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NASA-CR-178043

19860013103

NASACONTRACTORREPORT178043

2

A PRELIMINARYDESIGNFORFLIGHTTESTINGTHE t.

FINDSALGORITHM .,

A, K, CAGLAYAN AND P,M GODIWALA

CHARLES RIVER ANALYTICS INc,

CAMBRIDGE, MA 02138

[i,._"i_. _ u''_:_'._,,"

.mFI\ t____) _-"-,.,_

LANGLEYRF_SF.ARL]H CE?ITER

CONTRACT NAS1-17719 LI2RARY,NASA

L,......' V!R3',;;'.A

MARCH1986 ...-.....-T,,.,,

; NASA

NationalAeronautics and

SpaceAdministration

LangleyResearchCenter

Hampton,Virginia23665

TABLE OF CONTENTS

Page

i. INTRODUCTION ........................................ 1

2. ESTIMATION PERFORMANCE .............................. 5

2.1 Emulation Review ............................... 5

2.2 Improved Estimation Performance ................ 7

2.3 Estimation Performance with Piecewise Constant

Gains .......................................... 24

3. FAILORE DETECTION PERFORMANCE ....................... 40

3.1 Failure Detectability Analysis ................. 40

3.2 Baseline Failure Detection and Isolation

Performance .................................... 54

3.3 New Detection Strategy ......................... 58

3.4 Detection Performance with Piecewise Constant

Gains .......................................... 66

4. CONCLOSIONS AND RECOMMENDATIONS ..................... 73

REFERENCES .......................................... 79

i

LIST OF TABLES

Table 2.1: Empiricalstatisticsfor sensor flight data

channeldifferences 6

Table 2.2: Design values for no-failfilter noise

parameters 8

Table 2.3: No-fail filter residualsstatistics:nominal

update frequencyof 20 Hz 23

Table 2.4: No-fail filter residualsstatistics:gain

update frequencyof 4 Hz 34

Table 2.5: No-fail filter residualsstatistics:gain

update frequency of 2 Hz 34

Table 2.6: No-fail filter residualsstatistics:gain

update frequencyof 1 Hz 38

Table 3.1: Design values for measurementsensor noise

parameters used by the detectors 56

Table 3.2: Baseline bias failure detection performance

summary 57

Table 3.3: No-fail filter residuals and likelihood ratio

statistics for moving windows of 1 and i0

samples: nominal run 61

Table 3.4a: Bias failure detection summary with new

detection test 63

Table 3.4b: Bias failure detection summary with old

detection test 65

Table 3.5: Effect of piecewise constant gains on detection

time with failures injected at 82.10 s 68

Table 3.6: Effect of piecewise constant gains on detection

time with failures injected at 145.40 s 69

Table 3.7: Effect of piecewise constant gains on detection

time with failures injected at 238.70 s 70

iii

LIST OF FIGURES

Figure 2.1: Estimated aircraft ground track and altitude

profile i0

Figure 2.2: Horizontal velocity estimate time histories ii

Figure 2.3: Vertical velocity profile and roll attitude

estimate 12

Figure 2.4: Pitch and yaw attitude estimates 13

Figure 2.5: Horizontal wind estimates and aircraft

latitude vs. longitude track 15

Figure 2.6: Longitudinal and lateral accelerometer bias

estimates 16

Figure 2.7: Vertical accelerometer and roll rate gyro

bias estimates 17

Figure 2.8: Pitch and yaw rate gyro bias estimates 18

Figure 2.9: No-fail filter residuals for MLS azimuth

and elevation 19

Figure 2.10: No-fail filter residuals for MLS range

and IAS 20

Figure 2.11: No-fail filter residuals for IMU roll

and pitch 21

Figure 2.12: No-fail filter residuals for IMU yaw 22

Figure 2.13: Longitudinal position and pitch attitude

estimation error with 4 Hz gain update

frequency 26

Figure 2.14: Longitudinal and lateral accelerometer bias

estimates with 4 Hz gain update frequency 27

Figure 2.15: Vertical accelerometer and roll rate gyro bias

estimates with 4 Hz gain update frequency 28

Figure 2.16: Pitch and yaw rate gyro bias estimates with

4 Hz gain update frequency 29

Figure 2.17: Longitudinal and lateral accelerometer bias

estimates with 2 Hz gain update frequency 31

v
Figure 2.18: Vertical accelerometer and roll rate gyro bias

estimates with 2 Hz gain update frequency 32

Figure 2.19: Pitch and yaw rate gyro bias estimates with

2 Hz gain update frequency 33

Figure 2.20: Longitudinal and lateral accelerometer bias

estimates with 1 Hz update rate 35

Figure 2.21: Vertical accelerometer and roll rate gyro

bias estimates: 1 Hz update rate 36

Figure 2.22: Pitch and yaw rate gyro bias estimates:

1 Hz update rate 37

Figure 3.1a,b: Incremental information behavior for

longitudinal accelerometer during initial

flight segments 44

Figure 3.1c,d: Incremental information behavior for

longitudinal accelerometer during aircraft

maneuver and final descent 45

Figure 3.2a,b: Incremental information behavior for lateral

accelerometer during initial flight segments 46

Figure 3.2c,d: Incremental information behavior for lateral

accelerometer during aircraft maneuver and

final descent 47

Figure 3.3a,b: Incremental information behavior for vertical

accelerometer during initial flight segments 48

Figure 3.3c,d: Incremental information behavior for vertical

accelerometer during aircraft maneuver and

final descent 49

Figure 3.4: Incremental information behavior for roll

and pitch rate gyros in aircraft maneuver

flight segment 50

Figure 3.5: Incremental information behavior for yaw

rate gyro in aircraft maneuver flight segment 51

Figure 3.6: Incremental information behavior for MLS

azimuth and range in aircraft maneuver

flight segment 52

Figure 3.7: Incremental information behavior for IAS and

IMU roll attitude in aircraft maneuver flight

segment 53

vi
i. INTRODUCTION

This supplemental Final Report presents the progress made

in NASA Contract NASI-17719, entitled "Evaluation of Fault

Tolerant Concepts", over the results reported in [i]-[2]. The

main objective of the effort in this phase has been to reduce the

program size of the FINDS (Fault Inferring Nonlinear Detection

System) algorithm [6], and to increase its execution speed

without compromising on the aircraft state and sensor bias

estimation performance or failure detection/isolation performance

presented in [i]-[2]. The modified algorithm has been tested

using about five minutes of sensor flight data for the NASA ATOPS

B-737 aircraft in a Microwave Landing System (MLS) environment.

This report summarizes the modifications made to the

FINDS algorithm in order to achieve the objectives of the current

study. In summary, these modifications have resulted in a

considerably smaller program size accommodating government flight

computer constraints, and a faster execution speed allowing near

real-time operation. In addition, the changes resulted in a

significant improvement in the estimation and failure detection

performance results reported in [i]-[2].

The target flight computer selected for this study has a

dual configuration with each side having 128 Kb of memory. The

compiler selected for the target flight computer conforms to ANSI

FORTRAN 66 standards and also has a significant number of

extensions allowing real-time use. This target flight computer

has approximately a 255,000 Whetstones [4] floating point

performance in 32 bit single precision. At the start of this

study, the size of the FINDS program, implemented in FORTRAN 77

- 1 -
using double precision, was 340 Kb. On the host development

computer, having approximately 300,000 Whetstones floating point

performance in 32 bit single precision [5], the FINDS algorithm

ran 30 times slower than real-time with detectors off, and 120

times slower than real-time with detectors on.

Hence, the FINDS program had to be scaled down in size to

be ported onto the government flight computer. In addition, the

algorithm execution speed had to be significantly increased to

allow real-time operation. In this study, the following was

accomplished:

Reduction In Program Size:

Starting from a program size of 340 Kb in double

Precision FORTRAN 77, an equivalent single precision FORTRAN 66

program of size 116 Kb was developed, and ported onto the target

flight computer. This was accomplished by:

(a) eliminating the interactive input/output routines in the

code,

(b) converting the program from a double precision

implementation to single precision,

(c) reducing program variable dimensions to handle dual sensor

redundancy instead of triple redundancy,

(d) incorporating all sensor failure simulation routines into

an external preprocessor program, and

(e) deleting the radar altimeter from the sensor suite.

Increase In Execution Speed:

Starting from a FINDS program with an execution speed of

30/120 times slower than real-time (with detectors off/on) on the

host development computer, we have obtained an equivalent program

- 2 -
with an execution speed of 1.4 times slower than real-time on the

same machine. This was accomplished by:

(a) converting the code into single precision,

(b) replacing general purpose matrix computations with

specialized routines,

(c) using a constant state transition matrix in the system

model instead of a time-varying one,

(d) implementing piece-wise constant gains in the no-fail

filter, and

(e) replacing the FINDS multiple hypothesis test allowing

simultaneous detection and isolation with a sequential

detection and isolation test.

Improved Estimation Performance:

Through the course of this study, we have changed the

sensor noise design parameters used in the no-fail filter to

reflect a more cohesive use of the entire sensor complement in

the estimation process. In addition, we have modified the steady

state wind model used in the no-fail filter design. These

changes resulted in a better bias and aircraft state estimation

error performance, thus resulting in a better behaved (less time

correlated and closer to zero-mean) no-fail filter residuals

sequence.

Improved Detection Performance:

In this study, we have also significantly improved the

FINDS algorithm detection performance reported in [i]. The FDI

algorithm can now detect sensor failures, injected into the

flight data, considerably faster and without any false alarms.

False alarm performance improvement is due to the better

- 3 -
estimation performance. Based on a sensor failure detectability

analysis, detection speed was improved by replacing the multiple

hypothesis test (over a fixed window of expanded no-fail filter

residuals) implemented in FINDS with a set of mean detection

tests over various moving windows of the averaged no-fail filter

residuals. Low level MLS, IMU and IAS sensor failures are

detected instantaneously with the new detection strategy, while

accelerometer and rate gyro failures are detected within the

minimum time allowed by the information generated in the sensor

residuals based on the aircraft point mass equations of motion.

The discussion of the above modifications is organized in

this report as follows:

Chapter 2 presents the state and bias estimation

performance results of the no-fail filter along with an overview

of the flight data driven emulation. The detectability analysis,

FINDS false alarm and failure detection/isolation performance,

and initial results of the new detection strategy are presented

in Chapter 3. Chapter 4 contains a series of proposed

experiments for the modified FINDS algorithm on government flight

computers. Concluding remarks and further recommendations end

this chapter.

