expressed as:

E

 = °x E

l

 + °i E

2 (B.4.2)

Figure B-3 presents the variation of the state estimate covariance

matrix as a function of the parameters of the second order fading memory

filter. The two top plots are the variances of pseudorange and range rate

estimates caused by pseudorange measurement noise with standard deviation

of 1 m, i.e. the (1,1) and the (2,2) elements of Ej. The two bottom plots

are the comparable results for range rate measurement noise, i.e., the

(1,1) and (2,2) elements of E2« Using equation (B.4.2), the response to a

given measurement noise can be computed. Figures B-4 and B-5 present

similar results for the third order fading memory filter and for the second

order Kalman filter. The variables R and S in the figures are defined in

[12]. These variables are related .to the statistics of the process and

measurement noise assumed in the derivation of the Kalman filter, and serve

to define the relevant filter parameters.

In the Demonstration system the standard deviations of pseudorange and

range rate measurements were 1.8 m and 0.6 m/s, respectively, at an SNR of

34 dB-Hz. For a third order filter with time constant of 0.14 s and range

rate weight 0.1, the resulting pseudorange estimate has a standard

deviation of 0.6 m, mostly due to pseudorange measurememt noise. In a

similar way, the range rate estimate standard deviation, 0.4 m/s, is mostly

due to range rate measurement noise.

The results presented in the figures are related to filter bandwidth.

For a single-input single-output filter, the one-sided bandwidth is

(Hz) (B.4.3)

where

o?N = variance of input noise

2

°OUT = variance of output noise

T = time between samples

B-17
The filters discussed so far have two1

 inputs and two or three outputs, thus

the definition of bandwidth is not straightforward. Nevertheless, the (1,1)

element of E1 can be used to obtain the pseudorange bandwidth, and the

(2,2) element of E2 can be used to obtain the range rate bandwidth. For a

third order fading memory filter with a time constant of 0.14 s and range

rate weight of 0.1, these bandwidths are 2 Hz and 16 Hz for pseudorange and

range rate, respectively.

B.4.3 Response to Dynamics

The selection of a tracking filter is driven by two conflicting

requirements: the filter should smooth the noise on the measurement, while

tracking high platform dynamics, without losing lock. In this section we

evaluate the responses of the filters to various dynamic conditions.

The modeled dynamics are divided into three groups. The first includes

trajectories where the pseudorange is a polynomial in time. Examples are

constant velocity and constant acceleration, where the pseudorange is a

second order or third order polynomial in time. The measure of filter

performance is the steady state lag error. The second order tracking

filters have no steady state tracking errors -under constant velocity and

operate with errors proportional to the acceleration when under constant

acceleration. The third order tracking filter has no steady state

pseudorange error when under either constant velocity or constant

accceleration.

A second group of trajectories includes those represented by piecewise

polynomials, with the segments separated by discontinuities in one of the

derivatives. Examples are trajectories with step changes in velocity or

acceleration. The filter response is composed of a transient error that

converges to the steady state error discussed above. The peak of the

transient error and the settling time are both of interest. Figures B-6 and

B-7 show responses of second and third order filters to step acceleration.

The errors due to step dynamics can be treated as a limiting case for

continuously changing dynamics. For example, the peak transient error due

to 100 g/s jerk for 1 s is comparable to that due to a 100 g acceleration

step.

The third group of trajectories are those represented by a sinusoid,

i.e. pseudorange, range rate and acceleration, which are all sinusoids of

the same frequency with appropriately scaled amplitudes and phases. These

trajectories model platform turns. As shown in Figure B-8, because the

filters are linear, tracking errors also have the form of sinusoids.

In the following subsections, variation of filter response as a

function of the filter parameters are evaluated for four trajectories: a

velocity step of 100 m/s, an acceleration step of 100 g, constant

acceleration of 100 g, and circular motion at 50 g with a period of 8 s.

Due to the linearity of the system, results can be extended to other

velocities and accelerations.

B-18
B.4.3.1 Second Order Fading Memory Filter

Results for the second order fading memory filter are presented in

Figures B-9 and B-10. Peak pseudorange transient error caused by a velocity

step increases with filter time constant and with range rate weight. On the

other hand, peak range rate transient error is almost as high as the

velocity step, and does not depend heavily on the filter variables. Peak

pseudorange transient error caused by an acceleration step increases with

filter time constant and with range rate weight. Peak range rate transient

errors increase with the increase in filter time constant, but decreases

with increasing range rate weight.

When under constant acceleration, and T«T, steady state pseudorange

lag error for w=0 is

9

a = T2a (B.4.4)

where

a = acceleration

e = pseudorange error

T = filter time constant

T = sample time

w = range rate weight

a = exp(-T/T>

Peak pseudorange errors for circular motion increase with increasing

filter time constant and with increasing range rate weight. Peak range rate

errors for circular motion increase with increase in filter time constant

and decrease with increase in range rate weight.

B.I.3.2 Third Order Fading Memory Filter -

Results for the third order fading memory filter are presented in

Figures B-11 and B-12.

The peak pseudorange transient error caused by a 100 m/s velocity step

increases with filter time constant and decreases with range rate weight.

For weights of 0.1 and higher, pseudorange error is under 1 m. The peak

range rate transient error is almost as high as the velocity step, and does

not depend heavily on filter variables. Peak pseudorange transient error

caused by an acceleration step increases with filter time constant and

decreases with range rate weight. Again, for weights of 0.1 and higher,

pseudorange error is under 1 m for a 100 g/s step. Peak range rate

transient error increases with increase in the filter time constant, but

decreases with increasing range rate weight.

Peak pseudorange and range rate errors for sinusoidal motion increase

with increasing filter time constant and decrease with increasing range

B-19
rate weight as shown in Figure B-12. Steady state error due to

acceleration is zero for the third order filter.

B.4.3.3 Second Order Kalman Filter

Results for the second order Kalman filter are presented in Figures

B-13 and B-14. These results are similar to those of the second order

fading memory filter.

B.4.4 The Demonstration Tracking Filter

The tracking filter for the Demonstration has to meet several

requirements. Some, such as loss-of-lock conditions and computational

efficiency, are absolute and must be met. Others, such as noise bandwidth

and dynamic response, can be selected using a-priori optimization criteria.

The in-lock condition is that under all specified dynamics, AMLE

detection must occur within the AMLE window. Using conservative safety

margins, we define the maximum tracking errors in pseudorange and range

rate to be 50 m and 80 m/s, respectively, since the AMLE ranges are ± 73 m

and ±.160 m/s. We consider only fixed gain filters, hence the filter

update computation time is a function of only the order of the filter. The

dynamic response criteria is that when under 50 g circular motion or under

50 g step acceleration, the pseudorange error shall not exceed 15m. The

required noise response is not as significant as the dynamic response as

long as the standard deviation of the pseudorange estimate is at most half

of the standard deviation of the pseudorange measurement.

The third order fading memory filter appears superior to the second

order filters. It has better dynamic response, especially in the range rate

estimation, at a cost of minor degradation in noise performance. The longer

computation time of a third order filter can be accommodated. The filter

selected is the third order fading memory filter, with a time constant of

0.14 s and a range rate weight of 0.1.

Peak transient pseudorange and range rate errors due to a 100 g step

acceleration are 0.4 m and 48 m/s, respectively. Peak pseudorange and range

rate errors in a 50 g, 8 s, circular motion trajectory are 0.05 m and 7 m/s

respectively. All of these errors are less than the maximum allowable

dynamic errors.

The noise reduction of this filter depends on the ratio of the

standard deviations of the input pseudorange and range rate measurements.

Figure B-15 shows the noise reduction factors as functions of this ratio.

For the Demonstration system, the pseudorange and range rate noise are

reduced by 3.5 and 1.2, respectively, at SNRs above 32 dB-Hz. These are

different at 32 dB-Hz, because "outliers" cause the ratio of the standard

deviations to change.

