National Aeronautics and Space Administration

An Introduction to Global Navigation
Satellite Systems

Ben Ashman
Navigation and Mission Design Branch
Goddard Space Flight Center, Greenbelt, MD

Training on GNSS | Pathum Thani, Thailand | 14-19 January 2019

Navigation Satellite Concept
and History

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Training on GNSS 2019 | Pathum Thani, Thailand

2Navigation•

Navigation is the process of determining position and direction•

Generalization of the problem: estimate unknown parameters based on related observations= parameter vector (e.g., Cartesian position and velocity, our “state”)= observation vector (i.e., set of measurements)= observation noise vector (i.e., measurement error)= relation between parameter set and observation set (i.e., measurement model)•

Given a parameter set, we seek an observation set, a relation between our parameters andobservations, and an estimator•, in order to form an estimate:

Elegant and effective solutions have been devised by humans and other species for millennia

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From left: day and night bird migration [20], astrolabe 1619 [21]Training on GNSS 2019 | Pathum Thani, Thailand

3

Navigation (continued)•

Relative navigation
Dead reckoning: monitor rate of travel and heading using a compass; prone to error, especially at sea
Landmark bearings: angles to two known landmarks will constrain position in two dimensions•

Absolute navigation: latitude and longitude (clocks vs. celestial)
Latitude: Measure the elevation of pole star above the horizon with a sextant or astrolabe
Longitude: Very good clock or celestial (sextant for the elevation of celestial bodies above the horizon,
accurate clock to determine the time of observations, almanac to find the predicted position of the body,magnetic compass to determine azimuth and maintain course continuity between celestial observations)

Latitude (left) and longitude (right) [1]
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Radionavigation•

Measurements: distances from known
transmitter locations via the measurementof radio frequency signal transit time
Solution to the estimation problem:
trilateration, the determination of absolute

400

or relative locations of points by300

measurement of distances using the200

geometry of circles, spheres, or triangles•

Ground based:
LORAN (1940s), Omega (1960s)•

Satellite-based:
Sputnik I (1957), Parus and Tskikada,Transit, MOSAIC, and SECOR (1960s)

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Y•

receiverbeacon 1
beacon 2
beacon 3

500

100
0
-100
-200
-200

0

200

400

600

X
Trilateration in 2 dimensions

Training on GNSS 2019 | Pathum Thani, Thailand

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GNSS
•

Global Navigation Satellite Systems (GNSS): radionavigation perfected•FeaturesAccuracy: 3D accuracies of a few meters and down to millimeters for users withspecialized equipment and processing
Availability: signal availability anywhere on Earth with a clear view of the sky
Integrity: the assurance that expected performance will be realized
SPACE SEGMENTCONTROL SEGMENT

Monitor Station
Ground Antenna
MasterControlStationNational Aeronautics and Space Administration

USER SEGMENT

Components of Global Positioning System (GPS) [3]Training on GNSS 2019 | Pathum Thani, Thailand

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GNSS (continued)•

Space segment
Constellation of satellites in near-circular, Medium Earth Orbits (~20,000 km) or
Geosynchronous Earth Orbits (~36,000 km), each satellite equipped with atomic clocks•

Control segment
Network of ground stations and antennas that perform monitoring of the constellation, checkfor anomalies, generate new orbit and clock predictions, build and send upload to spacecraft•

User segment
GNSS receivers—specialized radios that track GNSS signals and produce position andvelocity solutions, typically with low-cost clocks

GPS Control Segment
Greenland
AlaskaSchriever AFB
Colorado
Vandenberg AFB
California

New Hampshire
USNO Washington

United Kingdom

Cape Canaveral
FloridaSouth Korea

Bahrain

Hawaii

Guam

Ecuador

Ascension

Uruguay

Master Control Station
Ground Antenna
Air Force Monitor Station

GPS Space Segment [4]National Aeronautics and Space Administration

Kwajalein

Diego Garcia

South Africa

Australia

New
Zealand

Alternate Master Control Station
AFSCN Remote Tracking Station
NGA Monitor Station

GPS Control Segment [5]

GPS Receivers [6]UpdatedMay 2017
Trainingon
GNSS 2019 | Pathum Thani, Thailand

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GNSS applications•

Applications of satellite navigation are
everywhere•

Military•

Civilian
Transportation
Public services
Precise machine control
Timing and frequency
Surveying
Surveillance
Recreational Space
Scientific applications•

US spends about $1.0B-$1.5B on GPS
annually•

Annual direct economic benefit estimated atabout $70B, 0.4% GDP*

*www.gmps.gov/governance/advisory/meetings/2015-06/Leveson.pdf
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GNSS constellations•

GNSS is an umbrella term for satellite constellations that broadcast signals from space forradionavigation
Systems with global coverage: GPS (United States), Galileo (European Union), GLONASS(Russia), BeiDou (China)
Systems with regional coverage: NAVIC (India), QZSS (Japan)

NAVIC
GNSS constellations, augmentations, and regional constellations [7]National Aeronautics and Space Administration

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9Approximate GNSS Timeline

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GNSS status and future development
GPS
US
(24+)

National Aeronautics and Space Administration

GalileoEU(27)

GLONASS
Russia(24)

BeidouChina(35)

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GNSS status and future development•

Status of current GNSS constellations
GPS (US) - Fully operational with global coverage since 1995, 31 satellites in orbit, GPSIII
SV01 available for launch and SV01-10, issued a request for proposals in February 2018 forthe next block of satellites, GPS IIIF, awarded to Lockheed Martin Sept. 2018
GLONASS (Russia) – Full operational capacity / global coverage achieved in 1995, lost andthen regained in 2011, 23 satellites currently operational, modernization efforts underway
Galileo (European Union) – First launch in 2005, full operational capacity expected in 2020
with 27+ satellites, initial services available now with 16 full operational satellites in orbit
BeiDou (China) – currently providing service in Asia-Pacific, expected to reach global
coverage in 2020 with 35 satellites, includes MEO, HEO, and GEO sats.
NAVIC – Provides service to India region with GEO/GSO satellites, now operational, 7satellites
QZSS – Provides service to Japan region, HEO orbits for improved performance in urban
canyons, compatible with GPS, operational status in late 2018 with 4 satellites, future
expansion planned.
SBAS – Numerous regional Satellite Based Augmentation Systems (SBAS), e.g., WAAS,
EGNOS, SDCM, enhance GPS performance and integrity especially for civil aviation•

International collaboration is facilitated through the International Committee on GNSS (ICG) andother forums with the objective of inter-operability among the different constellations

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12Satellite-based augmentation systems(SBAS)•

Wide Area Augmentation System (WAAS)
Commissioned in 2003 and operated by the U.S. Federal Aviation Administration (FAA), toenable aircraft navigation in the U.S. National Airspace System (NAS)•European Geostationary Navigation Overlay System (EGNOS)
Three geostationary satellites and a network of ground stations
Augments the US GPS satellite navigation system in Europe•

Japan's Multifunction-Transport-Satellite Satellite Augmentation System (MSAS)
MSAS for aviation use was commissioned in 2007•

India's GPS and Geo-Augmented Navigation System (GAGAN)•

Russian System of Differential Corrections and Monitoring (SDCM)

SBAS: Satellite-based GNSS augmentations [23]National Aeronautics and Space Administration

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Other augmentations• Nationwide Differential GPS System (NDGPS):

Ground-based augmentation system of ~80 sites operated by the U.S.
Coast Guard, Federal Railroad Administration, and Federal Highway
Administration, to provide increased accuracy and integrity to U.S. users
on land and water.
• Local Area Augmentation System (LAAS):

Augmentation to GPS that focuses its service on the airport area
(approximately a 20-30 mile radius)
Broadcasts correction message via a very high frequency (VHF) radio datalink from a ground-based transmitter
LAAS is a US activity led by the FAA, but other nations are developing theirown ground based augmentation system projects• NASA Global Differential GPS (GDGPS) System:GDGPS is a commercial high accuracy (~ 10cm) GPS augmentation
system, developed by the Jet Propulsion Laboratory (JPL) to support realtime positioning, timing, and orbit determination requirements.