- 4 -
2. ESTIMATION PERFORMANCE

In this chapter, we discuss the various changes made to

the no-fail filter in the FINDS algorithm in order to improve

estimation error performance. In the first section, we present a

brief overview of the flight data driven emulation, and the

modifications made to the flight data interface with respect to

the sensor failure injection modules. This is followed by a

discussion of the sensor noise statistics utilized by the no-fail

filter. In the next section, estimation error performance is

analyzed by examining the aircraft state estimates and body

mounted sensor bias estimates. This section ends with a

discussion of the statistics of the no-fail filter residual

sequence which forms the inputs to the detection and isolation

algorithm analyzed in the next chapter. In the last section, we

discuss the effects of using piecewise constant no-fail filter

gains on the estimation error and execution speed.

2.1 Emulation Review

As discussed in [i], the flight recorded sensor data

contained a usable third channel only for the rate gyros. Hence,

a dual redundant sensor complement has been used throughout this

study. A second channel has been simulated for the MLS

measurements since only a single channel of azimuth, elevation

and range measurements was available from the flight data. As

mentioned in the introduction chapter, the radar altimeter

measurements have also been deleted from the sensor complement.

Thus the current version of the emulation goes to 266-267 seconds

- 5 -
when the aircraft reaches radar altimeter height, at which point

the FINDS program execution is halted.

A sensor difference signal error analysis, similar to the

one performed in [i], now gives us a new set of empirical

statistics for the sensor flight data up to 266 seconds. These

empirical statistics which determine the sensor noise parameters

are given in Table 2.1. The mean values of these difference

signals clearly indicate the presence of sensor biases,

especially for the longitudinal accelerometer and rate gyros. It

should also be noted that the whiteness test performed on these

sensor flight data channel differences does not show any major

deviations from the results shown in Table 2.2 in [i].

Table 2.1: Empirical statistics for sensor flight data

channel differences

SENSOR MEAN STD.DEV. MAX MIN UNITS

Acc.-Long. -1.99E-01 +4.37E-02 -3.81E-02 -3.85E-01 m/s/s

Acc.-Lat. +7.92E-02 +5.01E-02 +2.73E-01 -I.15E-01 m/s/s

Acc.-Vert. +6.51E-02 +I.17E-01 +5.12E-01 -3.57E-01 m/s/s

Gyro-Roll -2.66E-01 +4.47E-02 -1.03E-01 -4.44E-01 deg/s

Gyro-Pitch -2.12E-01 +4.66E-02 -3.44E-02 -3.90E-01 deg/s

Gyro-Yaw +I.07E-01 +3.11E-02 +1.82E-01 -6.09E-03 deg/s

IAS +8.96E-01 +2.28E-01 +2.05E+00 -3.03E-01 m/s

IMU-Roll +6.88E-02 +1.06E-01 +3.37E-01 -2.37E-01 deg

IMU-Pitch -1.32E-01 +2.27E-01 +3.01E-01 -5.98E-01 deg

IMU-Yaw -4.54E-03 +8.54E-02 +6.57E-01 -7.11E-01 deg

- 6 -
Finally, the sensor failure injection modules in the

emulation have now been incorporated into an external flight data

preprocessor routine to simulate failed sensor data. In addition

to reducing the program size by about 30 Kb, this change also

preserves the input functionality of the failure injection

routines. Thus, the FINDS algorithm can still be tested with the

same simulated failures as in [i].

2.2 Improved Estimation Performance

In this study, the no-fail filter performance has been

evaluated by the behavior of the no-fail residual sequence; an

approximately zero mean and white sequence under no failures

imPlies satisfactory state and bias estimates. However, as

explained in section 3.2 of [i], the 'best' estimation

performance does not necessarily result in the 'best' failure

detection performance since the filter makes less use of noisier

sensors, thus reducing the associated failure signatures on the

residuals. Hence, the design values for the no-fail filter noise

parameters have been chosen so as to not only reflect the

empirical statistics presented in Table 2.1, but also to ensure

that the filter makes adequate use of all sensors in generating

the aircraft state estimates. Table 2.2 shows these design

values for the no-fail filter process noise (associated with

input sensors and wind dynamics) and measurement sensor noise

variances. All of the results presented in this report have been

obtained by using these parameters.

- 7 -
Table 2.2: Design Values for no-fail filter noise parameters

VARIABLE NOISE S.D. REPLICATIONS UNITS

PROCESS NOISES:

Acc.-Long. 5.00E-02 1 m/s/s

Acc.-Lat. 5.00E-02 1 m/s/s

Acc.-Vert. 5.00E-02 1 m/s/s

Gyro-Roll 5.00E-02 1 deg/s

Gyro-Pitch 5.00E-02 1 deg/s

Gyro-Yaw 5.00E-02 1 deg/s

X-Wind-rw 1.00E-01 N/A m/s

Y-Wind-rw 1.00E-01 N/A m/s

MEASUREMENT NOISES:

MLS-Azim. 6.00E-02 1 deg

MLS-Elev. 6.00E-02 1 deg

MLS-Range 6.00E+00 1 m

IAS 3.00E+00 2 m/s

IMU-Roll 2.50E-01 2 deg

IMU-Pitch 5.00E-01 2 deg

IMU-Yaw 3.00E-01 2 deg

Another change made in the filter design has been the

introduction of a new steady-state wind model. In [i], the

horizontal wind model assumed zero process noise, and a time

constant of i000 seconds. These wind estimates showed a marked

dependence on aircraft maneuvers. In this study, we have

introduced a process noise of 0.i m/s on both the 'x' and 'y'

direction winds in the runway frame, and the time constant has

been reduced to 100 seconds. These values have been chosen so as

to model a slowly time-varying wind component (with an RMS value

of approximately 1.0 m/s) in addition to the steady-state winds.

Another modification is that the no-fail filter now uses

a constant state transition matrix as opposed to a time-varying,

state dependent one [6], [8] which had to be updated by the

- 8 -
partials of the input transition matrix at every iteration. This

change has reduced the execution time by almost 20% in addition

to bringing the program size down by 5 Kb, without making any

major impact on either the state or bias estimation performance.

- Moreover, this change has resulted in the decoupling of the

no-fail filter's translational dynamics part (aircraft position,

velocity and horizontal winds) from the rotational kinematics

part (aircraft attitudes).

The no-fail filter now uses only one replication of the

MLS sensor measurements. Since the second channel for these

measurements had to be simulated in order to have a complete dual

redundant sensor suite, this second channel is now kept in standby status to be used only in the event of a MLS failure (similar

to the set-up for input sensors). Based on the earlier sensor

error analysis of [i], the MLS sensor noise is assumed to be

white.

We now present the aircraft state estimate time-histories

for the nominal emulation run with the no-fail filter design

based on the parameters given in Table 2.2. Beginning at time

zero, this run ends at 266.2 seconds when radar altimeter height

is attained. Figure 2.1 shows the aircraft ground track, and

altitude profile as the aircraft goes through various flight

segments from runway approach to altitude hold, and runway

alignment to final descent. Figure 2.2 depicts the horizontal

velocity estimates, with the y-runway direction velocity

highlighting the runway alignment maneuver. The aircraft

vertical velocity profile and roll attitude estimate time history

- 9 -
-8.99 -3.99 1.00

(m) [*1.E+03]

-14.0

EX

m

'<t

to -+-----y----r------r---.------,---.,.--...,.---L-IL19.0

o -+-_---'__...l.--_-.L.__L.-..__---L._-.l__...l...----.--I-

,........,

t<)

o m

+ '<t

W ..-- ..-- I

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t'1

I

o

~i=+============~===::::===========t0

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W to

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to

I

200. 270.

o

o -+-..L----,-----r-----r--r-----r-----.---.---___+_ lXJ I I

1-10.0 60.0 130.

TIME (s)

Figure 2.1: Estimated aircraft ground track and altitude profile

- 10 -
o

°L(_ " i t i

I0 1 I I

- 10.0 60.0 150. 200. 270.

TIME (s)

o

0 , I , I l I ,

F

oo 1

0

d

_-" ' I i I ' I i

L_o.o 60.0 130. 200. 270.

TIME (s)

Figure 2.2: Horizontal velocity estimate time histories

- ii -
0

co

_ 0

_ J

N 0

wd

ol

t,'i ' I ' I ' I '

Llo.o 6o.o 13o. 2oo. 270.

TIME (s)

u_ V

c,i

' I I I ' I i

,- 0.0 60.0 130. 200. 270.

TIME (s)

Figure 2.3: Vertical velocity profile and roll attitude estimate

- 12 -
130. 200. 270.

TIME (s)

60.0

en

en -+---'---,r---~-~--..-----r-----,----.-----+-

L10.0

o

O-+--.---------'__--'-_----'-__-'-_--'-_---L__""""--_-t-

"

W

I en

en

o

,,-.,.0

01 • Q) t')

"0

"-.../

130. 200. 270.

TIME (3)

60.0

o

1C) -t---'------,----.-------,--,-----,-----.--. .-

L1O.0

(f) 1C)

n... t')

w .-

I

1C)

o -f--.-------I----L-__-.L__l.....-_----L.._

o

,,-.,.C\l

01.-

Q) I

"0

"-.../

Figure 2.4: Pitch and yaw attitude estimates

- 13 -
are shown in Figure 2.3. These figures show that the altitude is

held constant while performing the bank maneuver for runway

alignment. Figure 2.4 shows a pitch down attitude of magnitude

2-4 degrees through most of the emulation run except for the

alignment maneuver at which time the aircraft pitches up at

approximately the same angle. Figure 2.4 also shows the yaw

attitude estimate time history. Finally, the new horizontal wind

estimates and aircraft latitude versus longitude track are shown

in Figure 2.5. The wind estimates portray a gradually

diminishing crosswind starting at 10 m/s and reducing to 2 m/s at

the end of the run. The results also imply the presence of more

wind gusts at lower altitudes as evidenced by the higher noise

residuals in the IAS sensor during the latter segments of the

flight.

The major impact of the new wind model is the quicker

convergence of the normal operating biases for the body mounted

accelerometers as depicted in Figures 2.6 and 2.7. As opposed to

the approximately 60-70 seconds needed by the no-fail filter to

reach the steady-state bias estimate, these bias estimates now

converge to steady-state values in about 40 seconds. Comparisons

to earlier results (Figures 3.8-3.9 in [i]) also show a more

stable steady-state behavior implying smaller covariance

statistics for the bias filter. Figure 2.7 also shows the bias

estimate for the roll rate gyro and Figure 2.8 gives the bias

estimate time histories for the pitch and yaw gyros. These bias

estimates do not show any major change from earlier results.

- 14 -
o

q_ z I I I I I I

l_W

- E

1 i

o __/ v

z _ /_-_-"

W

/

/

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,- ' I ' I ' I '

L_:o.o 6o.o 13o. 2oo. 27o.