B-20
B.I.5 Tracking Filter for a Complete Receiver

There are two methods of tracking filter implementation. The more

powerful method inputs the pseudorange and range rate observed by all the

signal channels into a single tracking filter, and simultaneously solves

for all of the navigation parameters. The second method tracks the dynamics

of the signal from each satellite separately, forming smoothed estimates of

pseudorange, range rate and perhaps acceleration, and then forms a

memoryless flash solution for the navigation parameters, without further

smoothing. This method is not as powerful as the first, but it often has

distinct implementation advantages without significant loss in performance.

Many navigation receivers use a combined method, in which the individual

signals are tracked and smoothed in phase locked loops, and then the loop

outputs are further smoothed in the navigation filter. A special case is

when all channels use the same tracking filter, with fixed steady state

gains, followed by a flash solution for position, velocity, and time. For

this case, the position errors due to random noise are determined by the

measurement standard deviation multiplied by the Geometric Dilution of

Precision (GDOP) factor, while the magnitude of position error due to

unmodeled dynamics is identical to the error of a single channel under the

same dynamics, i.e., with no GDOP factor applied [11].

B.5 SIMULATED DEMONSTRATION SYSTEM

The software simulation program is summarized in the following

subsections.

The main reasons for simulating the GPS High Dynamic Receiver are

to establish independent confirmation of system performance. In the

simulation, the relevant operations performed by the actual Demonstration

System are modeled, taking into account the various degradations and losses

suffered by the signal as it propagates through the system. Once a

reliable correspondance has been established between simulation predictions

and hardware results, additional simulations can be used to verify

potential improvements offered by possible extensions and modifications to

the current system, before incorporating the proposed changes into the

existing hardware.

B.5.2 Simulation Description

The software simulation is based on the following model. During each

T-second bit interval, the received P-code signal can be modeled as a

sinusoidal carrier of frequency fL1 = 1.575 GHz and doppler-shift fd,

modulated by a time-delayed PN sequence of length N = 1023 and chip

duration TC = 0.1 microsecond. The unknown doppler-shift and time delay

(both, in general, slowly varying functions of time) are due to relative

motion between the two ends of the link. The received signal is observed

in the presence of additive thermal noise generated in the receiver's front

end. The receiver structure is based on the "maximum likelihood"

principle, according to which those values of delay and doppler frequency

are selected that maximize the likelihood function defined in B.1.2. The

B-21
implementation is approximate in the sense that decisions are based on a

discrete set of observables over a restricted delay-frequency window,

rather than on a continuum of values over the entire relevant section of

the delay-frequency plane.

In the receiver, in-phase and quadrature components are created by

mixing the received signal with properly phase-shifted local signals of

nominal frequency f^ The I and Q waveforms are filtered and subsequently

multiplied by nine replicas of the unfiltered PN sequence, each shifted in

time by the quantized delay estimate, and further delayed with respect to

one another by integer multiples of a lag. Over the T-second bit time, each

of the resulting waveforms is converted to 32 time-samples by means of

short-time integration over successive T/32 second intervals. The in-phase

and quadrature samples are combined to form complex numbers, and 32

(complex) zeros are appended to each sequence in order to improve frequency

resolution before the FFT is performed.

It is convenient to represent the received waveform as

r(t) = AD(t-T)p(t-T) cos <J> (t) + n (t) cos <f (t) + n (t) sin $ (t)

IT . C L S TL

(B.5.1)

where

= 2ir (fT , + f A t + *

and nQ(t) and ns(t) are independent Gaussian noise processes with identical

spectral densities Sn (f), and identical correlation functions

Rn (T)=(N0 /2)6(T). When the noise processes are integrated for T/32 s, the

mea n and variance of the noise samples become E(n ) =0, and

Var (n) = N0T/64. In the simulation, the magnitude of the complex signal

is set to one. Using this condition, the equivalent noise sample variance

is

V-X2 / VCT/ Y (B'

5

'

2)

(C/NQ)

Therefore, the variance of the noise samples can be determined once

the code power and the noise spectral level are specified. The attenuation

factor Y is required to account for the reduction in the effective noise

spectral level due to the filtering and multiplication operations (the.

reduction in signal level is accounted for in a signal correlation table).

B-22
While the noise samples for a given lag are essentially uncorrelated

random variables, noise samples between adjacent lags are not. This is

because the lag spacing is equivalent to one-half chip. This effect has

been taken into account in the generation of the noise sequences employed

in the software simulation program. .

The rest of the simulation follows closely the processing operations

carried out by the Demonstration Receiver. The sample sequence from each

lag serves as input to a 6^-point FFT, whose output is ultimately arranged

in the form of an 9x64 element array. The coordinates of the element with

the greatest magnitude are declared to be the "rough" estimates of delay

and frequency. Refined estimates are subsequently obtained by means of

three-point triangle interpolation for delay, and three-point parabolic

interpolation for frequency. These refined estimates are then used to

compute the final pseudorange and range rate estimates, and also serve as

input to the tracking filter described in Section BA The filter output

(which includes an acceleration estimate along with the smoothed

pseudorange and range rate estimates) provides the parameters needed to

project pseudorange and range rate estimates ahead by three bit-times. The

projected estimates are quantized, and subtracted from the observed input

trajectory in an attempt to maintain the delay-frequency plane centered at

all times. The projected (quantized) estimates are subsequently added back

into the AMLE output. Therefore, under normal operating conditions, the

projected estimates do not affect the accuracy of the final pseudorange and

range rate estimates generated either at the output of the AMLE or at the

output of the tracking filter.

During high-dynamic maneuvers, the received trajectory may change

significantly over 20 ms (the duration of a bit), possibly causing a

reduction in the detection SNR. Both the Receiver and the simulation

compensate for this effect by using pseudorange and range rate estimates to

determine if the observed delay changes by an entire lag within the bitinterval, and effectively increment the local PN code by a full lag when

this occurs. Significant degradations in detection SNR due to dynamics are

minimized by the use of this incremental compensation technique.

B.5.3 Simulation Operation and Results

The simulation program emulates the GPS high dynamic receiver

demonstration hardware. Upon activation, the program reads a data file

containing tabulated values of the Butterworth filter correlation function

(this correlation function was computed using the transfer-function of an

ideal third order Butterworth filter). Next, the program reads pseudorange,

range rate and acceleration data from an external data file containing the

trajectory parameters. The program then executes the necessary steps to

arrive at pseudorange and range rate estimates based on the available

trajectory information. The length of the simulation and the type of

trajectory are user-controlled items. A typical run may correspond to

simulated circular motion (sinusoidal acceleration, velocity and range

trajectories) of 32-second duration. The simulation output generally

consists of trajectory graphs as a function of time, along with a time

history of paeudorange, range rate and acceleration errors. Such an output

B-23
is shown in Fig. B-16, corresponding to circular motion with 50-g

acceleration and 8-second period, at an input SNR of 31 dB-Hz. The

trajectory error is measured at the output of the tracking filter. Note the

occasional appearence of large error spikes caused by "outliers" (defined

in Section B.3.2.3 )• Under benign dynamic conditions, outliers begin to

occur at approximately 31 dB-Hz, which defines the threshold of the

simulated GPS receiver. Operation a few dB below threshold is generally

feasible, until the SNR becomes so low that outliers begin to dominate the

detection statistics, at which point the receiver tends to lose lock.

B.6 FREQUENCY LOCKED LOOP

This section presents an alternate form of range rate tracking for the

Demonstration Receiver. While Section B.4 discusses a two-input, two- or

three-output filter that estimates pseudorange, range rate and acceleration

simulaneously, the following discussion focuses on tracking only the range

rate. Performance of the resulting frequency locked loop is compared to

that of the phase locked loop.

The AMLE measures the pseudorange (or time delay between the received

signal and a locally generated replica of the signal) and the Doppler

frequency offset between the two signals (which is proportional to range

rate). As seen in Figure B-17, the raw estimates of pseudorange and range

rate are passed through a two-input, two-output estimator-predictor that

provides feedback to the AMLE. The estimator-predictor uses the fact that

range rate is the derivative of pseudorange to improve the overall

performance of the tracking loop.