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International coordination• International coordination is critical to ensure compatibility andinteroperability• US has bilateral agreements or joint statements with all majorinternational GNSS service providers• International committee on GNSS (ICG) Established in 2005

under the umbrella of the United Nations to provide forum fordiscussion
Purpose is to promote voluntary cooperation on matters of mutual interestin order to ensure greater compatibility, interoperability, and transparency
among GNSS systems
13th ICG held in Xi’an, China in November 2018

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Benjamin Ashman, Ph.D.
Navigation and Mission Design Branch
Code 595, NASA Goddard Space Flight Center
Greenbelt, MD 20771
benjamin.w.ashman@nasa.gov

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GPS Introduction

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GPS history• Developed by the US Department of Defense
Early GPS program driver was Trident Missile Program (Submarine
launched ICBM)
Satellites carry a nuclear detonation detection payload• Early satellite navigation systems
TRANSIT (Doppler positioning)
Timation (first atomic frequency standards flown in space)
USAF 621B Program (use of PRN codes for ranging)• First prototype GPS satellite launched in 1978
• First Block II (Operational) GPS satellite launched 1989
• Full Operational Capability declared in 1994

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Current GPS constellation status•

31 space vehicles currently in operation
0 GPS IIA
12 GPS IIR
7 GPS IIR-M

Block II/IIA
Built by Boeing Aerospace
Launched 1989 - 1997

12 IIF•

several additional satellites in residual
status•Continuously assessing constellation
health to determine launch need•

Global GPS civil service performance

Block IIR/IIR-M
Built by Lockheed Martin
Launched 1997 - 2009

commitment met continuously sinceDec 1993

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Block IIF
Built by Boeing AerospaceFirst Launch in 2010

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GPS – three segments

SPACE SEGMENTCONTROL SEGMENT

Monitor Station
GroundMasterAntenna
Control Station
USER SEGMENT

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GPS space segment• Nominal 24 satellite constellation
Semi-synchronous, circular orbits(~20,200 km/10,900 nautical
miles altitude)
Repeating ground tracks(11 hours 58 minutes)
Six orbital planes, inclined at 55
degrees, four vehicles per planeØ Designed for global coverage (at least 4 sats in view)• Redundant cesium and/or rubidium clocks on board eachsatellite• There have been 1-4 replenishment launches per year inrecent years

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GPS control segment
SPACE VEHICLE
Broadcasts the Signal in Space (SIS) PRN codes,
L-band carriers, and 50 Hz navigation message (stored in memory)

SPACE-TO-USER INTERFACEMONITOR STATIONn
Sends raw
observations to MCS

MASTER CONTROL STATIONn
Checks for anomaliesnnnNational Aeronautics and Space Administration

CONTROL-SPACE INTERFACE

Computes SIS portion of URE
Generates new orbit and clock
predictions
Builds new upload and sends to GA

GROUND ANTENNAn
Sends new upload
to SV

Training on GNSS 2019 | Pathum Thani, Thailand

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GPS control segment (cont.)•

The current operational control segment includes a master control station, an alternate master
control station, 12 command and control antennas, and 16 monitoring sites.

•

Data from Air Force and NGA monitor stations incorporated into Control Segment Kalman filter
solution.

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GPS user segment•

GPS receivers are specialized “radios” that track
GPS signals and produce position and velocity
solutions

Military Spacecraft(~$2,000,000)

Wide range of cost/sophistication depending on theapplication•

Signals from 4 or more GPS satellites are
required, but 8-10 are typically available at any
time•

Low cost civil (SPS) receivers typically track only
the L1 C/A signal•

Precise Positioning Service receivers havespecial keys that allow tracking of the encrypted
military codes transmitted on L1 and L2 signals•

High performance civil receivers use special
techniques to track the legacy military signals andnow track new signals provided by GPS andother GNSS systems

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Consumer/Recreation(~$100-500)

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Legacy GPS signal structure• Two L-band carrier frequencies
L1 = 1575.42 MHz

L2 = 1227.60 MHz• Two PRN Codes – Uniquely Identify
Each Satellite
C/A: Coarse Acquisition (Civilian) Code» Broadcast only on L1 carrier» Available to all users» Short code simplifies acquisition

P(Y): Military Code» Encrypted code sequence» Available only to authorized users on

both L1 and L2 carriers» Improved performance, jam resistance• PRN Codes are modulated with Navigation
Message Data
Provides ephemeris data and clock
corrections for the GPS satellites andadditional info
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Baseline GPS constellation [24]Training on GNSS 2019 | Pathum Thani, Thailand

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GPS modernization• Goals
System-wide improvements in:» Accuracy» Availability» Integrity

Robustness against interference
Improved indoor, mobile, and urban use
Interoperability with other GNSS constellations
Backward compatibility• Achieved throughModernized Space and Ground segments
New signals
Improved “CNAV” data message

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GPS modernization: new civil signals•

L2C @ 1227.60 MHz= 120*10.23 MHz (GPS IIR-M 2005)
Allows ionospheric error removal for civilian users
Two time-multiplexed PRN codes, one is dataless•L5 @ 1176.45MHz = 115*10.23 MHz (GPS IIF 2009)
Designed for safety of life applications
In highly protected ARNS band•

L1C @ 1575.42 MHz = 154*10.23 MHz (GPS III 2018)
Interoperable with other GNSS systems
Multiplexed Binary Offset Carrier modulation reduces interference with L1C/A, may allow
higher accuracy tracking•

All modulated with improved CNAV or CNAV-2 packetized data message with forward
error coding.
First demonstration conducted in Jun 2013.
Pre-operational CNAV now continuously broadcast with daily updates.