TIME (s)

€5 I I I

e,I

o

_- I I I

-77.05 --77.0 --76.95 -76.9 -76.85

ALON (deg)

Figure 2.5: Horizontalwind estimatesand aircraftlatitudevs.

longitudetrack

- 15 -
o

0 I ,

r

"° I

"m "I

E

<

I -

I" -- ---

o

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TIME (s)

c)

o

iN i I , I I I ,

I 0

m

o

(D

":. I ' I ' I '

L10.0 60.0 130. 200. 270.

Ti'_E (s)

Figure 2.6: Longitudinal and lateral accelerometer bias

estimates

- 16 -
o

J I l I i I i

_ .

NS <

I q

m

o

i i i ,

L_O.O 60.0 _30. 200. 270.

TIME(_)

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I

ID

"IJ

I cx

m I"

o_

' I ' i ' I '

L' 0.0 60.0 150. 200. 270.

TIME (s)

Figure 2.7: Verticalaccelerometerand roll rate gyro bias estimates

- 17 -
o

m I l I I I ,

q

I

,-,g

m I"

0

0

lfl ' I d I ' I '

Lto.o 60.0 130. 200. 270.

TIME (s)

o

I'- i I i I i I I

"--8

Q)

0

d i I ' I ' 1 '

-I0.0 60.0 130. 200. 270.

TIME (s)

Figure 2.8: Pitch and yaw rate gyro bias estimates

- 18 -
130. 200. 270.

TIME (9)

60.0

D'l

N

o-t-...L--r------r------,----r------,----.-----,---_+_

L10.0

D'l g--+--.--_.L--_-L..__L __---L._---lL-.._--l..-_---l___+_

N

« D'l

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n:: 0

f

D'l

,,-,,0

010

(l) •

\J

130. 200. 270.

TIME (9)

60.0

D'l

N

o-+--'----.-----.-----....----.------.----.-------..---+-

LlO.O

eng-+-.-__L-.._--l..-_---l__-1--_---l__-L._--1.__.+_

D'l "-,, 0

01 0

(l)

\J

.......,

-.J

W D'l

m 0

a::: 0

f

Figure 2.9: No-fail filter residuals for MLS azimuth and

elevation

- 19 -
o

O-+-~-L---l.-.----ll----l.-.----l--....l...------L---!-

130. 200. 270.

TIME (5)

60.0

o

I""--+-...L.--.---......----.r---......----.---r------r---!- ,...

1.-10.0

....

C-'

z

a:: m

[IJ m

a:: l""-

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o

,......0

E .... "'-J

130. 200. 270.

TIME (5)

60.0

0'1

0'1 ..,f-+--'---.---......----.r---......----.---r------r---+-

1-10.0

o

It)

N

o

o-+-~---JL---l.-.----l--....l...---.l--....l...------L---!­ It)

Ul

oct:

CD

0::

Figure 2.10: No-fail filter residuals for MLS range and lAS

- 20 -
OJ ::-+-.-_..1-__.l..-_----.J__-L.__--'--__-'--_----''___ _+_

130. 200. 270.

TIME (9)

60.0

OJ

It)

o

o

ci

OJ

::-+--L.--.----r-----,------r--~--_y_--.----_+_

L.10.0

:r:

a-

(IJ

0::

OJ

~-+--r--.....l---..L..------.J'-----L----1..---...1...---'----tOJ

,.....

o

o

o

"

o

o -+.....l---.----r------.------r--~--_y_---.----__t-

':"'10.0 60.0 130.

TIME (s)

200. 270.

Figure 2.11: No-fail filter residuals for IMU roll and pitch

- 21 -
0

0

I I ' I

L-0.0 80.0 130. 200. 270.

TIME (s)

Figure 2.12: No-fail filter residuals for IMU yaw

Note that the steady state biases of approximately -0.16

m/s/s, 0.075 m/s/s, 0.07 m/s/s, -0.27 deg/s, -0.23 deg/s, and

0.14 deg/s for the longitudinal, lateral, vertical

accelerometers, and roll, pitch, yaw rate gyros respectively

compare very favorably with the empirical statistics of Table 2.1

for the same sensors.

The overall improved performance of the no-fail filter

can truly be gauged by the residual time histories which are

shown in Figures 2.9-2.12. With reference to earlier residual

plots (Figures 3.11-3.14 in [i]), each of these residual

sequences shows a markedly smaller mean and uncorrelated

behavior. The residuals for MLS azimuth, elevation and IMU pitch

continue to show some correlation between aircraft maneuvers and

no-fail filter estimation errors. We also note that the few

- 22 -
unusually large residuals in the case of the MLS range sensor (at

approximately 47 seconds and 105 seconds) are caused by unusually

high range measurement errors at these time instants.

Table 2.3 presents the computed empirical statistics for

these no-fail filter residual sequences, calculated over the

entire flight data run. These low sample means and standard

deviations verify the extremely good estimation performance of

the no-fail filter, particularly when we compare these statistics

with the actual sensor noise parameters of Table 2.1. For

example, in the case of the IMU pitch attitude sensor, the rms

value of the difference signal is 0.263 deg/s whereas the rms

value of of the measurement residual is only 0.025 deg/s.

Similarly, the rms error decreased from 0.126 deg/s to 0.037

deg/s for the roll attitude sensor and from 0.93 m/s to 0.85 m/s

for the IAS sensor.

Table 2.3: No-fail filter residuals statistics : nominal update

frequency of 20 Hz

SENSOR MEAN STD.DEV. MAX MIN UNITS

MLS-Azim. +1.37E-03 +7.35E-03 +2.87E-02 -3.06E-02 deg

MLS-Elev. +4.22E-04 +8.26E-03 +3.28E-02 -2.45E-02 deg

MLS-Range +1.67E-01 +2.03E+00 +I.08E+01 -1.98E+01 m

IAS +1.44E-01 +8.36E-01 +4.66E+00 -4.19E+00 m/s

IMU-Roll -1.73E-03 +3.70E-02 +1.29E-01 -1.32E-01 deg

IMU-Pitch +3.19E-03 +2.50E-02 +1.40E-01 -7.29E-02 deg

IMU-Yaw +I.05E-02 +I.16E-01 +6.36E-01 -4.52E-01 deg

- 23 -
2.3 Estimation Performance With Piecewise Constant Gains

As discussed in the introductory chapter, the major

thrust of the current study is to increase the execution speed of

the FINDS algorithm for an actual flight test exercise. To this

end, one of the first changes made to the algorithm was to

convert it from a double precision implementation to a single

precision one; this conversion not only increased the execution

speed by a factor of two (on the host development computer) but

also decreased the program size by about i00 Kb (from a starting

size of 340 Kb). Another modification was the use of a time

invariant state transition matrix, as discussed earlier. Also,

specialized matrix routines were substituted for general purpose

matrix computations to take advantage of some of the inherent

system matrix properties. For example, a special positive

definite symmetric matrix inverse routine was used in place of a

generalized inverse one. These modifications reduced the

execution time from 30 times slower than real-time (for the

double precision, no detectors case) to about i0 times slower

than real-time. In order to increase the execution speed

further, we have investigated the suitability of using piecewise

constant gains in the no-fail filter. We present the results of

this analysis in this section.

A study of the no-fail filter gain time histories reveals

that these gains along with their associated covariance matrices

have a slowly time-varying behavior, except in the initial phase

of the emulation run. Hence, we have investigated the estimation

performance by updating these gains only at certain multiples of

- 24 -
the sampling period instead of updating them at every sampling

instant. This change has a favorable impact on execution speed

because it eliminates two seventh order matrix inversions, system

observation matrix updates and covariance matrix updates in the

intermediate sampling instants.

As a first step, the entire emulation run with detectors

off was repeated (similar to the previous section run) -- the

only difference being that the no-fail filter gain and covariance

calculations were performed at every fifth sampling instant, and

held constant in between. As expected, this modification cut

down the execution time considerably to about 3 times slower than

real-time. An analysis of the aircraft state estimate time

histories shows an increased initial transient period, but very

little difference is observed in the same state estimates in the

latter part of the flight. As a representative example, Figure

2.13 shows the difference between the aircraft x-runway position

estimates for the nominal run of the previous section and this

new run with no-fail filter gain update frequency of 4 Hz. It is

clearly seen that the maximum estimation error is during initial

filter transients, and gradually decays to almost zero. This

figure also shows the same estimation error time history for the

IMU pitch attitude. Here, we see that the estimation difference

rapidly diminishes as compared to the position estimate error.

This particular behavior can be attributed to the bias

estimation performance with constant gains and the relatively

longer time it takes for the accelerometer biases to reach steady

state than for the rate gyro biases. Figures 2.14-2.16 show the

- 25 -
130. 200. 270.

TIME (s)

60.0

Ol

m-+-...L-_r--_~_---,r--_~_----,r--_-r-_--,__-+-

I')

L10.0

o

O~-+-_.L-_--L__L-_--L__L-_-l-_---IL-_-+-

to

a::

a::

w Ol

I Ol

x

o

,........0

......, E N

130. 200. 270.

TIME (9)

60.0

m

~4-...l.--r----.---r----.---r---~----,r----+-

L1O.0

m

m

O-+-~_L-_-L_----Jl....-_-L_----Jl....-_-J-_---I__-+-

o

c::i

Figure 2.13: Longitudinal position and pitch attitude estimation

error with 4 Hz gain update frequency

- 26 -
o_

_ ) I t I t I ,

--ooi /.

x_

I

m I"

0

o

L.o.o 60.0 _3o. 200. 270.

TIME (s)

0

o , I , I , I ,

r,O-

_g

t_ .

E%.J

<_o..,,_It,_,_/--__

m

o

o

F} i I I I ' I I

L o.o 60.0 13o. 200. 270.

TIME (s)

Figure 2.14: Longitudinal and lateral accelerometer bias

estimates with 4 Hz gain update frequency

- 27 -
O

o

_- I I i I f I ,

E

t o W

m

o

ffl

_ l ' I ' i '

L 10.0 60.0 130. 200. 270.

TIME (s)

o

in

o , f , I , I ,

<o

Q)

m I"

0

o

LIO.O 60.0 130. 200. 270.

TIME (s)

Figure 2.15: Verticalaccelerometerand roll rate gyro bias

estimateswith 4 Hz gain update frequency

- 28 -
¢D

tn , i i I , I l O--

.d0

I

; ID O'J

I"

0

I

0

I

'd"

I'_ ' I i I i I

I_10.0 60.0 130. 200. 270.

TIME (s)

0

In° , I , I , I , I

o

u')

i.,') L

"_

m

I

o k o

ff'l

o

0

_. ' I ' I ' i '

10.0 60.0 130. 200. 270.

TIME (s)

Figure 2.16: Pitch and yaw rate gyro bias estimates with 4 Hz

gain update frequency

- 29 -
bias estimate time histories for the longitudinal, lateral,

vertical accelerometers, and roll, pitch, yaw rate gyros for this

particular run corresponding to the gain update frequency of 4

Hz. Note that in this case, the accelerometer biases take almost

i00 seconds to converge as opposed to 40 seconds for the nominal

run. Similarly, the rate gyro biases reach their steady-state

values in about 20-25 seconds instead of i0 seconds. Note also,

that the steady-state bias estimates at 4 Hz are the same as

those at 20 Hz.