Another interesting case is illustrated in Figure B-18, where a

separate tracking loop is used to track only the range rate. This form of

range rate (or frequency) tracking has the same structure as the standard

phase locked loop, except that the observable is frequency rather than

phase. For the rest of the discussion, it will be called Frequency Locked

Loop (FLL).

The standard PLL uses a multiply and accumulate (or multiply and

integrate) device as a phase detector, resulting in nonlinear periodic

discriminator characteristics. In some implementations, such as with an

AMLE, both the sine and cosine components are available and the

nonlinearity of the phase detector is avoided. This is called an

"arctangent phase detector." In either case to prevent ambiguities, the

absolute value of the phase error must remain under 0.25 cycles. In

contrast, the FLL discriminator for the Demonstration Receiver is linear

for frequency errors between -800 Hz and 800 Hz and has a period of 1600

Hz. The discriminators are presented in Figure B-19.

To compare the PLL and FLL, we assume that both loops use a single

input fading memory filter (B.4) as an estimator. The computational delay

inherent in implementation is neglected, thus a predictor is not needed. To

make a fair comparison, the PLL uses a third order filter while the FLL a

second order filter. With these assumptions, both filters have finite nonB-24
zero steady state errors, at the discriminator output, when the input

dynamics correspond to phase jerk. The steady state errors are

E(PLL) = jX3 (cycles) (B.6.1)

E(FLL) = JX2 (Hz) (B.6.2)

where

3

j = jerk, in cycles/s

X = aT/(l-a)

a = exp(-T/T)

T = time between samples

T = filter time constant

The input jerk, in m/s3, is obtained by multiplying j by the carrier

wavelength, in m. Note that as the filter time constant increases, the

value of x approaches the filter time constant, thus

E(PLL) a JT3 (cycles) (B.6.3)

E(FLL) « JT

2

 (Hz) (B.6.4)

The one-sided bandwidths of both filters are:

B(PLL) - (^

 (1

 -a)(l + 6a + 16a2 + 24a3 + 19q4) ^ .1^03 (B.6>5)

^

2T/ (1 + a)5

B(FLL) = I-L\

 (1

 -<*)(! + 4a + 5a ) 0-625 (B.6.6)

\v 9T / *} T '• (i + ar T»T

A convenient benchmark for the comparison of PLL to FLL is their lossof-lock conditions due to noise and due to dynamics. The loops have two

distinct modes of losing lock. At one extreme, even at high SNR high

dynamics cause the tracking error to fall outside the range of the

discriminator. At the other extreme, even in the absence of dynamics, the

SNR is so low that loss-of-lock occurs due to the noise. Both modes are

related to loop bandwidth since as the filter bandwidth increases, the lag

errors caused by dynamics decrease and the noise at the loop output

B-25
increases. Let the dynamic performance measure be the maximum phase jerk

before the loop loses lock. The value of the maximum jerk is:

1 -

Figure B-20 presents the maximum jerk in g/s as a function of filter

bandwidth. The maximum allowed tracking errors for the PLL and FLL are

selected to be 0.25 cycles and 800 Hz, respectively. We observe that for

the same filter bandwidth, the PLL loses lock at significantly lower

dynamics than the FLL. Also, the maximum phase jerk is a cubic function of

the bandwidth for the PLL while it is only a quadratic function for the

FLL, when T« T .

The noise performance measure is the input signal to noise spectral

density at which the loop loses lock. If we assume that both loops lose

lock at the same SNR (say SNRQ dB) then the loss-of-lock signal to noise

spectral density can be expressed as

(dB-Hz) (B.6.9)

Alternately, the loss-of-lock C/NQ is proportional to loop bandwidth.

This means that in Figure B-20 the label on the horizontal axis can be

replaced by (C/N0 )ii, with the appropriate change in units. These results

can be only partially extended to compare PLL and FLL tracking in the GPS

receiver. The PLL model does not account for the Costas loop, or for the

actual filters used in such loops. The FLL model does not evaluate the

effects of estimating pseudorange and range rate in separate filters. They

also do not account for the outlier (B.3) effects that occur both in PLLs

and FLLs, and for processing delays. Nevertheless, the basic tradeoff

between maximum phase jerk and minimum signal to noise spectral density is

believed to hold. As an example, Figure 5-2 presents PLL and FLL curves

having 3:1 and 2:1 slopes, respectively. The curves are anchored at known

operating points for GPS receivers: PLL curve uses 10 g/s jerk at 28 dB-Hz

specified for the HDIS receiver, while the FLL curve is defined by the 100

g/s jerk at 28 dB-Hz measured in the Demonstration.

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3
APPENDIX C

DETAILED TEST RESULTS

This appendix describes the High Dynamic GPS Receiver Validation

Demonstration tests in detail. It starts by defining the test conditions

and the statistical significance of the results (C.1 and C.2). Then, for

each category of tests, the rationale, test sequence and results are

presented. The tests are divided into four categories: AMLE evaluation

(C.3), tracking filter evaluation (C.4), tracking under high dynamic

conditions (C.5), and performance at low SNR (C.6).

C.1 TEST CONDITIONS

Each Demonstration test starts with a parameter selection phase,

wherein the operator defines the test environment via a set of parameters.

Each test is controlled in three areas: simulated trajectories, SNR

conditions, and AMLE configuration. This section defines the relevant

parameters and relates them to the test conduct.

C.1.1 Simulated Trajectories

The TIS simulates the Doppler signature associated with a required

trajectory by issuing a sequence of computer controlled frequencies to a

programmabl e frequenc y synthesizer. The synthesizer changes phase

coherently. There are three types of generic trajectories: constant

velocity, step acceleration, and circular motion. Each of the simulated

trajectories consists of five phases, as shown in Figure C-1a:

C-1
1. Initial - During the initial phase, typically 10 s to 15 s, the

simulated range rate is zero. Code acquisition is achieved and

verified and the average pseudorange bias is computed, so it can

be removed from subsequent pseudorange error measurements.

2. Ramp up - For 10 s to 30 s the simulated range rate is linearly

varied from zero to the maximum range rate of the test.

)

3. Test period - During the test period phase, the simulated range

rate is varied according to the specified trajectory, as shown in

Figure C-1b. In a constant velocity trajectory, the simulated

range rate is maintained constant. In a step acceleration

trajectory, the simulated acceleration is stepped between 0, a,

0, and -a, where a is the magnitude of the step acceleration. In

a circular motion trajectory, the simulated range rate has

sinusoidal variation.

4. Ramp down - This phase is the inverse of the ramp up phase. The

simulated range rate is linearly varied from its maximum value to

zero.

5. Final - During the final phase, typically 10 s to 15 s, the

simulated range rate is zero.

Most of the circular motion tests were conducted with a cycle time of

8 s, or radian frequency of 0.78 radians/s. For example, a 50 g circular

motion trajectory with cycle time of 8 s has peak pseudorange, range rate

and acceleration of 810 m, 630 m/s, and 490 m/s2, respectively.

The acceleration intervals in step acceleration tests were 6 s to 12 s

long. As an example, in a 50 g step acceleration trajectory with 6 s

acceleration the range rate changes from -1470 m/s to +1490 m/s (i.e. a

total change of approximately 9 mach numbers) in 6 s.

The operator has control over the following parameters:

1. In all tests - duration of the initial and ramp up phases.

2. In constant velocity tests - test velocity

3. In step acceleration tests - magnitud e and duration of

acceleration, and magnitude and duration of constant velocity.

Any subset of these specifications that completely defines the

trajectory is acceptable.

4. In circular motion tests - cycle time, peak pseudorange, range

rate, and acceleration. Again, any subset of these specifications

that completely defines the trajectory is acceptable.

C-2
C.1.2 SNR Conditions

Most tests were conducted at three SNR levels - high (60 dB-Hz),

medium UO dB-Hz) and low (3t dB-Hz). High SNR tests examine the signal

dynamic range and the performance of the instrumentation. Medium SNR tests

simulate operation with minimum nominal signal level, a 3.5 dB noise figure

front end, and a 0 dBi antenna. Low SNR is the condition that occurs when a

-6 dBi antenna is used, which is likely to happen in missile applications.