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GPS modernization: spectrum
Legacy Signals

As of 4/2017:
L2C broadcast from 19
satellites
L5 broadcast from 12
satellites

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GPS modernization: space segment status

https://www.gps.gov/systems/gps/space/#generations
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GPS modernization: ground segment•

Legacy ground system is known as the Operational Control System (OCS). Several
modernization efforts have been implemented or are in progress•

L-AII: Legacy Accuracy Improvement Initiative (completed 2008)
Added 10 NGA monitoring sites to bring total to 16•

AEP: Architecture Evolution Plan (2007-current)
Broad OCS system upgrade. Manages current modernized constellation•

LADO: Launch and early orbit, Anomaly resolution, and Disposal Operations (fielded2007)
Handles GPS satellites outside operational constellation•

OCX: Next Generation Operational Control Segment (contract awarded 2008,
multiphase rollout 2017-2021)
Eventually replace OCS, control GPS III•

Risk Mitigations to late OCX delivery
COps: GPS III Contingency Ops program (delivery in 2019)»

Enable GPS III’s “IIF features” prior to OCX Block 1 (2021)

MCEU: MCode Early Use - MCEU»OCS upgrades to support MCode operational testingwww.gps.gov, http://gpsworld.com/2016-in-review-gps-navigates-the-future/

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GPS III Status•

Newest block of GPS satellites
First to broadcast common L1C signal
Multiple civil and military signals;» L1 C/A, L1 P(Y), L1M, L1C,
» L2C, L2 P(Y), L2M,
» L5

Three Rubidium clocks
First launch in ~2018 timeframe•

Lockheed Martin in Denver CO awarded
contract for two (SV01/02) development andsix operational satellites (SV03-08), with option
for two more (SV09-10) exercised in 2016.

•

GPS III SV11+ awarded to Lockheed Martin
Sept. 2018. Will add:
Laser Retro-reflector Array

http://gpsworld.com/2016-in-review-gps-navigates-the-future/

Search and Rescue payload
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GPS documentation• System technical docs available on www.gps.gov• GPS IS-200:

Spec. of legacy C/A & P codes and NAV message
Rev E and beyond adds L2C and CNAV
• GPS IS-800:

Specification of L5, and L5 CNAV• SPS & PPS Performance standards

Defines the guaranteed level of performance in terms of Signal in Space(SIS) accuracy and Constellation design
Current system performance surpasses minimum spec and is improving.

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Benjamin Ashman, Ph.D.
Navigation and Mission Design Branch
Code 595, NASA Goddard Space Flight Center
Greenbelt, MD 20771
benjamin.w.ashman@nasa.gov

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GPS Space Applications

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Space Uses of Global Navigation
Satellite Systems (GNSS)• Real-time On-Board Navigation: Precision
formation flying, rendezvous & docking,station-keeping, Geosynchronous Orbit(GEO) satellite servicing• Earth Sciences: GPS as a measurement foratmospheric and ionospheric sciences,
geodesy, and geodynamics• Launch Vehicle Range Operations:
Automated launch vehicle flight termination;
providing safety net during launch failures &enabling higher cadence launch facility use• Attitude Determination: Some missions, suchas the International Space Station (ISS) are
equipped to use GPS/GNSS to meet theirattitude determination requirements• Time Synchronization: Support precise timetagging of science observations andsynchronization of on-board clocks

GPS capabilities to support space users will be further improved bypursuing compatibility and interoperability with GNSS
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35

Main radiometric
instrument:
NASA/JPL
BlackJack GPS
receiver modified to
track gravitysensing crosslinks,
and to form starcamera solutions,while producing cmlevel POD and 0.1
nanosecond
relative timetransfer.
The Onera
accelerometer was
also required to
produce accurate
gravity maps.

(image credit:
National Aeronautics and Space Administration
NASA)Results from GRACEGRACE data have significantly improved understanding of: the global water cycle, mass and energy
exchange within and between the Earth System components, the changes in ocean mass, thechanging dynamics of polar ice caps and large continental aquifers and improved the prospects for
assimilation of mass change data into climate models.
Examples of science applications include:

Sea level change
Surface and Deep Ocean Currents
Ocean heat storage
Polar and continental ice sheet melt
Earth system mass transport
Drought and flooding
Land surface total water storage
Modeling and assimilation
Earthquake assessment
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GPS use aboard Space Launch System
EM-1

EM-2

SM-1

Exploration Mission 1

Exploration Mission 2

Science Mission 1

2021
Block 1: ICPS
Cargo

2022
Block 1: ICPS
4 Crew

2023
Block 1B Cargo
Europa Clipper

Cis-Lunar
Space Mission
to confirm
vehicleperformanceand operational
capability.

First crewed
mission, toconfirm vehicle
performanceand operational
capability, sameprofile as EM-1.

First cargo
missionconfiguration.

13 CubeSat
Payloads

Orion Capsule+ Crew

EuropaClipper toJupiter

Cis-Lunar Trajectory
11-21 days

Honeywell SIGI with SPS
Trimble Force 524D (L1 C/A
Code Only) for Orbit
Determination, Trans-Lunar
Injection Burn and End-ofMission disposal burn.

Multi-TLI
Lunar Free Return
8-21 days

SIGI w/SPS Force 524D

Jupiter Direct
2.5 years

Honeywell Mercury SPS for
High-Alt SLS Vehicle Nav.

EM-4

EM-5

Exploration Mission 3

Exploration Mission 4

Exploration Mission 5

2024
Block 1B: EUS
4 Crew

2025
Block 1B: EUS
4 Crew

2026
Block 1B: EUS
4 CrewFirst Orion
Docking to
extract Habitat
Module from
EUS, deliver to
Lunar Orbit
Platform Gateway

Deliver
Logistics
Module to
Lunar
Gateway

Deliver
Airlock
Element to
Lunar
Gateway

LOP-G
Habitat Module

LOP-G
Logistics
Module

LOP-G
Airlock
Element

EM-3

Near-Rectilinear Halo
Orbit (NRHO)
16-26 days

Near-Rectilinear Halo
Orbit (NRHO)
26-42 days

Near-Rectilinear Halo
Orbit (NRHO)
26-42 days

Honeywell Mercury SPS for
High-Alt SLS Vehicle Nav.

Honeywell Mercury SPS for
High-Alt SLS Vehicle Nav.

Honeywell Mercury SPS for
High-Alt SLS Vehicle Nav.

SLS Mission Data is based upon SLS-DDD-284, Space Launch System Mission Configuration Definition, Draft Version, October 2018.

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Restore-L

2022(image credit: NASA)
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National
Aeronautics and Space Administrationge credit:
NASA)

PACE MISSIONPACE will extend and improve NASA’s
20 plus years of global satellite
observations of our living ocean,
atmospheric aerosols, and clouds andinitiate an advanced set of climaterelevant data records. By determining
the distribution of phytoplankton, PACE
will help assess ocean health. It will
also continue key measurements
related to air quality and climate.
Science Goals
To extend systematic ocean color,atmospheric aerosol, and cloud data
records for Earth system and climate
studies. To address new and emerging
science questions by detecting abroader range of color wavelengths
that will provide new andunprecedented detail.
National
Aeronautics
and Space Administration(imagecredit:NASA)

Key Mission Characteristics• Hyperspectral ocean color
instrument• Two multi-angle polarimeters• Launch readiness date: Fall 2022
• 675 km (419 mi) orbital altitude• Sun-synchronous, polar orbit• Global coverage every two days
• Managed by Goddard Space Flight
CenterGPS Antenna Characterization
Experiment (ACE)
Overview• GPS L1 C/A signals from GEO are available at a
ground station through a “bent-pipe” architecture• Map side lobes by inserting advanced, weak-signal
tracking GPS receivers at ground station to record
observations from GEO
Data Collection & Visualization• Trace path of GEO vehicle in antenna frame of each
GPS vehicle• Reconstruct full gain pattern after months of tracking

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ACE Results Average Transmit Gain –Block IIR••

In-flight averaged over all SVNs in block in 1 deg x 1 deg bins
Remarkable similarity between average flight and ground measurements– Note matching patterns in nulls around outer edge
In-Flight