Plots of the no-fail filter residual sequence errors with

respect to the nominal run also show the same trends as the state

estimate errors. Table 2.4 presents the computed statistics for

this new set of measurement residuals. The no-fail filter

estimation performance at 4 Hz compares favorably with the

performance at the nominal 20 Hz as demonstrated by the relative

closeness of the residual statistics in Tables 2.3 and 2.4.

Similar runs were made by keeping the gains and

covariances constant over 10, 15 and 20 time iterations. With

respect to execution speed, these runs were 2, 1.5 and 1.3 times

slower than real-time on the host development computer. The same

estimation error/difference analysis performed in each of these

cases shows similar trends as the 4 Hz. gain update frequency

case, with the only difference being a longer convergence time

for the gains and hence for the state estimates. These

convergence rates can again be traced back to the bias estimation

performance. Figures 2.17-2.19 show the bias estimate time

histories for the case when the gain update frequency is 2 Hz.

- 30 -
O_

€_ , I , I i I ,

o A I

- f/}

I"3

' Ii ?

m o

tO}

u'}

I"

(D

C)

L.o.o 6o.o _30. 200. 270.

TIME (s)

o

0

Q

€',,I

"V'

I"

o

ffl

e,l ' l - I ' I

1"-10.0 60.0 130. 200. 270.

TIME (s)

Figure 2.17: Longitudinal and lateral accelerometer bias

estimates with 2 Hz gain update frequency

- 31 -
O

co I , I I I ,

Q

c)

0

_, ,

°

o _ j .

° - _ vV

Q

"-" ' I ' i _

"o.o 60.0 _3o. 200. 270.

TIME (s)

o I I l I , I i

Q

o

Q

I"

_ CN

I"

I

m

0

I

O

Q

_" i I I I J "" i

_-'o.o 60.0 130. 200. 270.

TIME (s)

Figure 2.18: Vertical accelerometer and roll rate gyro bias

estimates with 2 Hz gain update frequency

- 32 -
(D

tn t I , I , I f

O)

_ 0

I

I

0

m

o

I

O)

',d"

I'_ ' I i I ' I t

Llo.o 60.0 13o. 200. 270.

TIME (3)

Figure 2.19: Pitch and yaw rate gyro bias estimates with 2 Hz

gain update frequency

- 33 -
Table 2.4: No-fail filter residuals statistics : gain update

frequency of 4 Hz

SENSOR MEAN STD.DEV. MAX MIN UNITS

MLS-Azim. +1.78E-03 +8.28E-03 +3.76E-02 -3.10E-02 deg

MLS-Elev. +2.83E-04 +7.44E-03 +3.48E-02 -2.16E-02 deg

MLS-Range +I.12E-01 +2.02E+00 +1.05E+01 -1.95E+01 m

IAS +1.05E-01 +7.92E-01 +4.66E+00 -4.23E+00 m/s

IMU-Roll -1.56E-04 +3.66E-02 +1.27E-01 -1.27E-01 deg

IMU-Pitch +4.74E-04 +2.46E-02 +1.38E-01 -7.76E-02 deg

IMU-Yaw -2.05E-05 +1.lIE-01 +6.14E-01 -4.56E-01 deg

Table 2.5: No-fail filter residuals statistics : gain update

frequency of 2 Hz.

SENSOR MEAN STD.DEV. MAX MIN UNITS

MLS-Azim. +I.18E-03 +8.34E-03 +3.28E-02 -2.95E-02 deg

MLS-Elev. +3.38E-04 +7.02E-03 +3.13E-02 -2.22E-02 deg

MLS-Range +1.01E-01 +1.97E+00 +1.07E+01 -1.92E+01 m

IAS +5.13E-02 +7.57E-01 +4.67E+00 -4.24E+00 m/s

IMU-Roll -I.IIE-04 +3.63E-02 +1.25E-01 -1.26E-01 deg

IMU-Pitch +5.33E-04 +2.48E-02 +1.38E-01 -8.07E-02 deg

IMU-Yaw +3.55E-04 +I.10E-01 +6.06E-01 -4.53E-01 deg

- 34 -
o -+~_J-_---ll..-_

o

ci -+-i-ood'u----t-H-----,..----t.-t------------.,f270.

o

It)

r-- -+-'---r-----,,.-----r---rI--.,---"t"""1---r-----jfL...10.0 60.0 130. 200.

TIME (s)

.

r

200. 270.

_--L.'--..1-.-_..L__.--t_

1:so.

TIME (5)

60.0

o

It)

N-+-'---r---,...----r---r---r----r---r---1-

(..10.0

I

m

---.

en

""-en

""-0 E It)

'-'~

Figure 2.20: Longitudinal and lateral accelerometer bias

estimates with 1 Hz update rate

- 35 -
130. 200. 270.

TIME (9)

60.0

I I I

" - .....

~~ -

v .....

v V \

V - A .....

-VI

I -r---r--. mI')

o

L10.0

m

m

0

v

--: ,-..

!II

"""

!II

"""E m,.... ........ q

I

m m.....

0

130. 200. 270.

TIME (9)

60.0

o

~_+....L...--r---r__---r---r---r----...----r---~

L10.0

o

o

I"l

"

o

o

"

q-+-r-_...L.-_--l__--I...__...L.-_---''-_--I...__..J......._---'~

o

a..

I

m

Figure 2.21: Vertical accelerometer and roll rate gyro bias

estimates: 1 Hz update rate

- 36 -
0

i I -.._ I , I , L

° !

t

o

I

"_" tI

,

m

O

I

1-' 0.0 60.0 130. 200• 270.

TIME (s)

°6 _I---_

°o I i --_.... ' I ' ' ' -

1-10.0 60.0 130. 200. 270.

TIME (s)

Figure 2.22: Pitch and yaw rate gyro bias estimates:

1 Hz update rate

- 37 -
Table 2.5 gives the residual sequence statistics for the same

case and, again, we see a stable filter estimation behavior.

Finally, for the purpose of comparison, Figures 2.20-2.22

depict the bias estimation performance of the no-fail filter with

a gain update frequency of 1 Hz. As expected, the biases take an

extremely long time to converge; yet, the no-fail filter residual

sequence statistics shown in Table 2.6 continue to verify a good

estimation performance.

Table 2.6: No-fail filter residuals statistics : gain update frequency of 1 Hz.

SENSOR MEAN STD.DEV. MAX MIN UNITS

MLS-Azim. +3.32E-04 +8.52E-03 +2.99E-02 -3.95E-02 deg

MLS-Elev. +5.96E-04 +6.76E-03 +3.49E-02 -2.28E-02 deg

MLS-Range +8.72E-02 +1.97E+00 +I.12E+01 -1.94E+01 m

IAS +2.29E-02 +6.95E-01 +4.68E+00 -4.01E+00 m/s

IMU-Roll -2.73E-05 +3.58E-02 +1.23E-01 -1.28E-01 deg

IMU-Pitch +1.01E-03 +2.52E-02 +1.32E-01 -9.35E-02 deg

IMU-Yaw +4.17E-04 +1.08E-01 +6.24E-01 -4.51E-01 deg

In this chapter, we have presented the performance

results for the no-fail filter with detectors inactivated. For

the nominal emulation run, we have obtained a significant

improvement in estimation performance by making some design

modifications. Using piecewise constant gains and other changes,

we have speeded up the execution performance to 1.3 times slower

- 38 -
than real-time on the host development computer. The next

chapter deals with the failure detection and isolation

performance of the FINDS algorithm.

- 39 -
3. FAILURE DETECTION PERFORMANCE

In this chapter, we present the changes made to the FDI

algorithm in FINDS which resulted in an improvement in detection

performance and execution speed. In particular, we present the

FDI performance with a series of injected bias failures, given

the estimation performance of the no-fail filter of the previous

chapter. The first section deals with the results obtained from

a detectability analysis performed on the bank of first order

detectors driven by the expanded innovations of the no-fail

filter. The next section presents the performance of the FDI

algorithm with the same set of bias failure runs as in [i]. In

the next section, we present a new detection strategy which takes

advantage of the improved no-fail filter estimation performance,

and is capable of detecting sensor failures significantly faster.

In addition, this new detection strategy allows the entire FINDS

algorithm to execute at almost the same speed as the no-fail

filter. Preliminary failure detection results using this new

detection strategy are also presented. These results validate

the detection performance predicted by the detectability

analysis. In the final section, we present the results of our

analysis involving the update of the no-fail filter gains at

lower frequencies.

3.1 Failure Detectability Analysis

Referring back to equation (2.3.20) in [6], we have the

following recursive relation for the i'th detector information

matrix:

- 40 -
A

pTl(k+i 1 /k+l) = pTl(k 1 /k)+Cl(k+l,x(k+i/k))R-l(k+l)Ci(k+l,x(k+i/k))

_llko/k 0

with P ) = 0

where k0 denotes the time at the start of a residual window

R is the expanded innovations covariance matrix

C. is the failure observation matrix for the i'th 1

detector

The above expression hypothesizes the occurence of a particular

failure at time k0, and zero information about the bias jump

magnitude at that instant. The second term on the right hand

side of the above equation can be viewed as the incremental

information to the i'th detector at every subsequent time instant

after time k0. The time rate of change of this incremental

information determines the failure signature, and hence, the

detectability of any given sensor [8]-[9].

Figures 3.1a-d show the behavior of the normalized (by

sensor noise standard deviation) incremental information for the

longitudinal accelerometer during four different phases of the

nominal emulation run:

(a) initial phase after filter start-up, when the bias

estimates exhibit significant transients;

(b) before the runway alignment maneuver but after bias

estimates have converged to steady-state;

(c) during the runway alignment maneuver; and

(d) final descent towards touchdown.

Figure 3,1a clearly shows the low level of incremental

information available to the longitudinal accelerometer detector

in the initial transient phase of the no-fail filter. This is

- 41 -
due to the large error covariance for the longitudinal

accelerometer bias estimate during this initial transient stage.

Any failure in this sensor during this phase would be

significantly compensated by the longitudinal accelerometer bias

estimate leading to a low failure signature on the residuals.

Once the bias estimate for that accelerometer converges (i.e.,

the associated error covariance is reduced), then the behavior of

the incremental information changes as seen in Figures 3.1b-d.

In each of these plots, we see a gradual rise in incremental

information from the start of the residual window. This behavior

is due to the use of the accelerometers in the no-fail filter as

inputs. These figures also show that the detectability of the

longitudinal accelerometer is essentially independent of aircraft

maneuvers or flight segments.