In addition, tests were performed at SNRs lower than 31 dB-Hz to examine

the receiver performance at very low SNRs and to determine the minimum SNR

for reliable tracking.

The operator controlled the SNR by changing the fixed and variable

attenuators in the signal path (see chapter 4). The measured values (signal

power, noise power, and fixed attenuator) were entered in the TIS computer.

The computer used these and the values of noise bandwidth and predetermined SNR calibration to compute the SNR.

C.1.3 AMLE Configuration

The AMLE configuration is determined by two controls: feedback to the

AMLE window and selection of interpolation formulas. During normal

tracking, there is feedback to center the window on the predicted

pseuddrange and range rate. For some of the tests this feedback is

disabled, so the AMLE function can be evaluated over the complete window.

After identifying the pseudorange and range rate that maximize the

AMLE function over a discrete set of points, interpolation formulas are

used to estimate the location of the AMLE peak. The operator can select

among several different formulas both for the pseudorange and the range

rate. Detailed descriptions of the formulas appear in Appendix B.

C.2 STATISTICAL SIGNIFICANCE

The main objective of the Data Evaluation Subsystem (DBS) is to

provide statistical evaluation of receiver performance. Specifically, the

DES computes the sample mean and sample standard deviation for a finite

sample set, and uses these as approximations to the mean and standard

deviation of the corresponding random variables. This section discusses the

processing steps and the quality of the approximation. It shows that for

typical tests, two to ten minutes, the rms pseudorange and range rate noise

were within 0.1 m and 0.1 m/s, repectively, of the standard deviation of

the corresponding random variable, with probability 95 percent.

The DES computes three error measures for each of the pseudorange,

range rate and acceleration variables: AMLE noise, total tracking error,

and filtered noise. The AMLE noise is the variable at the output of the

AMLE minus the same variable for the simulated trajectory. At low SNR, AMLE

noise is dominated by (random) thermal effects, justifying the term

"noise". The total tracking error is the variable at the output of the

C-3
tracking filter minus the same variable for the simulated trajectory. For a

specific test, the total tracking error is affected by the random input, or

AMLE noise, and by the deterministic lag introduced by the tracking filter.

The third error measure, filtered noise, is generated when the lag

introduced by the tracking filter is subtracted from the total tracking

error.

Neither the AMLE noise, nor the filtered noise, are Gaussian

variables. They contain instrumentation effects, biases and other nonrandom components. Still, for SNRs above 32 dB-Hz, both are approximated by

Gaussian noise, and the AMLE noise samples are approximately independent.

At lower SNRs, outliers (see B.3) occur, changing the statistical

characteristics of these variables.

The statistical significance results presented in the remainder of

this section are accurate only when the Gaussian noise approximation is

valid. This is generally true for the AMLE noise and the filtered noise at

SNR above 32 dB-Hz. Specifically excluded are the total tracking errors.

The generic term "noise" refers both to AMLE noise and filtered noise.

In DES data processing, the non-zero sample mean of pseudorange noise

is interpreted as clock bias between transmitter and receiver, and is

removed. This is done because the Demonstration system can not separate the

clock offset from the simulated pseudorange. The sample mean of the range

rate noise was usually under 0.05 m/s, which is close to the modelled zero

mean of the random variable.

The sample means and standard deviations are used as estimates of the

means and standard variations of the corresponding random variables. The

quality of the approximations can be represented by confidence intervals.

For example, a 95 percent confidence interval for the mean of the random

variable is the interval, centered at the sample mean, that includes the

sample mean with probability 95 percent. Size of the confidence intervals

depends on three quantities: the number of independent data points, the

sample mean and the sample variance.

Data were recorded at the rate of ten points per second, each point

representing 0.02 s. The data before the filter are statistically

independent from point to point. The data after the filter are

approximately independent as long as the filter time constant is longer

than the 0.1 s sample spacing, which is the case for the selected third

order fading memory filter with a time constant of 0.14 s. Thus, the number

of independent data points can be computed by multiplying the test duration

in seconds by 10, the number of samples per second. Typical tests lasted

two to ten minutes, resulting in 1200 to 6000 points.

Given sample mean, sample standard deviation, and confidence level,

the confidence interval for the mean of the random variable is:

{M-b, M+b} (C-1)

C-U
where:

b = zS/(N-1)°'5

M = sample mean

S = sample standard deviation

N = number of data points

z = 1.96 for 95$ confidence level

2.58 for 99$ confidence level

3.30 for 99.9$ confidence level

As an example, let the pseudorange sample set contain 6000 points, the

sample standard deviation be 1 m, and the confidence level be 95 percent.

Then the mean of the random variable is within 0.025 m of the sample mean,

with probability 95 percent. A similar result applies to range rate data.

This example is typical of the Demonstration tests, where at SNRs higher

that 32 dB-Hz, the sample standard deviation (or sample rms) were less than

1 EM and 1 m/s, for pseudorange and range rate, respectively.

The confidence interval for the standard deviation of the random

variable is:

{aS, bS} (C-2)

where:

a = (1/(1+d))J-5

b = (1/(1-d))°-5

d = z(2/N)°'5

z = 1.96 for 95$ confidence level

2.58 for 99$ confidence level

3.30 for 99.9$ confidence level

For the previous example, The standard deviation of the random

variable is between 0.98 and 1.02 of the sample standard deviation, with

probability 95 percent.

C.3 APPROXIMATE MAXIMUM LIKELIHOOD ESTIMATION EVALUATION

Approximate Maximum Likelihood Estimation (AMLE) is performed in three

steps. First, discrete correlation data are collected over a bit time, and

converted, by FFT, to the frequency domain. The result is a 64 by 11 window

of FFT energy values. Then the peak energy over the AMLE window is

identified, providing rough estimates of pseudorange and range rate.

Finally, interpolation formulas are applied to the discrete AMLE values,

generating finer estimates of the pseudorange and range rate. The AMLE

evaluation tests measure the shape of the discrete AMLE function, evaluate

various interpolation formulas, and assess the effect of NCO setting and

input SNR on the AMLE pseudorange error.

C-5
The rms pseudorange and range rate errors caused by the originally

selected AMLE interpolation formulas are 0.5 m and 0.1 m/s, respectively.

Better formulas, introduced after the end of the formal tests, reduced the

rms errors to less than 0.1 m and 0.1 m/s, respectively.

C.3.1 Measurement of Discrete AMLE Function

The discrete AMLE function was measured in six tests, all conducted

under high SNR conditions:

1. SCH100 - In this test the simulated pseudorange was varied at 0.5

m/s for 500 seconds. The AMLE was restricted to maximize over

frequency only, for lag 6, the center lag. The maximum amplitude

over the AMLE window was recorded. Neglecting the effects of

maximizing over frequency, this results in the cross correlation

function between the simulated signal and the local code. Figure

C-2a shows the maximum AMLE amplitude (in internal units) as a

function of the simulated pseudorange. The resulting shape

resembles the triangular autocorrelation function of PN

sequences. The deviation of this waveform from triangular is

caused primarily by the receiver lowpass filter. The "random"

variation is caused primarily by instrumentation effects.

2. SCH101 - This test is similar to SCH100, except that the

maximization is not restricted to lag 6. Figure C-2b shows that

the maximum amplitude as a function of pseudorange is the

envelope of nine overlapped correlation functions, separated by

one half P code chip (i.e. one correlator lag). For pseudorange

within the nine lag window, the maximum amplitude does not fall

below 0.75 of the maximum amplitude when the codes are aligned

(-2.5 dB). This means that there is at most 2.5 dB variation in

detectability of the correct lag, as a function of pseudorange,

modulo the pseudorange spacing. The width of the window is nine

lags, rather than eleven, since the first and last lags are

excluded from the maximization, and are used only for

interpolation.

3. SCH102 - In this test the simulated pseudorange was constant,

while the NCO frequency was swept at 0.01 Hz/bit (0.5 Hz/s). The

sweep lasted 500 s with NCO frequencies between -125 Hz and +125

Hz. The test simulated fixed pseudorange with changing Doppler.

The AMLE was restricted to maximize over the zero frequency bin.