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Ground43

ACE Results Average Transmit Gain –Block IIA/IIF••

Averaged over all SVNs in block in 1 deg x 1 deg bins
IIF side lobes are shifted 45 deg in azimuth from other blocks

IIA

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IIF

44

GPS ACE Conclusions• GPS ACE architecture permits tracking of extremely weak signals overlong duration– MGPSR produces signal measurements well into back lobes of GPS vehicles– 24/7 GPS telemetry provides near continuous tracking of each PRN• First reconstruction of full GPS gain patterns from flight observations– Block averages of IIR, IIR-M show remarkable consistency with groundpatterns• Demonstrates value in extensive ground testing of antenna panel– Characterized full gain patterns from Blocks IIA, IIF for the first time
– Patterns permit more accurate simulations of GPS signal availability for future
HEO missions• Additional analysis of pseudorange deviations indicate usable
measurements far into side lobes• Dataset available at: https://esc.gsfc.nasa.gov/navigation
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Recent Results: Lunar GPS•

NASA has recently published two studies looking at the feasibility of GPS navigation
at lunar distances:• ION GNSS+ 2017: Winternitz, et al1• Published MMS Phase 2 results using GPS to 25 RE• Projected MMS performance to lunar distance• AAS GN&C 2018: Ashman, et al2• Looked broadly at GPS visibility for different antennas and C/N0 receiverthreshold values• Validated results vs. MMS and GOES-16 flight data•

These studies represent early GPS-only analyses that could be used as basis for
WG-B in-depth analysis.

1Winternitz, Luke B., Bamford, William A., Price, Samuel R., "New High-Altitude GPS Navigation Results from the MagnetosphericMultiscale Spacecraft and Simulations at Lunar Distances," Proceedings of the 30th International Technical Meeting of The Satellite
Division of the Institute of Navigation (ION GNSS+ 2017), Portland, Oregon, September 2017, pp. 1114-1126.
2Ashman, Benjamin W., Parker, Joel J. K., Bauer, Frank H., “Exploring the Limits of High Altitude GPS for Future Lunar Missions,”
National
AeronauticsAstronauticaland Space Administration
AmericanSociety Guidance and Control Conference, Breckenridge, Colorado, USA, February 2–8, 2017.

46

NASA’s Magnetospheric MultiScale (MMS)
Mission• Discover the fundamental plasma physics processof reconnection in the Earth’s magnetosphere.
• Coordinated measurements from tetrahedral
formation of four spacecraft with scale sizes from400km to 10km
• Flying in multiple highly-elliptical orbits:– Phase 1 1.2x12 RE (magnetopause) Mar ‘14-Feb ‘17– Phase 2B 1.2x25 RE (magnetotail) May ‘17-present– 2019: Apogee raise to 1.2x29 RE

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2017 MMS study:
Concept Lunar missionl Study: How will MMS receiver perform if used on a conceptual Lunar mission with 14dBi highgain antenna?
l GPS measurements simulated & processed using NASA GEONS filter.
l Visibility similar to MMS Phase 2B, as high-gain makes up for additional path loss§

Avg visibility: ~3 SVs; C/N0 peaks > 40dB-Hz (main lobes) or > 30 dB-Hz (side lobes)l Range/clock-bias errors dominate – order of 1-2 km; lateral errors 100-200 m§

With atomic clock, or, e.g., periodic 2-way range/Doppler, could reduce range errors to meas. noise level

Top: Signals tracked and radial dist to Earth (red)and Moon (cyan); Bottom: C/N0

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Filter position formal (3σ) and actual errors

48

2018 Lunar GPS Visibility Study• GPS constellation modeled as accurately
as possible, including sidelobe signals;
validated with GOES-16 and MMS flightdata• Calibrated models applied to outboundlunar near-rectilinear halo orbit (NRHO)GPS receiver reception with 22 dB-Hz
acq/trk threshold
Peak
Antenna
Gain

1+
Vis.

4+
Vis.

Maximum
Outage

7 dB

63%

8%

140 min

10 dB

82%

17%

84 min

14 dB

99 %

65%

11 min• A modest amount of additional antenna
gain or receiver sensitivity increases
coverage significantly
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2018 Lunar GPS Visibility Study
Conclusions

number of visible SVs
30

35

•

25

30

receiver threshold [dB-Hz]

These results show useful
onboard GPS navigation at
lunar distances is achievable
now using currently-available
signals and flight-provenreceiver technology.
• A modest increase in gain or
receiver sensitivity increases
visibility significantly.
• Future work must extend these
specific studies to fullnavigation analysis of cis-lunar
spacecraft, including effects of
DOP, and utilizing the fullcapability of multi-GNSS
signals.
• ICG WG-B is a natural forum
for these discussions andanalyses, in keeping with the
ICG-12 recommendation foranalysis for cis-lunar missions
National
Aeronautics
and Space Administration
andbeyond.

20

25

15

20
10

15
5

10

10

20

30

40

50

60

altitude [R E]

Number of satellites visible by altitude andreceiver threshold
50

Potential Future Application:
Lunar Orbital Platform—Gateway• NASA Exploration Campaign: Next step isdeployment and operations of US-led Lunar
Orbital Platform—Gateway (previously known as
Deep Space Gateway)• Step-off point for human cislunar operations,
lunar surface access, missions to Mars
• Features include:
•
•
•
•
•

Power and propulsion element (PPE) – targeted for 2022
Human habitation capability
Docking/rendezvous capability
Extended uncrewed operations (not continuously crewed)
Lunar near-rectilinear halo orbit (NRHO)• Gateway conceptual studies are continuing with
ISS partners––

Requirements to be baselined in 2018
To be followed by Broad Agency Announcement forpartnerships• Gateway represents a potential application for
on-board GNSS navigation• NASA will continue providing updates to WG-B asplans develop.
https://www.nasa.gov/feature/nasa-s-lunar-outpost-will-extendhuman-presence-in-deep-space
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51

Potential Future Application:
Lunar Orbital Platform—Gateway

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52

Global Exploration Roadmap•

The GER is a human space exploration roadmap developed by
14 space agencies participating in the International Space
Exploration Coordination Group (ISECG)‒ First released in 2011. Updated in 2013 and 2018.