Figures 3.2a-d and 3.3a-d show the incremental

information behavior, in the same four flight phases, for the

lateral and vertical accelerometers, respectively. Both plots

3.2a and 3.3a depict the same low-level information available to

the lateral and vertical accelerometer detectors due to bias

estimation uncertainty as in 3.1a. However, once these bias

estimates converge, Figures 3.2b-d and 3.3b-d show a definite

increase in the incremental information, and thus, an increase in

detectability for these accelerometers in the latter phases of

the flight, as the aircraft approaches the runway. This is

because the MLS azimuth and elevation sensors, which generate the

most significant signatures after lateral and vertical

accelerometer failures, become more sensitive to position errors

- 42 -
as the aircraft nears the runway. In contrast, the MLS range

sensor, which generates the most significant signature in the

case of a longitudinal accelerometer failure, has approximately a

constant sensitivity to position errors throughout the flight.

The same analysis performed on the rate gyros shows that

the detectability of these sensors is less dependent on flight

segments, in contrast to the accelerometers. This is because the

correlation between the rate gyros and IMU attitude measurements

arising from the rotational kinematics is essentially invariant

throughout the flight. The only exception here is during an

aircraft maneuver when the incremental information tends to show

a slightly increased slope. This implies that the rate gyro

failures, especially for roll and yaw, are more detectable during

an aircraft maneuver. Figures 3.4 and 3.5 show the incremental

information time history for the roll, pitch and yaw rate gyros

in the aircraft maneuver flight segment. The rapid increase in

the incremental information in these plots implies increased

detectability for these sensors, especially when compared to the

same plots for the accelerometers.

The measurement sensors portray a different incremental

information behavior than the input sensors as can be seen in

Figures 3.6 and 3.7, for the MLS azimuth and range, IAS and IMU

roll attitude sensors, respectively. For all the measurement

sensors, the incremental information depicts an immediate jump at

the beginning of a residual window, followed by an exponential

decay to a steady-state. This steady-state differs for the MLS

sensors from the other measurement sensors since the no-fail

- 43 -
O

I') , , I , I , I ,

0

N

6

Z

o

o

6 ' ', i

6.0 20.0 24.0 28.0 32.0

TIME (s)

o

I_ i I , I , I ,

d

0

6

o

6

o

o , i l

76.0 80.0 84.0 88.0 92.0

"riME C-)

Figure 3.1a,b: Incremental information behavior for longitudinal

accelerometer during initial flight segments

- 44 -
O

F) , , ! A I ,, , I ,

6

o

6

X

_z

0

i6

o6 i i I

1 _6. 140. 144. 148. 152.

TIM_" (s)

o

o

6

I

h

_z

0

_=-

d

0

o , i I , ,

226. 230. 234. 238. 242.

"riME (,,)

Figure 3.1c,d: Incremental information behavior for longitudinal

accelerometer during aircraft maneuver and final

descent

- 45 -
0

,5

o

r4

6

Z

o

,r6

_..=.__..-.

J

o jl d t , , ,

16.0 20.0 24.0 2B.0 32.0

"riME (s)

o

I'3 i I , I , I i

6

o

o4

0

z

o

6

o

0 J i i

76.0 80.0 84.0 88.0 92.0

"riME(s)

Figure 3.2a,b: Incremental information behavior for lateral

accelerometer during initial flight segments

- 46 -
O

d

o

d

I

h

z

o

d

o

o I • •

1 ..36. 140. 144. 14B. 1,52.

TIME (s)

o

0

o

o

I

b.

_z

o

d

o

€_ I I I

226. 2,30. 234. 2,58. 242.

"riME (,)

Figure 3.2c,d: Incremental information behavior for lateral

accelerometer during aircraft maneuver and

final descent

- 47 -
o

I_ i I i ! i I I

0

o

6

I

b.

Z

0

0

/

o

6 , i ,

1B.O 20.0 24.0 28.0 32.0

TiME (s)

o

In = I t I = I =

6

P

i

_

d

! ,

- i

d

o

76.0 so.o s4.0 ss.o g2.0

TIME (s)

Figure 3.3a,b : Incremental information behavior for vertical

accelerometer during initial flight segments

- 48 -
o

I_ a I I I e . I ,, e .,

0

0

6

I

h

z

o

6

o

.36. 140. 144. 146. 152.

"riME (_)

o

6

o

N

o

I

U.

z

o

T,-

6

o

0 i l e

226. 230. 234. 238. 242.

"riME (,,)

Figure 3.3c,d : Incremental information behavior for vertical

accelerometer during aircraft maneuver and

final descent

- 49 -
o

I_ = I a I = I i

o

o

O.

_z

o

qr--

6

0

0 I J I I J

1,36. 140. 14.4. 148. 1,52.

"riME (,,)

0

I_ I . I = I = I =

6

o

6

0

I

h

z

o

t6

o

0 I ' " t i

,.'56. 14.0. 14.4. 148. 1,52.

"riME (-)

Figure 3.4: Incrementalinformationbehaviorfor roll and pitch

rate gyros in aircraftmaneuverflight segment

- 50 -
o

6

l

0

I

I

lu

z_

°

6 !

o

i _"I i .... ,

:38. 14.0. 144. 148. 152.

"riME (s)

Figure 3.5: Incremental information behavior for yaw rate gyro

in aircraft maneuver flight segment

filter uses only one replication of the MLS sensors as opposed to

dual redundancy for the IAS and IMU sensors. The behavior of

these incremental information plots is almost identical in each

of the four flight segments. Thus, the measurement sensors are

equally detectable throughout the flight.

We can now summarize the results of our detectability

analysis as follows:

i) For a measurement sensor, the incremental information

is highest at the beginning of a residual window with

a subsequent exponential decay to a steady-state. On

the other hand, for an input sensor, the incremental

information is lowest at the beginning of a residual

window with a gradual build-up to steady-state as the

- 51 -
o

N+---"----J.-_.....a.-__.L-_---' ........__-'-__l0

01

ci

0

CO

ci

0

I')

0

o

ci -+---..----.---~-- .,.--~--,....----,,.----+

136. 140. 144.

TIME (8)

148. 152.

o"!+-__"--_-.1.__.....a.-__-'--_---'__.........__-'-_ _+_

0

01

0

Cl

Z 0 0:: CO

ci

?;

0

I')

0

o

ci-+---..---~--~--,....----,.----"""T---r---t_

136. 140. 144.

TIME (8)

148. 152.

Figure 3.6: Incremental information behavior for MLS azimuth

and range in aircraft maneuver flight segment

- 52 -
o

_ 0

o_

6

o_

_< o

='d Z

0

o

o

(_ I I I

,36. 140. 14.4. 14-8. 152.

TIM_"(,)

0

, I I I , I ,

s.-

o

0)

€5

.T:

,,'d

Z

0

6

o

o i , i

38. 140. 14-4. 14.8. 152.

TIME (,)

Figure 3.7: Incremental information behavior for IAS and IMU

roll attitude in aircraft maneuver flight segment

- 53 -
failure gets propagated through the no-fail filter

dynamics.

2) Of the input sensors, the linear accelerometers take

the longest time to generate significant incremental

information, and are hence, the least detectable of

all the sensors.

3) Detectability of accelerometer failures increases as

the aircraft approaches the runway, especially for the

lateral and vertical accelerometers.

4) Rate gyro failures are more detectable than

accelerometer failures. Detectability for the rate

gyros is independent of flight segments.

5) Measurement sensor detectability is not a function of

either bias estimation performance or aircraft

maneuvers/flight segments.

6) Steady state incremental information for a particular

sensor is dependent upon the number of replications of

that type used by the no-fail filter and whether its

bias is estimated or not.

These observations become more evident as we examine the failure

detection performance of the FINDS algorithm in the following

sections.

3.2 Baseline Failure Detection and Isolation Performance

In this section, we present the bias failure detection

performance of the FINDS algorithm for the same series of

failures injected into the flight data as reported in [i]. As

- 54 -
discussed earlier, the no-fail filter residual sequence forms the

input to the detectors. Hence, the amount of use that the

no-fail filter makes of any particular sensor in its estimation

process determines its failure signature on the residuals and

thus, its detectability. In accordance with the estimation

performance presented in Chapter 2, the no-fail filter makes a

more balanced use of all the input and measurement sensors, in

contrast to the earlier results presented in [i]. The impact of

this improved estimation is reflected in the detection

performance summary presented here.

Note that for all the six bias failure runs discussed in

this section, the detector and sensor healer parameters are

essentially the same as given in Tables 3.4 and 3.5 in [i],

respectively. The only difference is in the detector sensor

noise design parameters since these parameters are chosen

depending upon the statistics of the no-fail filter residual

sequences. Table 3.1 shows these new sensor noise parameters

employed in the computation of the filter measurement residual

covariance used by the detectors.

Table 3.2 presents the detection performance summary of

the FINDS algorithm with injected bias failures, over a series of

six emulation runs. The failure onset times in these runs,

although in the same flight segment, are not exactly the same

instants as discussed in [i] but differ by a few seconds. Thus,

these failures occur at different instants within a decision

window than the earlier reported runs.

- 55 -
Table 3.1: Design values for measurementsensor noise parameters

used by the detectors

VARIABLE NOISE SD REPLICATIONS UNITS

PER REPL. USED

MLS-Azim. 3.00E-02 1 deg

MLS-Elev. 3.50E-02 1 deg

MLS-Range 5.50E+00 1 m

IAS 2.00E+00 2 m/s

IMU-Roll 1.30E-01 2 deg

IMU-Pitch 1.50E-01 2 deg

IMU-Yaw 5.00E-01 2 deg

By comparing the sensor noise values used by the no-fail

filter in [i] and the current study, we observe that the current

no-fail filter (i) has a new wind model, (ii) uses the MLS, IAS

and vertical accelerometer sensors less, and (iii) uses the IMU

attitudes and lateral accelerometer more than before. This is

clearly evident in the detection times for these respective

sensors as compared to Table 3.13 in [i]. Thus, in run 3, the

lateral accelerometer failure gets detected faster than before

whereas in run 4, the detection time for the vertical

accelerometer failure is higher than in [i]. Similarly, we see

significantly faster detection times for the IMU attitude sensor

failures, and a slightly higher detection time for the rate

gyros. There is no major change in the case of the MLS sensors,

but an IAS failure, by virtue of its higher sensor noise

characteristics, takes longer to get detected.