Figure C-3a shows the maximum AMLE amplitude (in internal units)

as a function of the NCO setting. The resulting shape is of the

sin(x)/x variety, with first nulls at 50 Hz, agreeing with the

shape of the FFT filter. The dispersion of the results at zero

NCO frequency is attributed to instrumentation effects. During

the tests, the feedback to the NCO was always quantized to a

multiple of 50 Hz, excluding zero, thus eliminating the

dispersion.

C-6
4. SCH104 - This test is similar to SCH102, except that the

maximization was restricted to frequency bin 1. Figure C-3b shows

that the resulting response has a similar shape to that of C-3a,

shifted by 25 Hz. Again the dispersion of results at zero NCO

frequency is apparent.

5. SCH105 - This test is similar to SCH102, except that the

maximization was not restricted. Figure C-3c shows that the the

maximum amplitude is the envelope of sin(x)/x type curves with

nulls at 50 Hz and spacing of 25 Hz. The minimum amplitude, at

the intersection of filters is 0.9 of the peak amplitude

(-0.9 dB). Thus detectability varies at most 0.9 dB with

frequency, and the average amplitude is 0.3 dB relative to the

peak. This figure was used in the processing loss budget.

6. SCH103 - This test is similar to SCH105, except the sweep covers

the range of -800 Hz to +800 Hz. Figure C-3d shows the maximum

AMLE amplitude as a function of the NCO setting. The resulting

shape is the envelope of 64 of the filters shown in C-3a,

separated by 25 Hz. The peaks of the waveform are on a sin(x)/x

shape with nulls at 1600 Hz. This is caused by the lowpass

filtering by integration over the correlation time, 1/1600 s. The

amplitude at 800 Hz is 0.6 of the peak at 0 Hz. This agrees with

the theoretical degradation of 2H =0.63 (-4 dB).

C.3.2 Effect of Code Adjustment

As shown in Appendix B, the clocking of the local P code generator

must be adjusted each correlation interval to maintain the alignment of the

local code and the predicted incoming code, to within one lag. The effect

of this adjustment was demonstrated by two tests. In the first, the

adjustment mechanism was active, while in the second it was deactivated.

The tests show that in the absence of code adjustment, there is a

significant reduction in signal level at the AMLE output, at high dynamics.

1. 841218T1 - This test measured the effect of range rate on the

amplitude of the AMLE, with normal receiver configuration. The

TIS simulated a 1 g acceleration from 0 m/s to 5000 m/s. Figure

C-4a shows maximum AMLE amplitude vs. simulated range rate,

showing no degradation due to range rate.

2. 841218T2 - This test is similar to 841218T1, except that the

range rate adjustment was disabled. Figure C-4b shows that as the

range rate increases, the signal at the AMLE output decreases,

(i.e. the SNR decreases). Comparison between this test and the

previous one illustrates the significance of code adjustment.

C-7
C.3.3 Evaluation of Original Interpolation Formulas

The estimation of the peak of the continuous AMLE is performed by

interpolating between points of the discrete AMLE. The procedure has three

steps: first, the point with the highest AMLE amplitude is identified, then

two adjacent points in frequency and two adjacent points in pseudorange are

selected, and last, interpolation formulas are applied for pseudorange and

range rate. Originally, four interpolation formulas were evaluated. The

formulas are:

a. Triangular fit to the AMLE power output

b. Triangular fit to the AMLE amplitude output

c. Parabolic fit to the AMLE power output

d. Parabolic fit to the AMLE amplitude output

The formulas are described in Appendix B. To evaluate the formulas,

tests were conducted at high SNR and under low dynamics. In all these tests

the feedback that repositions the AMLE window was disabled. To evaluate the

range rate interpolation formulas, the range rate error was computed as a

function of the simulated range rate, where the simulated range rate is

modulo a range rate bin (approximately 4.75 m/s), then the rros range rate

error was computed. The rms errors for the four interpolation formulas are

shown in Table C-1. Formula (d), parabolic interpolation of amplitude, has

the lowest error, 0.1 m/s, and was chosen. The range rate error vs. range

data is shown in Figure C-5a.

Table C-1 - Range rate Interpolation Formulas Evaluation

case

a

b

c

d

METHOD

triangular

triangular

parabolic

parabolic

INPUT

power

amplitude

power

amplitude

RMS

(m/s)

0.102

0.201

0.236

0.106

FOURIER COEFF

(m/s)

0.110

0.279

0.270

0.100

C-8
The evaluation of pseudorange interpolation formulas was performed in

a similar way. The pseudorange error was computed as a function of the

simulated pseudorange, where the simulated pseudorange is modulo a

pseudorange bin (approximately 14.7 m). The rms pseudorange errors for the

four formulas are presented in Table C-2. Formula (b), triangular

interpolation on amplitude, has the lowest error, 0.5 m, and was chosen.

Pseudorange error vs. pseudorange is presented in Figure C-5b.

Table C-2 - Pseudorange Interpolation Formulas Evaluation

case

a

b

c

d

METHOD

triangular

triangular

parabolic

parabolic

INPUT

power

amplitude

power

.

amplitude

RMS

(m)

0.865

0.512

1.529

0.984

FOURIER COEFF

(m)

0.128

0.073

0.418

0.223

C.3.4 Evaluation of Upgraded Interpolation Formulas

After the end of the formal demonstration, new interpolation formulas

were Introduced, both for pseudorange and range rate. The formulas,

described in Appendix B, are based on fits to the empirical shape of the

AMLE function. Figure C-6 presents the pseudorange and range rate errors.

Unlike the performance of the previous interpolation formulas, the upgraded

formulas introduce very little bias in the Interpolation process. The rms

biases are under 0.1 m and 0.1 m/s in pseudorange and range rate,

repectively.

C.3.5 AMLE Pseudorange Bias Versus SNR and NCO

Since the AMLE operation is nonlinear, the performance of the AMLE at

medium and low SNR may be different than at high SNR. In a similar way, the

NCO setting may affect the AMLE errors. A series of tests measured the AMLE

pseudorange errors at low, medium and high SNR, and at various NCO

settings. The tests showed that rms errors caused by the AMLE processing,

i.e., after averaging of random noise, are independent of SNR and NCO

setting.

C-9
C.4 TRACKING FILTER EVALUATION

The pseudorange and range rate estimates generated by the AMLE are

processed by a tracking filter. The filter has three objectives: to reduce

the measurement noise, to estimate the receiver state (e.g., pseudorange,

range rate, and acceleration), and to provide pseudorange and range rate

predicts to the AMLE window. The tracking filters considered for the

Demonstration Receiver are formulated and analyzed in Appendix B.4. This

section describes the experimental results of filter evaluation tests.

Three classes of tracking filters were evaluated: second order fading

memory filters, third order fading memory filters, and second order Kalman

filters. In each class, 12 to 15 filters with different parameter

combinations were tested. The common test bed was a 50 g step acceleration

test, with peak range rate of 1470 m/s. The filters were compared in terms

of noise response, steady state tracking error, and transient errors.

All test results agreed with theory. This is significant because it

indicates that there were no significant unmodelled error sources. As a

result of these tests, a third order fading memory filter with time

constant of 0.14 s and range rate weight of 0.1 was selected for the rest

of the demonstration tests.

The following sections describe the filter evaluation tests in detail.

C.4.1 Second Order Fading Memory Filter

The second order fading memory filter operates on the raw pseudorange

and range rate estimates and produces smooth estimates of the same

variables. For a fixed update rate, it is defined by two parameters: filter

time constant and range rate weight. Fifteen combinations of time constant

and weight were selected, and the tests were repeated at high and low SNR,

for a total of 30 tests.

Figure C-7 shows typical pseudorange and range rate errors as

functions of time. This particular example is for a filter with a time

constant of 0.14 s and range rate weight of 0.01. In general, the second

order fading memory filter has zero pseudorange and range rate errors when

the simulated range rate is constant, but generates lag errors in both

variables when under constant acceleration. The lag errors are proportional

to the acceleration. No transient overshoot errors are caused by the step

acceleration. The fast variation of pseudorange error is caused by the

original pseudorange interpolation formula.