•

The non-binding strategic document reflects consensus on
expanding human presence into the Solar System, including– Sustainability Principles, spaceflight benefits to society– Importance of ISS and LEO

www.globalspaceexploration.org
www.nasa.gov/isecg– The Moon: Lunar vicinity and Lunar surface– Mars: The Driving Horizon Goal
National Aeronautics and Space Administration

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53

GNSS Navigation Domain

National Aeronautics and Space Administration

10+ international lunar
exploration missions
planned for next 10 years;
many opportunities fordemonstration of lunar
GNSS capabilities

Global Exploration Roadmap

National Aeronautics and Space Administration

NASA-USAF SSV Collaboration• Oct 13 2017: Joint NASA-USAF Memorandum ofUnderstanding (MOU) signed
MOU addresses civil Space Service Volume (SSV) requirements
Scope relevant to GPS IIIF acquisition process» Civil space early insight into Block IIIF design relevant to SSV performance» Access to Block IIF, III, and IIIF technical data

• MOU results to-date:US civil space rep. from NASA supported GPS IIIF source selection team as SSV
technical expert
Built positive, collaborative relationships with IIIF acquisition team; provided civil
space insight continuing through design and production
NASA received released GPS IIF antenna pattern measurements per MOU and tosupport NASA Space Launch System need

MOU supports SSV signal continuity goals
for future space users
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56

Automatic Flight Termination System(AFTS)••••

Independent, self-contained subsystem mounted
onboard a launch vehicle
Flight termination / destruct decisions madeautonomously via redundant Global Positioning System(GPS)/Inertial Measurement Unit (IMU) sensors
Primary FTS for unmanned Range Safety Operations
and being considered as Primary FTS for human spaceflight (Commercial Crew and SLS)
Advantages:– Reduced cost—decreased need for ground-based assets– Global coverage (vehicle doesn’t have to be launched froma range)– Increased launch responsiveness– Boundary limits increase due to 3-5 second gain from nothaving Mission Flight Control Officer (MFCO)– Support multiple vehicles simultaneously (such as flyback
boosters)

April 2006: WSMR
Sounding Rocket

Mar 2007:SpaceX F1

Sept 2010: WFF
Sounding Rocket

Enabling low cost, responsive, reliable access to space for all users

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57

GAlileo Receiver for the ISS(GARISS)•

Objectives:– Demonstrate combined GPS/Galileo (L5/E5a)navigation receiver on-orbit with upload of Software Radio
waveform– Add waveform to Space Telecommunications Radio
Systems (STRS) waveform repository•

Approach/Benefits:– Adapt existing Galileo PNT code to Software DefinedRadio (SDR) inside ScAN Test Bed (STB) onboard
International Space Station (ISS)– Demonstrate operations, conduct PNT experiments on
ISS– Flexibility of SDR technology, STRS operating environment•

Timeline:– Initial discussions at International meetings (mid-2014)– Project formulation/export license (mid-2016)– Waveform design and development (late 2016-mid 2017)– Qualification and test the Galileo/GPS
waveform (mid 2017-late 2017)
National
and Space
Administration– Aeronautics
On-orbit
testingand experiments (2018)

ISS
STB onISSGARISS waveform
development is anelement of
NASA/ESA
cooperation
involving multiple
centers, Qascom
58On-orbit waveform integrationand testing•••

Moved integration and testing to on-orbit operations April 2018
Successful on-orbit acquisition, track and PVT solution
Full function for GPS and Galileo processing established at qualification review(May 2018) :• Acquisition and Time to First Fix (TTFF) requirements are met for Galileo and for
combined GPS/Galileo• GPS-only on-orbit PVT availability > 20%• Galileo -only on-orbit PVT availability > 40%• Achieved Combined Galileo/GPS PVT availability greater than 90%• ~64m RMS positional error (3D)
• First-ever on-orbit direct acquisition of L5/E5a (no L1 aiding)

Requirement(50 m)
3D ErrNational Aeronautics and Space Administration

59Real-Time Monitoring of GPS, GLONASS,
BeiDou, Galileo, and QZSS by the GDGPSSystem• Real-time (6 sec latency) orbit
determination operations• Additional hourly precise orbit
determination operations• Real time environmental
monitoring: earthquakes, space
weather, tsunamis• Differential Code Bias Monitoring for all
GNSS signals at high rate (especiallyneeded to monitor GPS Flex Power)

National Aeronautics and Space Administration

60

Cion – NASA’s new Software-Defined GNSSRadio Science Instruments for Cubesats
Low cost, low power, high performance space GNSS receiver for POD and radio occultations (RO)• Designed by JPL and built by Tyvak for initial use on GeoOptics’ CICERO RO Constellation• Based on the PicoZed off the shelf OEM computer and JPL’s TriG GPS receiver design• A NASA Class D version of this design has
recently been completed
Key Cion Features:• 3 antenna inputs with 4 down converterseach• 1.2 GHz Dual Core Arm processor• 30cm X 10cm X 6cm• 1 kg• ~10 watts at 12 VDC• Can be coupled with an external receiver to increase number ofchannels available for radio science

Tyvak-Built Cion Reciever

Successful operations on CICERO in orbit since March 2018,providing GPS and GLONASS radio occultation data
• Coupled with a Novatel GPS+GLONASS POD receiver• Launch of additional CICERO satellites anticipated in 2018
National Aeronautics and Space Administration

61

Summary•

NASA is engaged in numerous space-based GNSS initiatives that are bearing great fruit forscience and future mission development•

The NASA civil GNSS space user fleet is growing and expanding into new regimes
•
•
•

•

GRACE retired after 15 years of groundbreaking science
Space Launch System (SLS) has five upcoming cislunar exploration flights with GPS onboard
Restore-L and PACE will add to NASA’s extensive use of GPS in LEO

NASA studies on cislunar use of GPS show high level of potential performance in lunar orbit
with modest investments in receiver system capabilities.
•

The int’l Gateway project and the Global Exploration Roadmap provide numerous opportunities forin-depth study and inflight demonstrations.

•NASA’s GPS Antenna Characterization Experiment (ACE) has gathered and published themost extensive dataset on GPS antenna patterns for space users to-date, enabling a newseries of high-fidelity mission simulations in the SSV.

•

NASA technology developments have achieved numerous milestones:
•
•
•
•

•

Automatic Flight Termination System (AFTS) is providing operational GPS-based range safety since
2017
GARISS achieved the first direct acquisition of L5/E5a in space, and is exceeding its performancerequirements in initial flight tests
JPL GDGPS system is providing real-time monitoring of GPS, GLONASS, Galileo, BDS, QZSSNew JPL Cion GNSS receiver for CubeSats is operational on-orbit

We encourage GNSS providers to report on their activities to support the global space user
community and enhance the utility of interoperable GNSS in space
National Aeronautics and Space Administration

62

GPS Signal Structure

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63

Outline
I.

GNSS signals

IV.

Time reference, orbits, coordinate frames

II.

GNSS receivers

V.

Navigation solution

III.

Measurements

Block IIF GPS Satellite [2]National Aeronautics and Space Administration

Training on GNSS 2019 | Pathum Thani, Thailand

64

GPS signal structure•

What is required of a radionavigation signal?
1. Propagation delay between transmitter and receiver can be measured
2. Transmitters can be distinguished, enabling geometric diversity
3. Modulation allowing the signal to propagate through space•

For any signal p(t) combined with Additive White Gaussian Noise (AWGN) n(t),correlation with a copy of p(t) maximizes the output signal to noise ratio (SNR) (i.e., optimal
estimator in the Maximum Likelihood sense), so p(t) is designed to have a correlation shape thatsatisfies signal requirements 1 and 2•

Delay estimation
Consider a known, continuous-time signal p(t) generated at the transmitter that arrives at thereceiver with some delay tau:
In order to estimate tau, a local replica of p(t) is formed at the receiver with test delay tau tilde.
The delay estimate, tau hat, is the test delay that maximizes the average (over TI) of theinner product:

National Aeronautics and Space Administration

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65

GPS signal structure: code•

Autocorrelation in terms of alignment error,:

The ideal autocorrelation function would be•

Multiple signals are required in order to form a position estimate, however. The trilateration
problem relies on geometric diversity. One means of distinguishing transmitters is to minimize
the cross correlation of signals from different transmitters:•