The most important difference between these two sets of

bias failure summaries is the absence of any false alarms in any

of the six current emulation runs. Moreover, the current version

- 56 -
Table 3.2: Baseline bias failure detection performance summary

RUN SENSOR FAILURE DETECTION FAILURE LEVEL UNITS

NO. TYPE INJ.AT (s) TIME (s) INJECTED ESTIMATED

1 MLS-Elev. 81.55 0.20 0.18 0.186 deg

2 IMU-Yaw 67.60 0.05 4.0 4.042 deg

MLS-Azim. 111.25 0.15 0.18 0.154 deg

MLS-Range 225.75 0.25 40.0 39.179 m

3 IAS 59.70 0.70 9.0 9.906 m/s

Gyro-Roll 141.20 0.75 0.90 1.339 deg/s

Acc.-Lat. 241.60 4.90 1.275 4.868 m/s/s

4 IMU-Roll 93.80 0.35 1.50 1.232 deg

Acc.-Vert. 200.90 5.30 1.471 26.066 m/s/s

5 IMU-Pitch 81.65 0.05 2.0 1.276 deg

Gyro-Yaw 153.35 2.40 2.0 2.331 deg/s

Acc.-Long. 222.45 6.85 1.471 6.184 m/s/s

6 Gyro-Pitch 179.85 1.05 1.0 0.254 deg/s

of the FINDS algorithm has a 115 Kb program size and an execution

speed of 30 times slower than real-time as opposed to the

previous version which had a program size of 340 Kb and an

execution speed of 120 times slower than real-time on the host

development computer.

Since the major thrust of this current effort is to adapt

the FINDS algorithm to a real-time operation without compromising

on either estimation or detection performance, this modified

FINDS algorithm, with its smaller program size and an improved

and well balanced detection performance, still needed further

changes. The implementation of the bank of detectors, by virtue

of its slow speed of execution, was the main target for further

- 57 -
modifications;hence, it has been replaced by a new detection

strategy presentedin the next section.

3.3 New Detection Strategy

The FDI algorithm in FINDS has an extremely fast

detection performance with no false alarms, but a slow execution

speed. This is largely because of the implementation of the bank

of first order detectors. For instance, with the current sensor

suite, a total of 17 detectors need to be executed at every time

instant. Moreover, the performance of this implementation is

also affected by the use of a fixed length detector window which

is necessary in order to minimize computational resources. This

constraint makes the detection time and failure level estimate

dependent on the time of failure onset within a particular

detection window. Finally, by using the expanded residual

sequence as inputs (as necessitated by the isolation algorithm),

the detection strategy does not make optimum use of the excellent

statistics of the no-fail filter averaged residuals. In order to

alleviate these inherent limitations, a new failure decision test

has been implemented for the FINDS algorithm, as discussed below.

Given an m-dimensioned vector r with a Gaussian

distribution with mean ]Iand covariance R, then

N (r - p)T R-I (_ _ I/)

has a Chi-square distribution with m degrees of freedom [i0],

where r is the sample mean of r over N samples.

From Table 2.3 it is seen that the no-fail filter

residuals have an extremely small mean value across the entire

- 58 -
emulation run. Moreover, Figures 2.9-2.12 show the uncorrelated

behavior of each of these residual vector entries. Thus, we can

perform a detection test on the no-fail filter residuals (without

performing an isolation test) over a moving window, as follows.

Given the residual sequence of the no-fail filter defined by [6]:

A

r(k) = y(k) - h(x(k/k-l)) - Db(k-l)

where

y(k) = [yl(k) + y2(k)]/2

compute the sample mean of this residual sequence over a moving

window :

k

_(k) - N rlj)

j=k-N+l

Then, perform the following test of mean by computing the

likelihood ratio

(_: N (rT(k) R-I r(k))

and comparing to a predetermined threshold, in order to decide on

a sensor failure. This test procedure can be implemented for

different moving windows Ni. In the event of a failure decision,

a failure isolation test is made by running the bank of detectors

over the last N. no-fail filter residuals. i

Table 3.3 shows the statistics of these averaged

residuals and the associated likelihood ratios for the nominal

- emulation run of section 2.2. Both the previous simulation

version and the current flight data driven emulation version of

the FINDS algorithm show that measurement sensor failures

propagate through the no-fail filter dynamics almost

- 59 -
instantaneously. On the other hand, it takes a longer amount of

time for the input sensor failure signatures to show up in the

no-fail filter residuals. This observation is also validated by

the incremental information analysis of section 3.1. Hence, two

different moving windows have been incorporated in the new

detection strategy; one of length 1 sample for measurement sensor

failure detection, and the other of length i0 samples to detect

input sensor failures. The computed means and standard

deviations of these residuals are essentially the same for both

moving windows of length 1 and i0 samples, thus highlighting the

uncorrelated nature of these residuals.

The minimum/maximum values for the likelihood ratio are

empirically calculated as 13.5 for the moving window of 1 sample

and as 63.4 for the window of i0 samples. Hence, a Chi-square

test with a Type I error size of 0.01 (which implies a threshold

of 18.5 with the given seven degrees of freedom) would yield no

false alarms for the decision window of length i. On the other

hand, a test threshold of 65-70 would yield no false alarms in

the case of the moving window of length 10, thus implying a lower

Type I error size.

Using the above threshold values, we have made a series

of runs where a failure is injected into a specific sensor at

different flight segments in the emulation. Table 3.4a presents

the results of this series of test runs. The first set of runs

include a sensor failure occuring at 82.10 seconds into the

flight, when all bias estimates have converged and the bank

maneuver is yet to be executed. In the case of the input

- 60 -
Table 3.3: No-fail filter residuals and likelihood ratio

statistics for moving windows of 1 and i0

samples: nominal run

SENSOR MEAN STD.DEV. MAX MIN UNITS

MOVING WINDOW OF 1 RESIDUAL SAMPLE

MLS-Azim. +1.37E-03 +7.35E-03 +2.87E-02 -3.06E-02 deg

MLS-Elev. +4.22E-04 +8.26E-03 +3.28E-02 -2.45E-02 deg

MLS-Range +1.67E-01 +2.03E+00 +1.08E+01 -1.98E+01 m

IAS +1.44E-01 +8.36E-01 +4.66E+00 -4.19E+00 m/s

IMU-Roll -1.73E-03 +3.70E-02 +1.29E-01 -1.32E-01 deg

IMU-Pitch +3.19E-03 +2.50E-02 +1.40E-01 -7.20E-02 deg

IMU-Yaw +1.05E-02 +I.16E-01 +6.36E-01 -4.52E-01 deg

LRT-01 +8.73E-01 +9.43E-01 +1.35E+01 ---

MOVING WINDOW OF 10 RESIDUAL SAMPLES

MLS-Azim. +1.36E-03 +5.31E-03 +1.64E-02 -1.63E-02 deg

MLS-Elev. +4.28E-04 +6.84E-03 +2.06E-02 -2.01E-02 deg

MLS-Range +1.68E-01 +1.67E+00 +6.36E+00 -1.34E+01 m

IAS +1.44E-01 +7.76E-01 +3.58E+00 -3.15E+00 m/s

IMU-Roll -1.66E-03 +2.89E-02 +7.28E-02 -7.97E-02 deg

IMU-Pitch +3.26E-03 +1.88E-02 +I.12E-01 -4.73E-02 deg

IMU-Yaw +1.08E-02 +1.08E-01 +4.81E-01 -3.70E-01 deg

LRT-10 +8.08E+00 +6.45E+00 +6.34E+01 ---

sensors, we see a significant decrease in detection time as

compared to earlier results. As for the measurement sensors

(except IAS), the failure is detected without any delay, yielding

- 61 -
a corresponding detection time of zero seconds. This is due to

the instantaneous jump in the incremental information, i.e., an

immediate signature on the measurement residuals at failure onset

time.

The IAS sensor failure does not get detected in the same

instantaneous manner because of the low failure level injected.

Due to the no-fail filter's use of dual redundant IAS sensors,

the 9 m/s failure gets averaged and a jump of approximately 4.5

m/s is seen in the IAS residual. Since the sensor noise design

value for the IAS sensor in the detectors is 2 m/s, this

corresponds to a 2.25-_ failure. This low failure level is not

adequate enough to push the likelihood ratio above the threshold

set for the moving window of 1 sample -- but the cumulative

effect on the moving window of 10 samples is enough to detect the

failure 8 or 9 samples after its occurence. This example shows

the sensitivity of this new detection strategy. In fact, test

runs were made by injecting a 15 m/s failure in the IAS sensor,

which looks like a 2.5-a failure in the no-fail filter averaged

measurements and generates a 7.5 m/s jump in the IAS residual,

which corresponds to a 3.7-_ failure to the detectors. This

failure does get detected with a zero detection time, similar to

the other measurement sensors.

In the second series of runs, we have singular failure

occurences in each sensor at 145.40 seconds, in the middle of the

aircraft maneuver for runway alignment. Interestingly, the

lateral and vertical accelerometers show a decrease in detection

time of 0.45 and 0.10 seconds, respectively. Also, the yaw rate

- 62 -
Table 3.4a: Bias failuredetectionsummarywith new

detectiontest

SENSOR FAILURE LEVEL DETECTION TIME

TYPE INJECTED FOR FAILURE INJECTED AT

82.10 S 145.40 S 238.70 s

Acc.-Long. 1.47 m/s/s 4.05 s 3.95 s 3.75 s

Acc.-Lat. 1.28 m/s/s 5.20 s 4.75 s 2.70 s

Acc.-Vert. 1.47 m/s/s 4.95 s 3.85 s 2.10 s

Gyro-Roll 0.90 deg/s 0.45 s 0.35 s 0.40 s

Gyro-Pitch 1.0 deg/s 0.45 s 0.50 s 0.50 s

Gyro-Yaw 1.0 deg/s 1.65 s 1.45 s 1.50 s

MLS-Azim. 0.18 deg 0.0 s 0.0 s 0.0 s

MLS-Elev. 0.18 deg 0.0 s 0.0 s 0.0 s

MLS-Range 40.0 m 0.0 s 0.0 s 0.0 s

IAS 9.0 m/s 0.45 s 0.40 s 1.20 s

IMU-Roll 1.50 deg 0.0 s 0.0 s 0.0 s

IMU-Pitch 2.0 deg 0.0 s 0.0 s 0.0 s

IMU-Yaw 4.0 deg 0.0 s 0.0 s 0.0 s

gyro shows a slightly higher detectability during maneuvers and

hence, gets detected 0.20 seconds faster in this flight segment.

The rest of the input sensors do not show any appreciable change

in detection time and the measurement sensor failures (except

IAS) are again detected instantaneously.

The third set of runs included specific sensor failures

occuring at 238.70 seconds into the emulation, with the aircraft

on its final descent path and about 4000 m from the runway.

- 63 -
Again, we see that the lateral and vertical accelerometer

failures have a significant decrease in detection time,

validating our observations from the detectability analysis. The

longitudinal accelerometers and rate gyros do not show any change

in detection time across the three runs as expected from the

incremental information analysis. The measurement sensor

failures are again detected without any delays. The IAS sensor

failure, however, takes longer to detect during this phase of the

flight because of the presence of wind gusts, ground effects and

the larger magnitude IAS residuals as seen in Figure 2.10.