Figure C-8 shows the coordinates of the AMLE maximum amplitude for the

same test. The frequency detection occurs in bins -20 to +20. When compared

to the total AMLE window width of 64 bins, this represents over 60$ of the

window width. This indicates that if the dynamics are increased from 50 g

to 80 g, detection will occur on the window edge, and regardless of the

random noise the receiver will lose lock. The pseudorange detection occurs

mostly in bin 6 and rarely in bins 5 and 7. When compared to a total window

C-10
width of 11 bins, the pseudorange detection raises less concern about loss

of lock than the frequency (or range rate) detection.

Figure C-9 presents the lag errors due to dynamics as functions of

filter parameters, for high and low SNR. The errors appear independent of

the SNR level. The pseudorange error increases with increase in filter time

constant and with increase in range rate weight. In fact, for time constant

of 0.14 s, only filters with range rate weight of under 0.02 meet the 10 m

maximum error required by the Plan. The range rate error increases with

increase in filter time constant, but has a minimum value when the range

rate weight is between 0.02 and 0.1. Still, with a filter time constant of

0.14 s, the minimal range rate error is 60 m/s and, as seen in Figure C-8,

the AMLE is close to loss of lock. The poor range rate performance when

under constant acceleration is the main reason this filter was not selected

for the rest of the Demonstration.

Figure C-10 summarizes the rms noise at the filter input and output,

under low SNR conditions. The noise before and after the filter was defined

in C.2 as the AMLE noise and the filtered noise. The rms noise at the input

of the tracking filter is independent of the filter parameters, and is

approximately 1.8 m and 0.6 m/s for pseudorange and range rate,

respectively. The filter reduces the pseudorange rms noise to 0.5 m to

0.8 m, depending on the filter parameters. The improvement increases as

filter time constant and range rate weight are increased. The effect of the

filter on range rate is similar to the effect on pseudorange, except that

it is more sensitive to change in range rate weight. In fact, at range rate

weight of under 0.05, the range rate noise at the filter output is higher

than that at the input.

Similar results were obtained at high SNR. The main difference from

low SNR cases is that there is a smaller improvement in the pseudorange rms

noise. This is because at high SNR the pseudorange noise is dominated by

AMLE bias and not by random noise.

In summary, the second order fading memory filter, though providing

adequate noise response and pseudorange response when under 50 g dynamics,

is rejected because of high range rate error when under high dynamics.

C.4.2 Third Order Fading Memory Filter

The third order fading memory filter operates on the raw pseudorange

and range rate estimates and produces smooth estimates of pseudorange,

range rate and acceleration. For a fixed update rate, it depends on two

parameters: filter time constant and range rate weight. Twelve combinations

of these parameters were selected, and the tests were repeated at high and

low SNR, for a total of 24 tests.

As shown in B.4, the third order fading memory filter has zero

pseudorange and range rate error when the acceleration is constant. It has

pseudorange and range rate errors proportional to jerk, when under constant

jerk. In the case of step acceleration trajectory, the only lag errors are

expected during the transient following the acceleration step. Figure C-11

C-11
presents typical pseudorange and range rate errors as functions of time,

derived for a filter with a time constant of 0.14 s and range rate weight

of 0.01. The transient pseudorange error is less than 0.2 m and cannot be

separated from the ambient noise. The transient range rate error appears as

a step error that decays within one or two filter time constants.

Figure C-12 presents the coordinates of the AMLE maximum amplitude for

the same test. Unlike the second order filter results, the frequency

detection deviates from the vicinity of the zero bin only during the short

transient. For filters with identical time constant and range rate weight,

the peak frequency deviation for third order filter is 14 bins, which is

significantly smaller than that of the second order filter, 20 bins. The

smaller deviation indicates that the third order filter can track higher

dynamics, without loss of lock, than the second order filter. The

pseudorange detection for the third order filter is in bins 5 to 7,

similar to the second order filter.

Figure C-13 presents the peak transient errors caused by the step

acceleration as functions of SNR and filter parameters. The pseudorange

transient error cannot be reliably separated from the ambient noise. The

peak transient range rate error increases with increasing filter time

constant and with decreasing range rate weight.

The effect of the tracking filter on the AMLE pseudorange and range

rate noise is shown in Figure C-14, for the low SNR case. Performance of

the third order filter is similar to that of the second order filter.

Again, when the range rate weight is less than 0.05, the rms range rate

noise at the output of the tracking filter is higher than that at the

input. Results are similar for high SNRs, except that the pseudorange noise

reduction by the filter is smaller than for the low SNR case. This is

because the noise is dominated by the AMLE bias and instrumentation effects

rather than by random effects.

In summary, the third order fading memory filter exhibits many desired

features, both in noise performance and dynamic performance. The filter

selected for the rest of the demonstation is a third order filter with

filter time constant of 0.14 s and range rate weight of 0.1. At 34 dB-Hz,

it reduces the pseudorange and range rate rms errors by 3.5 and 1.2,

respectively. In a 50 g step acceleration test, the peak transient errors

are 0.2 m and 24 m/s, respectively.

C.4.3 Second Order Kalman Filter

The second order Kalman filter operates on the raw pseudorange and

range rate estimates, producing smooth estimates of the same variables. It

depends on three variables: standard deviation of pseudorange input,

standard deviation of range rate input, and standard deviation of receiver

acceleration* Details of filter formulation and a model for process noise

are given in B.4. After normalizing the standard deviation of the

pseudorange measurement to 1 m, the filter can be defined in terms of two

variables: standard deviation of range rate (SIGV) and standard deviation

of acceleration (SIGA). Twelve combinations of SIGV and SIGA were selected,

C-12
and tests were repeated at high and low SNR, for a total of 24 tests.

Results are similar to those of the second order fading memory filter

except that for the Kalman filter it is easier to adjust the filter

parameters to obtain lower range rate error. Figure C-15 shows an example

of results from a test using a Kalman filter with SIGV=10 and SIGA=6000.

The pseudorange and range rate errors are proportional to the acceleration,

i.e. no errors at constant velocity. For this particular selection of

parameters, there is almost no range rate error. Figure C-16 presents the

locations of the AMLE maximum amplitude during the test, revealing peak

frequency deviations of ± 1 bins.

Figure C-17 present the errors induced by acceleration as functions of

filter parameters and SNR level. As seen, the SNR level has no effect on

the errors.

Figure C-18 summarizes the rms noise before and after the tracking

filter. The rms range rate noise is not decreased by the filtering, and for

some parameter combinations it even increases. The rms pseudorange noise is

decreased by the filter, with the amount of decrease depending on the

filter parameters. Similar results were obtained at high SNR.

In summary, the second order Kalman filter offers similar performance

to that of the second order fading memory filter. When selecting a Kalman

filter, the range rate error can be reduced, at a cost of increased rms

noise at the output of the tracking filter. The superior range rate

performance of the Kalman filter makes it a candidate for tracking at very

high dynamics, e.g., accelerations in excess of 100 g; however, the

corresponding pseudorange error may not be acceptable.

C.5 TRACKING UNDER HIGH DYNAMIC CONDITIONS

The tests described in this section evaluate the Demonstration

Receiver performance under various dynamics. Three types of generic

trajectories are considered: constant velocity, step acceleration and

circular motion. Performance is characterized for low, medium, and high

SNR. The third order fading memory filter, selected in the previous

section, is used for all the tests.

The total tracking errors consist of two components: a dynamic

component, caused by the tracking filter lag error, and a static component,

caused by random noise and instrumentation effects. The static effects

include some indirect dynamic-dependent components. To separate the two

components, the filtered noise, or the noise at the output of the tracking

filter, is defined as the total tracking error minus the theoretical

dynamic lag, where the theoretical dynamic lag is the error when passing

the input trajectory through the receiver tracking filter.

As shown in Figure 6-9, the total pseudorange tracking error is very

close to the filtered pseudorange noise even for dynamics as high as 50 g,

40 g/s, circular motion. This is true because the theoretical pseudorange

C-13
lag error for this case is 0.04 m rms. This approximation cannot be used

directly when the dynamic component is not small relative to the static

component.