These auto- and cross-correlation properties could be achieved with infinitely long random
sequences of +1 and -1, known at the transmitter and receiver, and unique to each transmitter

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66

GPS signal structure: code•

This is accomplished using Pseudorandom Noise (PRN) codes
Must be deterministic and finite for practical implementation, but sufficiently long and noiselike to approximate the desired autocorrelation and cross-correlation properties•

GPS Coarse Acquisition Code (C/A code) solution: Gold codes (modulo-2 sum of two linear
feedback shift registers)
Periodic sequence of {+1,-1} pulses called chips, unique to each GPS satellite, length 1023
with period of 1 ms (i.e., fchip = 1.023 MHz)

Selection of GPS C/A code [8]National Aeronautics and Space Administration

Training on GNSS 2019 | Pathum Thani, Thailand

67

GPS signal structure: carrier•

Third navigation signal requirement: modulation allowing the signal to propagate through space•

Radio frequencies used for satellite navigation—must penetrate atmosphere•

Apparent frequency at the receiver is Doppler shifted due to the relative motion of the transmitterand receiver

where

and

EM spectrum [9]National Aeronautics and Space Administration

Training on GNSS 2019 | Pathum Thani, Thailand

68

GNSS carriers•

A variety of carrier frequencies are used by GNSS providers
Color code: Blue—open signals, Red—restricted or encrypted signals
L5

L2

L1

1170 1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300
Frequency (MHz)

1560 1570 1580 1590 1600 1610

GPS
Current
GLONASS
SBAS

Galileo
QZSS

IRNSS
Proposed
BeidouProposed
GLONASS•GPS L1 (fL1 = 1.57542 GHz) will be used as an example in this presentation

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69

GPS signal structure (continued)•

Finally, signal is also modulated with 12.5 minute navigation message, a 50 bps binary
sequence containing time tags, GPS satellite ephemerides (i.e., transmitter locations), etc.

•

Time domain signal:+1 GPS Data Message

20ms

d (t )
50bps

-1
+1

Repeating 1023 Chip “PRN Spreading Code” (20 per data message bit)p(t)1.023Mbps-1

CarrierwL1 =1.57542 GHz+1-1

Composition of GPS signal in time domain [3]•+1Received L1 frequency signal from the i-th satellite

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70

GPS signal structure (continued)•

Received L1 signal from the i-th satellite•

Frequency domain signal:

1. Data Message Spectrum
0 Hz

50 Hz

Signal is “Spread”

2. Data x PRN Code Spectrum

0 Hz

1.023 MHzfrequency

3. Data x Code x Carrier Spectrum
This is the transmitted signal
0 Hz

1.023 MHz1.57542 GHz

Composition of GPS signal in frequency domain [3]National Aeronautics and Space Administration

Training on GNSS 2019 | Pathum Thani, Thailand

71

GNSS receivers•

Receiver has three main tasks:
1. Acquisition: Determine which satellites are visible and estimate the propagation delay
and Doppler associated with each
2. Tracking: Refine the delay and Doppler estimates and track these features as theychange over time
3. Navigation: Use measurements from all visible signals to estimate the receiver’s positionand velocity•

First the radio frequency signal is downconverted to an intermediate frequency (IF) forprocessing

BPF h(t)fc = fIF

Re(•)

I

ADC
fs > B

complex
IF data2cos(ωLO)
BPF h(t)fc = fIF

Im(•)

Q

ADC
fs > Bi-2sin(ωLO)

National Aeronautics and Space Administration

RF front end [10]Training on GNSS 2019 | Pathum Thani, Thailand

72

GNSS receivers: acquisition•

Acquisition seeks to determine whether a particular satellite is visible (via its unique PRN) andestimate its delay (modulo one code period, 1 ms) and Doppler•

Correlation of an incoming signal with a local replica, mismatched in frequency and delay, forms
what is known as an asymmetric ambiguity function:

Ambiguity function magnitude complete [3] (left) and zoomed in [11] (right)•

Delay and Doppler values are tried over a search space. Correlation magnitudes are comparedto the noise floor—if the carrier to noise spectral density exceeds a threshold, the signal isdetermined visible and the delay and Doppler at the correlation peak are used to seed tracking.

•

Pre-detection integration time, TI, is an important parameter in detecting weak signals.

National Aeronautics and Space Administration

Training on GNSS 2019 | Pathum Thani, Thailand73

GNSS receivers: tracking•

Tracking seeks to refine the delay and Doppler estimates produced by acquisition
1. Input signal is correlated with a local replica
2. Correlation result is filtered to produce error terms that quantify the difference between the
input and local signal
3. A feedback process makes adjustments to the local signal replica according to the error
terms

•

In addition to converging on the input signal delay and Doppler parameters, the tracking of a
dynamic signal allows for measurements of changing signal features and more accurate
estimates of the signal to noise ratio•

Most receivers compute three correlations
per signal: Early, Prompt, and Late
Phase of prompt corr. gives error signal for
carrier tracking
Comparing size of Early and Late corr.
gives error signal for PRN code tracking•

Coupled feedback loops DLL and PLL
maintain lock on code and carrier signal
parameters

National Aeronautics and Space Administration

Code and carrier tracking [3] from [11]Training on GNSS 2019 | Pathum Thani, Thailand

74

GNSS measurements•

GNSS observables (i.e., receiver outputs)
1. Pseudorange: propagation delay plus receiver clock bias (measured from the PRN code
to a fraction of a chip: ~meter level accuracy)
2. Doppler: measured frequency shift of the received carrier
3. Carrier phase: measured fractional and accumulated whole cycle phase of the carrier(measured to small fraction of 19 cm cycle: ~mm precision)
4. C/N0: carrier to noise spectral density estimate in dB-Hz

National Aeronautics and Space Administration

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75

GNSS measurements: pseudorange•

Pseudorange measured from the i-th satellite (“pseudo” because of receiver clock bias):

time of reception
according toreceiver clock

National Aeronautics and Space Administration

time oftransmission
according tosatellite clock

Training on GNSS 2019 | Pathum Thani, Thailand

76

GNSS measurements: pseudorange•

Pseudorange measured from the i-th satellite (“pseudo” because of receiver clock bias):

time of reception
according toreceiver clock•

time of transmission
according tosatellite clock

Transmission and receive times each expressed as a sum of the “true” time (i.e., the time
according to a common time standard, such as GPST) plus an unknown bias

National Aeronautics and Space Administration

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77

GNSS measurements: pseudorange•

Pseudorange measured from the i-th satellite (“pseudo” because of receiver clock bias):

true receiver
position•broadcast satellite
position

Propagation delay:ri is the geometric range between the i-th transmitting satellite and the receiver, |x – xit|
Qi is the satellite orbit error
IiL1 is the delay due to the ionosphere, a region of ionized gas in the upper atmosphere where
the time varying density of free electrons and ions introduces a dispersive (frequency
dependent) delay
Ti is the delay due to the troposphere, the lowest region of the atmosphere, a non-dispersive
medium consisting of dry gases and water vapor
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78

GNSS measurements: pseudorange (cont.)•

Propagation delay:

Acquisition and tracking measure code phase, i.e., ambiguous time of transmission modulo one code period(1 ms for GPS C/A code, or approximately 300 km):
The navigation message must be decoded to form a pseudorange•