Table 3.4b presents the results for the same series of

three test runs using the old detection strategy. A comparison

of these failure detection times with those of Table 3.4a

shows that the new detection strategy performs significantly

better. Note also that the failure detection times with the old

detection strategy do not exhibit the trend across the three

series of test runs predicted by the incremental information

analysis. This is due to the dependence of the old detection

strategy on the failure onset time within a given fixed detection

window.

It is also important to note that all of the above runs

with the new detection strategy execute at almost the same speed

as the no-fail filter estimator; actual time tests indicate that

a run with the new detection algorithm takes approximately i0 % ~

more execution time than corresponding 'estimation only' runs.

With this implementation, the failure isolation and sensor

reconfiguration modules get activated only after the detection of

- 64 -
Table 3.4b: Bias failuredetectionsummarywith old

detectiontest

SENSOR FAILURE LEVEL DETECTION TIME **

TYPE INJECTED FOR FAILURE INJECTED AT

82.10 s 145.40 s 238.70 s

Acc.-Long. 1.47 m/s/s 8.70 s 11.20 s 8.15 s

Acc.-Lat. 1.28 m/s/s 11.50 s 10.70 s 6.00 s

Acc.-Vert. 1.47 m/s/s 11.50 s 8.45 s 4.25 s

Gyro-Roll 0.90 deg/s 1.00 s 0.70 s 0.90 s

Gyro-Pitch 1.0 deg/s 0.75 s 0.75 s 0.90 s

Gyro-Yaw 1.0 deg/s n.d. n.d. n.d.

MLS-Azim. 0.18 deg 0.05 s 0.25 s 0.15 s

MLS-Elev. 0.18 deg 0.05 s 0.25 s 0.20 s

MLS-Range 40.0 m 0.05 s 0.25 s 0.10 s

IAS 9.0 m/s 0.20 s 0.45 s 1.25 s

IMU-Roll 1.50 deg 0.05 s 0.15 s 0.10 s

,

IMU-Pitch 2.0 deg 0.05 s 0.30 s 0.05 s

IMU-Yaw 4.0 deg 0.05 s 0.25 s 0.15 s

* A false-alarm of pitch rate gyro occurred 0.20 s after

failure injection

** Failure time of 82.10 s coincides with the beginning of a

detection/decision window; that is not the case with the

other two failure onset times

a failure, and this aspect of the new strategy is currently being

implemented.

A final comment regarding the use of replicated sensor

measurements is in order here. By using single replications of

- 65 -
all the measurement sensors in the no-fail filter and keeping

second replications as stand-by as in the case of MLS sensors,

lower levels of injected failures can be detected. However, this

would be at the expense of no-fail filter estimation performance

since the effective measurement noise in the averaged

measurements is lower than that in the individual sensor signals.

3.4 Detection Performance With Piecewise Constant Gains

In section 2.3 of the previous chapter, we have presented

the estimation performance of the no-fail filter with piecewise

constant gains and noted satisfactory state estimation, even for

the low gain-update frequency of 1 Hz, yielding low-mean, white

filter residual sequences. However, as the gain update frequency

is lowered, the bias estimates take longer to converge to

steady-state values. In this section, we present the effect of

these lower gain update frequencies on the failure detection

performance using the new decision test discussed in the previous

section.

The statistics for the no-fail filter residual sequences

obtained with gain update frequencies of 4 Hz, 2 Hz and 1 Hz

(shown in Tables 2.4-2.6, respectively) exhibit a small mean and

essentially uncorrelated behavior. Thus, the new decision test

can be performed on these residuals without violating any of the

assumptions. Moreover, since the minimum and maximum values of

these residual sequences lie within the same limits as the

no-fail filter residuals with nominal gain update frequency of 20

Hz, the same sensor failure likelihood ratio thresholds have been

- 66 -
used for all the gain update frequencies, thus yielding a false

alarm rate of zero with this flight data.

Table 3.5 presents the results (with the new detection

strategy) for specific sensor failures injected into the flight

data at 82.10 seconds. For our test runs, we have again used

no-fail filter gain update frequencies of 20 Hz, 4 Hz, 2 Hz, 1.33

Hz and 1 Hz. Considering the results of the 20 Hz update rate as

the baseline case, we see that for the input sensors,

accelerometer failure detection performance gets affected the

most as the update frequency is lowered. The main reason for this

is the relatively slow convergence of the accelerometer biases.

With gain update frequencies lower than 4 Hz, these bias

estimates have not yet converged to steady-state when the bias

failure is injected into the flight data.

Thus, with the accelerometer bias estimation error

covariance still high, these bias estimates begin to converge to

a new steady-state after the injection of the failure, thus

nullifying the effect of an accelerometer failure on the no-fail

filter residuals. In other words, the injected bias failure is

absorbed by the bias filter as it converges to a new steady-state

bias for the accelerometer. However, since rate gyro bias

estimates converge faster, the lower update frequencies have

relatively no effect on rate gyro failure detection performance.

° The exception to this is the yaw rate gyro -- its failures not

being detected at 1.33 Hz and 1 Hz update rates can be attributed

to the particular failure level injected combined with high noise

characteristics of the IMU yaw sensor. As for measurement

- 67 -
Table 3.5: Effect of piecewiseconstantgains on detectiontime

with failuresinjectedat 82.10 s

SENSOR DETECTION TIME WITH GAIN UPDATE FREQUENCY OF

TYPE 20 Hz 4 Hz 2 Hz 1.33 Hz 1 Hz

Acc.-Long. 4.05 s 5.25 s n.d. n.d. n.d.

Acc.-Lat. 5.20 s n.d. n.d. n.d. n.d.

Acc.-Vert. 4.95 s 11.0 s n.d. n.d. n.d.

Gyro-Roll 0.45 s 0.45 s 0.50 s 0.50 s 0.50 s

Gyro-Pitch 0.45 s 0.50 s 0.50 s 0.55 s 0.55 s

Gyro-Yaw 1.65 s 1.60 s 2.35 s n.d. n.d.

MLS-Azim. 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

MLS-Elev. 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

MLS-Range 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

IAS 0.45 s 0.45 s n.d. n.d. n.d.

IMU-Roll 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

IMU-Pitch 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

IMU-Yaw 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

NOTE : Failure level injected is the same as in Table 3.4a

n.d. = not detected

sensors, each of the MLS and IMU sensor failures get detected

instantaneously, for all the update rates. The exception here is

the IAS sensor due to the low failure level injected (as

explained in the previous section) as well as the direct

correlation between the linear accelerometers (and their bias

estimates) and IAS sensor.

- 68 -
Table 3.6: Effect of piecewise constant gains on detection time

with failures injected at 145.40 s

SENSOR DETECTION TIME WITH GAIN UPDATE FREQUENCY OF

TYPE 20 Hz 4 Hz 2 Hz 1.33 Hz 1 Hz

Acc.-Long. 3.95 s 4.50 s 6.0 s 6.15 s 7.90 s

Acc.-Lat. 4.75 s 5.90 s n.d. n.d. n.d.

Acc.-Vert. 3.85 s 4.50 s n.d. n.d. n.d.

Gyro-Roll 0.35 s 0.35 s 0.35 s 0.35 s 0.35 s

Gyro-Pitch 0.50 s 0.50 s 0.45 s 0.45 s 0.45 s

Gyro-Yaw 1.45 s 2.0 s 2.05 s 1.45 s 2.30 s

MLS-Azim. 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

MLS-Elev. 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

•MLS-Range 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

IAS 0.40 s 0.40 s 0.40 s 0.40 s 0.40 s

IMU-Roll 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

IMU-Pitch 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

IMU-Yaw 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

NOTE : Failure level injected is the same as in Table 3.4a

n.d. = not detected

Table 3.6 shows the results for a similar set of runs but

with the sensor failures injected at 145.40 seconds into the

flight. At this time, we see a general improvement in the

accelerometers and IAS sensor failure detection performance at

lower gain update frequencies. Roll and pitch rate gyro failure

detection performance does not get affected; however, yaw rate

gyro failure detection shows an improvement at the lower update

- 69 -
Table 3.7: Effect of piecewise constant gains on detection time

with failures injected at 238.70 s

SENSOR DETECTION TIME WITH GAIN UPDATE FREQUENCY OF

TYPE 20 Hz 4 Hz 2 Hz 1.33 Hz 1 Hz

Acc.-Long. 3.75 s 3.85 s 5.90 s 8.30 s n.d.

Acc.-Lat. 2.70 s 2.80 s 2.95 s n.d. n.d.

Acc.-Vert. 2.10 s 2.25 s 2.55 s 3.85 s n.d.

Gyro-Roll 0.40 s 0.40 s 0.40 s 0.40 s 0.40 s

Gyro-Pitch 0.50 s 0.50 s 0.50 s 0.50 s 0.50 s

Gyro-Yaw 1.50 s 1.50 s 1.50 s 1.55 s 1.55 s

MLS-Azim. 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

MLS-Elev. 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

•MLS-Range 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

IAS 1.20 s 1.20 s 1.20 s 1.30 s 1.45 s

IMU-Roll 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

IMU-Pitch 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

IMU-Yaw 0.0 s 0.0 s 0.0 s 0.0 s 0.0 s

NOTE : Failure level injected is the same as in Table 3.4a

n.d. = not detected

rates. All measurement sensors continue to exhibit excellent

detectability at every gain update frequency.

Finally, Table 3.7 presents the results with lower gain

update rates when sensor failures are injected in the final

flight segment at 238.70 seconds. Again, the accelerometer

failure detection performance shows an improvement. This is

- 70 -
caused by two factors; (a) the accelerometer bias estimates have

more time to converge to steady-state before the failure occurs,

and (b) from our detectability analysis, we know that the

accelerometers generate higher incremental information in this

last flight segment. The rate gyro sensors and all measurement

sensors exhibit the same performance as in the previous test run.

Using the new detection test at the various gain update

frequencies, the FINDS program runs take about I0 % more

computational time than the same runs for the no-fail filter

estimator with no detection test. Thus, for the different gain

update frequencies of 20 Hz, 4 Hz, 2 Hz, 1.33 Hz and 1 Hz, the

algorithm runs approximately ii, 3.5, 2.3, 1.7 and 1.4 times

slower than real-time, respectively, on the host development

computer.

In this chapter, we have presented an improved baseline

detection performance for the bank of detectors implementation.

A detectability analysis involving the incremental information

generated by various sensor failures has also been presented.