C.5.1 Constant Velocity Tests

The constant velocity tests measured the receiver performance at

velocities up to 10,000 m/s. The following tests were conducted:

1. CVHnn - These were five tests, 160 s each, with constant range

rate between 0.1 m/s and 10000 m/s, at high SNR.

2. CVMnn - These tests were similar to CVHnn, except at medium SNR.

3. CVLnn - These tests were similar to CVHnn, except at low SNR.

In these tests, the total tracking errors and the filtered noise

errors are the same, because the dynamic components of the pseudorange and

range rate errors are zero. Tables C-3» C-4, and C-5 summarize the rms

noise levels at the tracking filter input and output.

Figure 6-3 shows rms noise at the input and output of the tracking

filter. As the simulated range rate increases, there is slight increase in

rms noise caused by higher instrumentation errors. At very low velocities,

the rms errors increase because of AMLE bias introduced by the original

AMLE interpolation formulas. This effect disappears when using the upgraded

interpolation formulas.

Table C-3, - Constant Velocity Evaluation, High SNR

TEST

ID

CVH01

CVH02

CVH03

CVH11

CVH12

VELCTY

(m/s)

300.0

1000.0

3300.0

0.1

10000.0

RMS NOISE t RMS NOISE I

BEFORE FILTER ! AFTER FILTER !

RANGE

(m)

0.421

0.454

0.431

0.513

0.676

|

VELCTY! RANGE

(m/s) I (m)

0.062

0.071

0.116

0.049

0.185

0.044

0.063

0.082

0.484

0.146

VELCTY I

(m/s) !

0.050

0.057

0.064

0.114

0.101

C-14
Table C-4 - Constant Velocity Evaluation, Medium SNR

TEST

ID

CVM01

CVM02

CVM03

CVM11

CVM12

VELCTY

(m/s)

300.0

1000.0

3300.0

0.1

10000.0

RMS NOISE ! RMS NOISE

BEFORE FILTER ! AFTER FILTER

RANGE

(m)

0.923

0.950

1.000

0.916

1.144

VELCTY! RANGE

(m/s) I (m)

0.235

0.327

0.122

0.260

0.462

0.229

0.256

0.285

0.610

0.318

VELCTY

(m/s)

0.211

0.235

0.260

0.210

0.336

Table C-5 - Constant Velocity Evaluation, Low SNR

TEST

ID

CVL01

CVL02

CVL03

CVL11

CVL12

VELCTY

(m/s)

300.0

1000.0

3300.0

0.1

10000.0

RMS NOISE ! RMS NOISE !

BEFORE FILTER ! AFTER FILTER !

RANGE

(m)

1.739

1.856

1.845

1.735

2.128

VELCTY! RANGE

(m/s) ! (m)

0.496

0.691

0.794

0.506

1.206

0.480

0.527

0.567

0.807

0.642

VELCTY!

(m/s) !

0.416

0.484

0.525

0.420

0.652

C-15
C.5.2 Step Acceleration Tests

The step acceleration tests measured performance with step

accelerations of up to 100 g. The tests consisted of:

1. SAHnn - These were seven tests, 240 s each, with accelerations

between 3 g and 100 g, at high SNR. The acceleration lasted for

6 s.

2. SAMnn - These tests were similar to SAHnn, except at medium SNR.

3. SALnn - These tests were similar to SAHnn, except at low SNR.

Tables C-6, C-7» and C-8 list transient tracking errors and rms noise

at the inputs and outputs of the tracking filter.

Figure 6-5 shows the transient tracking errors. The transient

pseudorange error could not reliably be separated from the ambient noise.

The theoretical peak pseudorange error for 50 g step acceleration

trajectory is 0.2 m. The transient range rate error is proportional to the

acceleration and is approximately 50 m/s at 100 g, well within the tracking

capabilities of the system.

Figure 6-U shows rms noise at the inputs and outputs of the tracking

filter. These errors are independent of the acceleration. There is better

noise reduction at low SNR, where random errors dominate, than at high SNR,

where instrumentation effects dominate.

C-16
Table C-6 - Step-Acceleration Evaluation, High SNR

TEST

ID

SAH01

SAH02

SAH03

SAH04

SAH05

' SAH11

SAH12

! TRANSIENT DURING

I ACCELERATION

ACCEL

(g)

3.0

10.0

20.0

30.0

50.0

100.0

75.0

RANGE

(m)

(1)

(1)

(1)

(1)

(1)

(1)

(1)

VELCTY

(m/s)

1.6

4.5

10.0

14.0

25.0

•

48.0

35.0

RMS NOISE ! RMS NOISE !

BEFORE FILTER ! AFTER FILTER !

RANGE

(m)

0.1*59

0.138

0.449

0.480

0.489

0.486

0.447

VELCTY! RANGE

(m/s) ! (m)

0.145

0.109

0.139

0.147

0.180

0.249

0.203

0.167

0.135

0.199

0.201

0.375

0.319

0.338

"

VELCTY I

(m/s) !

0.178

0.108

0.127

0.120

0.177

0.218

0.185

(1) Transient pseudorange error is low, and cannot be separated from the

random noise reliably.

C-17
Table C-7 - Step-Acceleration Evaluation, Medium SNR

TEST

ID

SAM01

SAM02

SAM03

SAM04

SAM05

SAM11

SAM12

! TRANSIENT DURING! RMS NOISE I RMS NOISE !

! ACCELERATION ! BEFORE FILTER ! AFTER FILTER !

ACCEL

(g)

3.0

10.0

20.0

30.0

50.0

100.0

75.0

RANGE

(m)

(1)

(1)

(1)

(1)

(1)

(1)

(1)

VELCTY

(m/s)

1.8

5.0

10.0

15.0

.

25.0

47.0

36.0

RANGE

(m)

1.031

0.983

0.962

1.010

1.005

1.041

1.007

VELCTY! RANGE

(m/s) ! (m)

0.355

0.312

0.356

0.393

0.338

0.454

0.395

0.318

0.279

0.312

0.321

0.460

0.399

0.407

VELCTY!

(m/s) !

0.296

0.240

0.255

0.275

0.269

0.330

0.299

(1) Transient pseudorange error is low, and cannot be separated from

the random noise reliably.

C-18
Table C-8 - Step-Acceleration Evaluation, Low SNR

TEST

ID.

SAL01

SAL02

SAL03

SAL04

SAL05

SAL11

SAL12

! TRANSIENT DURING! RMS NOISE ! RMS NOISE !

! ACCELERATION ! BEFORE FILTER ! AFTER FILTER !

ACCEL

(g)

3.0

10.0

20.0

30.0

50.0

100.0

75.0

RANGE

(m)

(1)

(1)

(1)

(1)

(1)

(1)

CD

VELCTY

(m/s)

2.0

5.5

.

10.0

15.0

24.0

50.0

38.0

•

RANGE

(m)

1.676

1.581

1.602

1.697

1.652

1.761

.

1.654

• _

VELCTY! RANGE

(m/s) ! (m)

0.579

0.521

0.592

0.666

0.578

0.769

0.669

0.448

0.433

0.456

0.508

0.563

0.560

0.573

VELCTY!

(m/s) !

0.452

0.389

0.405

0.461

0.452

0.546

0.520

(1) Transient pseudorange error is low, and cannot be separated from

the random noise reliably.

C.5.3 Circular Motion Tests

Circular motion tests measured the tracking performance for a

simulated circular motion trajectory with acceleration up to 150 g and jerk

up to 157 g/s. The circular motion tests consist of the following:

1. CMHnn - These were five tests, each containing twenty loops of 8

s each, for a total of 160 s, with accelerations between 10 g and

100 g, at high SNR.

2. CMMnn - These tests were similar to CMHnn, except at medium SNR.

3. CMLnn - These tests were similar to CMHnn, except at low SNR.

Tables C-9, C-10, and C-11 summarize rms tracking errors and rms noise

at the inputs and outputs of the tracking filter.