Navigation message is organized into six
second subframes, each beginning with an
8-bit Telemetry word (TLM) and Hand-overword (HOW), the latter of which contains
the satellite time the subframe wastransmitted
svtime_of_transmission =svtime_of_subframe+bits_since_subframe_start*0.02+whole_cacodes_since_bit_start*0.001+whole_chips_into_current_cacode/1.023e6+frac_code_phase_chips/1.023e6;

National Aeronautics and Space Administration

Calculation of pseudorange using four satellites [12]Training on GNSS 2019 | Pathum Thani, Thailand

79Navigation solution: typical GPS error budget•

Error Source

Basic single frequency

Precise dual-freq, assisted

Ionosphere (< 1000 km)~3 m (single frequency,
using broadcast model)

Dual frequency<1 cm

Troposphere (< 20 km)

0.1-1 m

1 cm level using estimators,
advanced models

GPS orbits<2.0 m (broadcast ephem)

1 cm, Int. GNSS service (IGS)

GPS clocks<2.0 m (broadcast clock)1 cm (IGS)

Multipath (“clean”
environment)

0.5-1 m code

0.5-1 cm carrier

Receiver Noise0.25-0.5 m code

1-2 mm carrier

RSS range error

4m

2 cm

Typical GDOP2

2

RSS solution error

8m

4 cm

Disclaimer: for illustration purposes only

National Aeronautics and Space Administration

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80

GNSS measurements: pseudorange (cont.)•

Propagation delay:•

Orbit error
Maintained to within ~1 m RSS by Control Segment•

IonosphereGroup delay for pseudorange due to the ionosphere:
GPS ionospheric delay model: Klobuchar [13]where TEC is the Total Electron Content in a 1 m2 column
from the receiver the transmitter.
Ionospheric delay can be corrected by using measurementsfrom two frequencies (note frequency dependence, here
we use GPS L1) or through a model that predicts TEC
GPS uses the Klobuchar model, in which four parameters(defined by eight numbers in the navigation message) areused to define the daily zenith variation at the ionosphericpierce point
National Aeronautics and Space Administration

Geometry of zenith TEC (vertical TEC, VTEC) and slant TEC (STEC) [13]Training on GNSS 2019 | Pathum Thani, Thailand

81

GNSS measurements: pseudorange (cont.)•

Propagation delay:•

TroposphereNot frequency dependent, wet (< 0.25 m, large variation) and dry (~2 m, small variation)
components
Corrected using models (e.g., Hopfield) that incorporate empirical corrections—typicallyaverage meteorological parameters for latitude, longitude, and season•

Complete pseudorange expression:•

Relativity
Second-order Doppler shift: a clock moving in an inertial frame runs slower than a clock at rest
Gravitational frequency shift: a clock at rest in a lower gravitational potential runs slower thana clock at rest in a higher gravitational potential
GNSS space segment atomic clocks are offset to compensate for these effects—without
correction satellite clocks would gain almost 40 microseconds per day (~10 km range error)

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82

GNSS measurements: pseudorange (cont.)•

Propagation delay:•

Multipath
Reflected signals are received as delayed, attenuated replicas of the direct signal
Correlation shape of the combined signal causes an error in the code tracking loop that
depends on geometry, number and strength of reflections, and tracking loop design
E.g., one signal, noncoherent DLL:

Direct, building-reflected, and ground-reflected signal paths in multipath interference scenario [19]National Aeronautics and Space Administration

Direct, reflected, and composite correlations [10]Training on GNSS 2019 | Pathum Thani, Thailand

83

GNSS measurements (cont.)•

Measured Doppler shift is a combination of the changing geometric line of sight and theunknown receiver clock drift. Time derivative of the pseudorange:

recall:•unknown receiverclock drift

transmitter clock
drift approximately
known

Carrier phaseCan be measured with much higher precision than code phase (i.e., pseudorange), ~cm for
GPS, but ambiguous on the order of carrier cycles, 19 cm for GPS. Combine with code
measurements or use for precise measurement of change (Accumulated Delta Range)
Ionosphere also induces a delay, but opposite in sign relative to pseudorange, leading to acode/carrier divergence
Multipath also introduces an error in carrier phase measurements, as the geometry changes
and the received reflections cycle through constructive and destructive interference with thedirect signal. For a single reflection:

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84

GNSS measurements (cont.)•

Carrier phase (cont.)

Wall reflection

Ground reflection

Direct, building-reflected, and ground-reflected signal paths in multipath interference scenario [19]•Carrier to noise spectral density (C/N0) is the signal power divided by the measurement noise
power density. Unlike signal to noise ratio, SNR, this is independent of the receiver bandwidth B.
It is a power to noise density per unit frequency, expressed in units dB-Hz:

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85

GNSS measurements: link budget•

GNSS link budget
The received signal power is a combination of powerPowerspatialdensityspatial density produced by the transmitter at thereceiver and the effective area of the receive antenna:

Effective area is a measure of an antenna’s ability tocapture power in an electric field on the antenna from acertain direction, defined as:Power spatial density [1]An isotropic antenna radiates power equally in all directions. At a given distance from thetransmitter, R, the power density is simply the transmitted power divided by the surface areaof the sphere:

This accounts for spreading loss.

Spreading loss can be offset by focusing the transmitted power in a particular direction, aproperty described by the transmit antenna gain, GT. The power density at the receiver is:

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86

GNSS measurements: link budget•

GNSS received power
The power density at the receiver is:Thus for receive antenna gain GR the received power is given by the Friis transmission
formula:•Noise power per frequency unit:

Effective temperature used to characterize all noise, not just thermal•

Carrier to Noise Spectral Density

Typical values for GPS:TE = 290 K à N0 = -201 dBW-Hz, PR = -156 dBW à C/N0 = 45 dB-Hz
National Aeronautics and Space Administration

Training on GNSS 2019 | Pathum Thani, Thailand

87Summary of GNSS receiver procedure
1.

Point antenna toward sky signals

2.

Receiver acquires and tracks 4 or more signals

3.

At any given moment, latch code/carrier phase observables for 4+ signals

4.

Form pseudoranges from code/carrier observables, correct with error models

5.

Solve overdetermined system of nonlinear equations in least squares sense

6.

Output position, velocity, and time (PVT) to user

National Aeronautics and Space Administration

Training on GNSS 2019 | Pathum Thani, Thailand

88Outline
I.

GNSS signals

IV.

Time reference, orbits, coordinate frames

II.

GNSS receivers

V.

Navigation solution

III.

Measurements

National Aeronautics and Space Administration

Block IIF GPS Satellite [2]Training on GNSS 2019 | Pathum Thani, Thailand

89

GNSS time reference•

GNSS requires a common time scale forcomputing ranges•

GPS Time (GPST) is the operational timescale of GPS•

To keep satellites on GPST adequately,
atomic clocks are required
Corrections in the navigation message areused to synchronize satellites to GPSTFor example, to limit clock error to 1 m over
12 hrs requires drift < 8 x 10-14 s/s••

Tidal friction and other processes that cause a

GPST coarsely steered to align withsignificant redistribution of mass are slowing

Universal Consolidated Time (UTC) as

the Earth’s rotation, lengthening the solar day

maintained by the US Naval Observatory via

by ~2 ms / century

corrections in the navigation message•

Time systems [14]•UTC incorporates leap seconds to maintain

Traceability to UTC USNO enables precisealignment with sidereal time (UT1), but GPST

time and frequency transfer on a global

does not. This difference is a persistentscale

challenge for receiver designers and users.