This analysis has been used to formulate a new detection strategy

for the FINDS algorithm. We have presented the results of this

new decision test for sensor failures occuring at various phases

in the flight, and also for various no-fail filter gain update

frequencies. At the low update frequencies, the FINDS algorithm

executes at near real-time speed with no effect on the MLS and

IMU sensor failure detection performance. However, IAS, rate

gyro and accelerometer sensor failure detection performance gets

degraded at lower gain update frequencies, especially below 4

- 71 -
Hz., because of the degradation in the input sensor bias

estimation performance. In the case of gain update frequencies

below 4 Hz, the input sensor bias failures are not detected until

the very last segments of the flight as the bias estimates

converge to their steady state values.

- 72 -
4. CONCLUSIONS AND RECOMMENDATIONS

In this report, we have presented the modifications made

to the FINDS algorithm in order to improve its estimation and

failure detection performance, reduce the program size so as to

meet the candidate flight computer memory constraints, and

increase its execution speed to allow real-time operation for

flight test experiments.

The estimation performance has been improved by using a

new wind dynamics model along with modifications to the filter

design parameters. The major impact of the improved estimation

performance is the resulting false alarm rate of zero during all

the emulation runs with the flight data. The detection

performance has been significantly improved by implementing

tests-of-mean over various moving windows of the no-fail filter

residuals. With this new detection strategy, low level MLS, IAS

and IMU sensor failures can now be detected instantaneously. The

low level accelerometer and rate gyro failures are detected

within the minimum time allowed by the information generated in

the sensor residuals based on the aircraft point mass equations

of motion.

Using the dual configuration of the target flight

computer with each side having 128 Kb of memory as our basis of

reference, we have brought the program size of FINDS down from

340 Kb in double precision to an equivalent 115 Kb single

• precision implementation. This reduced size code has been ported

onto one computer of the dual target flight computer

configuration and the program operation has been verified.

- 73 -
On the host development computer computer which has a

294,000 Whetstones floating point performance in 32 bit single

precision, the FINDS algorithm can now execute at 1.3 times

slower than real-time using modifications which do not compromise

on the estimation performance. By implementing a new decision

strategy, we have also been able to perform failure detection

tests (without an isolation test) at 1.4 times slower than

real-time. Any further modifications to the FINDS algorithm to

make it execute in real-time now depend upon the actual flight

computer chosen for the experiment.

In this choice of a candidate computer for an eventual

flight test of FINDS, we have the following two options :

A) If the dual configured target flight computer with its

255,000 Whetstones floating point performance is

chosen for the flight computer, then we recommend the

following parallel processing solution by partitioning

the FINDS algorithm into two separate modules.

One computer would execute the translational dynamics

filter consisting of the linear accelerometers as

input sensors and MLS and IAS as measurement sensors.

The aircraft position, velocity and horizontal winds

would be the filter states along with the

accelerometer bias estimates, thus resulting in a

8-state and 3-bias configuration.

The second computer would execute the rotational

kinematics filter consisting of the rate gyros as

input sensors and the IMU as the measurement sensors.

This filter would estimate the aircraft attitudes and

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the rate gyro bias estimates, thus yielding a 3-state

and 3-bias configuration.

Hence, the original FINDS algorithm of order 17 (ii

states and 6 biases) using seven measurements

(necessitating seventh order matrix operations) would

be split up into two modules; translational dynamics

filter of order ii (8 states and 3 biases) using four

measurements, and the rotational kinematics filter of

order 6 (3 states and 3 biases) using three

measurements. Since both modules can be run in

parallel on the dual target flight computer

configuration, this would effectively involve only

fourth order matrix operations at every sample. On

each computer, the new detection test would be

implemented, testing the occurence of a failure in any

sensor used by the no-fail filter on that side.

Moreover, the isolation test after the detection of a

sensor failure would involve only those sensors used

by that particular filter. This split up of the FINDS

algorithm would have no impact on either estimation or

detection performance since the modifications made in

the current study have resulted in decoupling the

translational dynamics from the rotational kinematics.

Using this option, we estimate that the FINDS

algorithm with the baseline gain update frequency of

20 Hz would execute at approximately three to four

times slower than real-time. Then, the use of a

moderately slow gain update rate (4 Hz for instance)

- 75 -
would bring the program execution down to real-time.

If needed, a front-end microprocessor interface

between the flight data acquisition bus and the target

flight computer can be used to read in the flight

data, and perform variable assignments and dropout

tests, thus speeding up the algorithm execution

further. This effort would involve the restructuring

of the FINDS algorithm implementation from its current

form.

B) As a second option, we propose the use of a flight

computer which is about four times faster than the

target flight computer used in this study, i.e. a

computer with approximately a 1,000,000 Whetstones

floating point performance in 32 bit precision. On

such a computer, the FINDS algorithm with the new

detection strategy would run approximately 2.5 times

slower than real-time at the baseline gain update

frequency of 20 Hz. In this case, we recommend a

multi-rate implementation of the algorithm in which

the no-fail filter's bias-free and bias computations

are performed at different speeds. For instance, the

execution of the bias-free filter at 1 Hz and the bias

filter at 20 Hz would allow overall real-time

execution without compromising either estimation or

accelerometer failure detection performance. This

effort would involve modifications to the code if the

extra computational speed is obtained with an array

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processor, or a modest restructuring of the algorithm

if the speed is due to a faster CPU.

Using either option, we recommend the following sequence

of flight test experiments:

i) Analyze the aircraft state and sensor bias estimation

performance of the no-fail filter (with no detection

and isolation test) in flight under maneuver,

turbulence and different steady-state wind conditions

through various flight paths. Flight tests at

different days would be required to ensure not only

varying wind conditions but also different

accelerometer and rate gyro biases.

2) Using the flight data collected in step i, analyze

(off-line) the false alarm performance of the FINDS

algorithm under the various flight segments and

aircraft maneuvers. At this stage, we also recommend

performing a statistical sensor error analysis as done

in [i], to ensure that the postulated sensor noise

characteristics are correct. For instance, MLS range

sensor may have a constant high bias, thus requiring

the estimation of this parameter.

3) Analyze the failure detection performance of the FINDS

algorithm performing flight test involving various

steady-state winds and turbulence conditions and

aircraft maneuvers during which failures are injected

into the flight data. We recommend the following

procedure in which dynamically correlated sensor group

failures are studied separately:

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-- MLS range, IAS and longitudinal a ccelerometer

failures,

-- MLS azimuth and lateral accelerometer failures,

-- MLS elevation and vertical accelerometer failures,

-- IMU roll attitude and roll rate gyro failures,

-- IMU pitch attitude and pitch rate gyro failures,

-- IMU yaw attitude and yaw rate gyro failures.

During these experiments, after the detection of a

particular failure, the isolation test can be performed only for

the dynamically related sensor groups, thus minimizing

computational resources.

- 78 -
REFERENCES

[i] Caglayan, A.K. and Godiwala, P.M., "Evaluation of a Fault

Tolerant System for an Integrated Avionics Sensor

Configuration with TSRV Flight Data", NASA CR - 172589, June

1985.

[2] Caglayan, A.K. , Godiwala, P.M. and Morrell, F.R. ,

"Performance Analysis of a Fault Inferring Nonlinear

Detection System (FINDS) with Integrated Avionics Flight

Data", Proceedings of AIAA Computers in Aerospace V

Conference, Long Beach, CA, October 1985.

[3] Pines, S., "Terminal Area Automatic Navigation, Guidance,

and Control Research Using the Microwave Landing System

(MLS), Part 2 - RNAV/MLS Transition Problems for Aircraft",

NASA CR - 3511, January 1982.

[4] Curnow, H.J. and Nichmann, B.A., "A Proposed Benchmark for

Hardware Evaluation: The Whetstone Program", The Computer

Journal, No. i, 1976.

[5] Germann, J., "Performance Comparison: Enhanced Supermicro

and the VAX/780", UNIX/WORLD Journal, January 1984.

[6] Caglayan, A.K. and Lancraft, R.E., "A Fault Tolerant System

for an Integrated Avionics Sensor Configuration", NASA CR -

3834, September 1984.

[7] Caglayan, A.K. and Lancraft, R.E., "A Separated Bias

Identification and State Estimation Algorithm for Nonlinear

Systems", Automatica, Vol. 19, No. 5, September 1983.

[8] Caglayan, A.K. and Lancraft, R.E., "An Aircraft Sensor Fault

Tolerant System", NASA CR- 165876, April 1982.

[9] Caglayan, A.K., "Necessary and Sufficient Conditions for

Detectability of Jumps in Linear Systems", IEEE Transactions

on Automatic Control, Vol. AC-25, No. 4, August 1980.

[i0] Anderson, T.W., "An Introduction to Multivariate Statistical

Analysis", John Wiley & Sons, New York, N.Y., 1958.

- 79 -
Standard Bibliographic Page

1. Report No. 12. Government Accession No. 3. Recipient's Catalog No.

NASA CR-178043 I

4. Title and Subtitle 5. Report Date

A PRELIMINARY DESIGN FOR FLIGHT TESTING March 1986

THE FINDS ALGORITHM 6. Performing Organization Code

7. Author(s) 8. Performing Organization Report No.

A.K. Caglayan and P.M. Godiwala R8602

10. Work Unit No.

9. Performing Organization Name and Address

Charles River Analytics Inc. 11 Contract or Grant No.

55 Wheeler Street

Cambridge, MA 02138 NASI-17719 13. Type of Report and Period Covered

12. Sponsoring Agency Na_ne and Address

Contractor Report

National Aeronautics and Space Administration 14. Sponsoring Agency Code

Washington, DC 20546 505-66-41-05

l

15. Supplementary Notes

Langley Technical Monitor: Frederick R. Morrell

Final Report

16. Abstract

This report presents a preliminary design for flight testing the

FINDS (Fault Inferring Nonlinear Detection System) algorithm on a

target flight computer. The FINDS software was ported onto the

target flight computer by reducing the code size by 65%. Several

modifications were made to the computational algorithms resulting

in a near real-time execution speed. Finally, a new failure

detection strategy was developed resulting in a significant

improvement in the detection time performance. In particular, low

level MLS, IMU and IAS sensor failures are detected instantaneously

with the new detection strategy, while accelerometer and rate gyro

failures are detected within the minimum time allowed by the

information generated in the sensor residuals based on the point

mass equations of motion. All of the results have been demonstratec

by using five minutes of sensor flight data for the NASA ATOPS

B-737 aircraft in a Microwave Landing System (MLS) environment.

17. KeyWords(SuggestedbyAuthors(s)) 18. DistributionStatement

Fault tolerant systems, Sensor Unclassified - Unlimited

failure detection and isolation,

Integrated avionics flight data,

Flight computer constraints. Subject Category 06

19. Security Classif.(of this report) 120. Security Classif.(of this page) 21. No. of Pages 22. Price

Unclassified ] Unclassified 86 A05

For sale by the National Technical Information Service, Springfield, Virginia 22161

NASA Langley Form 63 (June 1985)