Figure 6-7 shows the rms tracking errors. The rms pseudorange error is

less than 0.6 m, it varies with the SNR, and it is almost independent of

acceleration. The rms range rate error is proportional to the acceleration

and is less than 11 m/s at 100 g. As shown in Figure 6-2, the range rate

C-19
error is sinusoidal and thus has a peak of 1.4 times the rms value.

Figure 6-6 shows the rms noise at the inputs and outputs of the

tracking filter. The increase in noise level at higher accelerations is

caused by higher instrumentation effects. Note that filtered noise is under

0.5 m and 0.8 m/s rms for pseudorange and range rate, respectively.

In addition, tests were performed using a cycle time of 6 s and

accelerations of 100 g and 150 g. The corresponding jerks are 104 g/s and

157 g/s, respectively. Figures C-19 and C-20 show the tracking errors and

the location of the AMLE maximum amplitude for the 150 g test.

Table C-9 - Circular Motion Evaluation, High SNR

TEST

ID

CMH01

CMH02

CMH03

CMH11

CMH12

ACCEL

(g)

10.0

20.0

50.0

100.0

75.0

RMS LAG ERROR

RANGE

(m)

0.2

0.1

0.1

0.2

0.2

VELCTY

(m/s)

1.1

2.2

5.4

10.7

8.0

RMS NOISE ! RMS NOISE !

BEFORE FILTER ! AFTER FILTER !

RANGE

(m)

0.476

0.462

0.445

0.475

0.505

VELCTY! RANGE

(m/s) ! (m)

0.109

0.119

0.200

0.298

0.251

0.234

0.141

0.157

0.144

0.199

'

VELCTY 1

(m/s) !

0.143

0.124

0.161

0.225

0.210

C-20
Table C-10 - Circular Motion Evaluation, Medium SNR

TEST

ID

CMM01

CMM02

CMM03

CMM11

CMM12

ACCEL

(g)

10.0

20.0

50.0

100.0

75.0

RMS LAG ERROR

RANGE

(m)

0.3

0.3

0.3

0.3

0.3

VELCTY

(m/s)

1.1

2.1

5.3

10.7

8.0

RMS NOISE ! RMS NOISE !

BEFORE FILTER ! AFTER FILTER !

RANGE

(m)

0.969

0.983

1.035

1.080

1.057

VELCTY! RANGE

(m/s) ! (m)

0.319

0.329

0.374

0.470

0.441

0.306

0.294

0.300

0.320

0.305

VELCTY!

(m/s) !

0.273

0.252

0.297

0.330

0.298

Table C-11 -.Circular Motion Evaluation, Low SNR

TEST

ID

CML01

CML02

CML03

CML11

CML12

I RMS LAG ERROR

!

ACCEL ! RANGE

(g) ! (m)

10.0

20.0

50.0

100.0

75.0

0.5

0.4

0.4

0.5

0.5

VELCTY

(m/s)

1.1

2.1

5.3

10.7

8.C

RMS NOISE ! RMS NOISE !

BEFORE FILTER I AFTER FILTER !

RANGE

(m)

1.590

1.593

1.693

1.859

1.802

VELCTY I RANGE

(m/s) ! (m)

0.653

0.594

0.635

0.760

0.701

0.471

0.446

0.486

0.519

0.537

VELCTY I

(m/s) !

0.434

0.426

0.454

0.528

0.505

C-21
C.6 PERFORMANCE AT LOW SNR

The purpose of these tests, also denoted "extended SNR tests", was to

determine the minimum SNR at which tracking is possible, and to evaluate

the rms pseudorange and range rate errors as a function of SNR. The tests

determined that the receiver can reliably track at SNRs down to 28 dB-Hz,

almost independent of dynamics.

Three tests were conducted at each SNR:

1. 3 g, 8 s, circular motion.

2. 50 g, 8 s, circular motion.

3. 100 g, 8 s, circular motion

In all the tests, the third order fading memory filter selected for

the Demonstration was used. The tests continued with lower SNR, in steps of

1 dB, as long as one minute of tracking without loss of lock was achieved.

Tables C-12 and C-13 summarize the rms pseudorange and range rate

noise at the inputs and outputs of the tracking filter.

Figure 6-8 shows the rms pseudorange noise at the output of the

tracking filter, for the different dynamics, demonstrating that the noise

performance and the loss of lock SNR are Independent of dynamics.

C-22
Table C-12 - Extended SNR, Circular Motion, 8 s, 50 g

! TEST

! ID

!

IXES101

I

IXES103

1

IXES105

IXES107

i

i

IXES109

i

i

IXES113

JXES115

J

IXES117

!

IXES119

I

JXES121

!XES123

IXES125

IXES127

SNR

(dB-Hz)

60.1

50.1

40.1

34.1

32.4

38.0

33'. 3

31.3

30.3

29.9

28.8

27.9

27.9

RMS NOISE ! RMS NOISE ! TOTAL RMS ERROR!

BEFORE FILTER ! AFTER -FILTER ! !

RANGE

(m)

0.39

0.50

1.03

1.70

2.37

1.31

2.36

3.13

4.00

6.23

8.06

12.55

12.70

VELCTY! RANGE

(m/s) 1 (m)

0.15

0.19

0.36

0.62

0.88

0.45

0.78

6.60

10.30

15.09

22.37

36.60

35.07

0.15

0.17

0.32

0.56

0.74

0.39

0.67

1.07

1.80

2.48

4.14

6.84

6.73

VELCTY! RANGE

(m/s) I (m)

0.13

0.16

0.28

0.50

0.67

0.35

0.73

2.42

5.32

6.99

12.03

24.03

20.82

0.13

0.16

0.31

0.56

0.87

0.38

0.67

1.07

1.80

2.48

4.12

6.84

6.72

VELCTY!

(m/s) !

5.39

5.40

5.40

5.43

5.52

5.41

5.47

5.95

7.59

8.90

13.77

25.56

22.56

C-23
Table C-13 - Extended SNR, Circular Motion, 8 s, 3 g

! TEST

! ID

1

!

1XES102

!

IXES104

!

IXES106

!

1XES108

IXES110

!XES114

!XES116

!

1XES118

I

IXES120

IXES122

I

IXES124

1

1XES126

IXES128

I

SNR

(dB-Hz)

60.1

50.1

40.1

34.1

32.4

38.0

33.3

31.3

30.3

29.9

28.8

27.9

27.9

RMS NOISE I RMS NOISE ! TOTAL RMS ERROR!

BEFORE FILTER ! AFTER FILTER ! I

RANGE

(m)

0.17

0.34

1.01

1.93

2.38

1.17

2.23

2.60

3.93

5.17

7.08

11.61

11.35

VELCTY! RANGE

(m/s) ! (m)

0.16

0.18

0.34

0.62

0.80

0.43

1.92

0.89

8.26

12.58

19.83

30.88

29.40

0.07

0.11

0.29

0.59

0.72

0.34

0.68

0.85

1.47

2.26

3.28

5.68

5.58

VELCTY! RANGE

(m/s) ! (m)

0.13

0.15

0.28

0.51

0.65

0.33

0.91

1.10

2.93

5.96

9.86

16.52

16.60

0.07

0.11

0.29

0.59

0.72

0.34

0.68

0.85

1.47

2.26

3.28

5.68

5.58

VELCTY!

(m/s) !

0.27

0.29

0.37

0.56

0.69

0.41

0.93

1.13

2.90

5.96

9.86

16.52

16.60

C-24
TEST

PERIOD

TIME

RAMP-DOWNl FINAL

(a). The Five Phases of a Typical Test

LLJ

o

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CONSTANT VELOCITY STEP ACCELERATION CIRCULAR MOTION

Figure C-1. Simulated Trajectories

C-25
100 150 200

SIMULATED PSEUDORANGE (m)

(a) MEASURED CROSS CORRELATION FUNCTION

250

100 150 200

SIMULATED PSEUDORANGE '(m)

(b) MEASURED AMLE FUNCTION VS. PSEUDORANGE

250

Figure C-2. AMLE Response Versus Pseudorange

C-26
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6000

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VELOCITY (m/s)

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Figure C-4. AMLE Amplitude Versus Velocity

C-28
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