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90

GNSS orbits•

Satellites make great reference points
Small number can provide global coverage
They can be precisely located•Orbital mechanics are well understood and satellite orbit
determination is a refined science; for GPS, for example,
the MCS estimates and predicts satellite orbits to lessthan 1 m•

Dual frequency observables from a network of monitor
stations used to estimate orbits and satellite clock biases•

Each GPS satellite broadcasts its ephemeris (valid for 24 hours) and an almanac (subset of ephemeris
parameters for every satellite in the constellation—notaccurate enough for navigation, but accurate enough for

Keplerian elements [16]a satellite search)•

International GNSS Service (IGS) and others maintainlarge networks of monitor stations, use advanced
techniques to locate satellites with cm-level accuracy

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91

GNSS Coordinate Frames•

Earth Centered Earth Fixed (rotating reference frame) versus Earth Centered Inertial (ECI)ECEF and ECI reference frames animation [15]•Explanatory video: https://youtu.be/DbYapFLJsPA

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92

GNSS Coordinate Frames•

GNSS orbit determination is performed in an inertial (non-rotating) frame
Example: Earth Mean Equator and Mean Equinox of the J2000 epoch (January 1, 2000 at
12:00 TT), x-axis is aligned with the mean equinox, z-axis aligned with the Earth’s spin axis
or celestial north Pole•

Terrestrial navigation is performed in an Earth-fixed frame (rotating with the Earth) for
convenience to users
Example: GPS uses the WGS84 frame, a 3-dimensional coordinate reference frame forestablishing geodetic latitude, longitude, and heights for navigation. Defined by the US
National Geospatial Intelligence Agency.

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93

Navigation solution•

Position estimation with pseudorange
Want to estimate receiver position and clock bias at some instant in time:

Given N > 4 pseudorange measurements (corrected for transmitter clock bias):

Standard approach is to solve as a non-linear least squares (NLLS) problem by GaussNewton method:

1. Linearize about initial guess
2. Solve linear least squares problem for3. Set4. Iterate

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94

Navigation solution: DOP•

In general, when solving the linear least squares problem•

The covariance of the least squares solution•

W (the inverse Gramian matrix) transforms measurement noise into solution noise•

In GPS, the i-th row of H is•Thus, W is determined by the geometry of the visible transmitters. Dilution of Precision (DOP):•

Examplesis

If transmitters are in a plane, H is rank deficient andIf transmitters are located at corners of a tetrahedron
National Aeronautics and Space Administration(minimum for N = 4)
Training on GNSS 2019 | Pathum Thani, Thailand95

Improving performance•

Multi-frequency receivers
Eliminate ionosphere as an error source through “ionosphere-free combination”•

Carrier phase observables
Millimeter rather than meter level measurement noise and negligible multipath error•

Differential measurements: Receivers in close proximity can be used to cancel common error
sources (e.g., Differential GPS, DGPS)
Ionosphere, troposphere, satellite orbit/clock can be cancelled by differencing measurements or solutions
Solution is relative•

Precision GNSS orbits and clocks
Available from global networks of reference receivers (e.g., International GNSS Service, ICG) for postprocessing and in near real-time•Augmentations
Additional transmitters and measurements enhance geometry•

Filtering
Incorporate dynamic constraints or additional measurement sources (e.g., inertial sensors)•

A combination of these techniques enables cm to mm level solutions

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References•

Luke Winternitz, “Introduction to GPS and other Global Navigation Satellite Systems,” in Proceedings of the
43rd Annual Time and Frequency Metrology Seminar, Boulder, CO, 14 June 2018.

•

James Garrison, AAE575: Introduction to Satellite Navigation and Positioning, Purdue University, Fall 2011.

•

Pratap Misra and Per Enge, Global Positioning System, 2nd ed. Lincoln, MA: Ganga-Jamuna Press, 2005.

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Benjamin Ashman, Ph.D.
Navigation and Mission Design Branch
Code 595, NASA Goddard Space Flight Center
Greenbelt, MD 20771
benjamin.w.ashman@nasa.gov

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Image references
1.

M. Pratap and P. Enge, Global Positioning System, 2nd ed. Lincoln, MA: Ganga-Jamuna Press, 2005.

2.

https://mk0spaceflightnoa02a.kinstacdn.com/wp-content/uploads/2014/12/GPS_IIF.jpg

3.

Luke Winternitz, “Introduction to GPS and other Global Navigation Satellite Systems,” in Proceedings of the 43rd Annual Time and Frequency Metrology
Seminar, Boulder, CO, 14 June 2018.

4.
5.

https://www.gps.gov/multimedia/images/constellation.jpg
https://www.gps.gov/multimedia/images/GPS-control-segment-map.pdf

6.

http://www8.garmin.com/aboutGPS/

7.

http://www.elenageosystems.com/GNSS.aspx

8.

https://natronics.github.io/blag/2014/gps-viz-1/

9.

https://smd-prod.s3.amazonaws.com/science-blue/s3fs-public/thumbnails/image/EMS-Introduction.jpeg

10.

B. Ashman, “Incorporation of GNSS Multipath to Improve Autonomous Rendezvous, Docking, and Proximity Operations,” Ph.D. dissertation, Purdue
University, 2016.

11.

M. Moreau, “GPS Receiver Architecture for Autonomous Navigation in High Earth Orbits,” Ph.D. dissertation, University of Colorado, 2001.

12.

http://insidegnss.com/wp-content/uploads/2018/01/IGM_janfeb12-Solutions.pdf

13.

https://link.springer.com/chapter/10.1007/978-3-319-42928-1_6

14.

http://www.navipedia.net/index.php/Transformations_between_Time_Systems

15.

https://youtu.be/DbYapFLJsPA

16.

https://en.wikipedia.org/wiki/Orbital_elements#/media/File:Orbit1.svg

17.

B. Ashman, J. Parker, F. Bauer, M. Esswein, “Exploring the Limits of High Altitude GPS for Lunar Missions,” AAS GN&C Conference, Breckenridge, CO,
American Astronautical Society, February 2018.

18.

J. Miller and J. Parker, “NASA GNSS Activities,” International Committee on GNSS 12, Kyoto, Japan, December 2017.

19.

G. McGraw, P. Groves, and B. Ashman, "Robust Positioning in the Presence of Multipath and NLOS GNSS Signals," Chapter 21 in 21st Century PNT,Jade Morton editor, 2018.

20.

National Geographic March 2018

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Image references (cont.)
21.

https://timeandnavigation.si.edu/navigating-at-sea/navigating-without-a-clock/celestial-navigation

22.

Winkler, S., Ramsey, G., Frey, C., Chapel, J., Chu, D., Freesland, D., Krimchansky, A., and Concha, M., “GPS Receiver On-Orbit Performance for the
GOES-R Spacecraft,” ESA GNC 2017, 29 May-2 Jun 2017, Salzburg, Austria.

23.

By Persimplex - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=18957671

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Optimality of correlation (cont.)•

See Introduction to Digital Communications by Michael B. Pursley

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