colloquium montenbruck slides

Satellite Navigation Colloquium > TUM > 13 Jan 2009

Real-Time Onboard Navigation of LEO Satellitesusing GPSO. Montenbruck, DLR/GSOC


Real-Time Onboard Navigation of LEO Satellitesusing GPS

Navigating in SpaceMission needs ...

... and how to meet them

Real-Time Navigation SystemsConcept

Models and measurements

Filter Design

ApplicationsSample Implementations

How good can we get?

Summary


Mission Needs ...

Timing (~ 1 µs)Synchronization of onboard clock

Local Orbital Frame (~ 10 m, ~ 1 cm/s)

Conversion of star camera attitude

Instrument pointing (nadir or other)

Geocoding (1 – 10 m)Blending of payload data with position information (SAR, optical)

Autonomous Instrument and Mission Operations (1 m – 100 m)Open-loop altimeter operations

Target and ground station acqusition


Example: Sentinel-3 Open Loop Altimeter Operations

Gate window 60 m

(R,T,N) pos rms < (3,6,6) m

(R,T,N) vel rms < (2,2,2) cm/s


... and how to meet them

Adequate maturity and availability of spaceborne GPS technologySingle-frequency (navigation)

Dual-frequency (science, POD)

Conservative, bulky, costly!

Performance in LEO compatible with Standard Positioning Service No urban canyons, lower ionosphere

Few satellites above the poles

Typical positioning accuracy of 10 (-20) m


Really?

Limited kinematic positioning accuracyPseudorange noise 0.1 m – 3 m

Broadcast ephemeris errors (SISRE 1-1.5 m)

Ionospheric delays (few m)

Other issuesInsufficient velocity accuracy (few cm/s)

Lacking continuity (gaps, bad PDOP, outliers)

Theoretical accuracy potential not fully exploitedConservative design and requirements engineering


Real-Time Navigation Systems

Improved accuracy (0.5-1 m 3D rms)Reduced impact of measurement noise

Optional elimination of ionospheric delays in single-frequency processing

Partial elimination of broadcast ephemeris errors

Reduction of velocity error (long-term averaging)

Continuity and predictabilityUse of dynamical trajectory model

ProblemsComputational complexity (coding, verification)

Processor load


Real-Time Navigation Cookbook

Montenbruck O., Ramos-Bosch P.; „Precision Real-Time Navigation of LEO Satellites using Global Positioning System Measurements“; GPS Solutions 12(3):187-198 (2008). DOI 10.1007/s10291-007-0080-x

Ingredients

Dynamical model

Numerical integration

Measurement model

Filtering


Reference System Considerations

Terrestrial Reference Frame (ITRF, WGS84)Standard for modeling of GPS orbits and observations

Baseline for modeling of Earth gravitational acceleration

Inertial Reference Frame (ICRF, EME2000)Standard for celestial body ephemerides (Sun, Moon)

Common baseline for satellite trajectory propagation

Rigorous transformation requires full knowledge of Earth orientationparameters

Pole coordinates

UT1-TAI time difference

Typical user needs accurate ITRF position, but relaxed ICRF accuracy


Earth-Fixed Formulation

ITRF formulation of real-time navigation systemssimplifies the filter design

reduces the sensitivity to EOP errors

but increases the complexity of the equation of motion(law of conservation of trouble)

Apparent accelerationCoriolis and centrifugal terms

Rotation vector from ICRF-ITRF trafotransformation and its derivative

Practical approximationConstant angular velocity

Polar motion offset between ITRF z-axis and rotation axis

Accuracy ~100 nm/s2

[ ] TUUωΩ

rΩΩvΩ

rωωvωa

⋅−=×=⋅⋅+⋅⋅−=

××+×⋅−=

ɺ

22CC

⋅≈

⊕ω00

Πω


Gravitational Accelerations

Earth gravity fieldSpherical harmonics expansion

Degree and order 20 to 50

Optional: solid Earth tide (k2)

Luni-Solar PerturbationsPoint mass model

Low-order analytical series of luni-solar coordinates (1‘ to 5‘)

Simplified ICRF-to-ITRF transfomation (precession, Earth rotation)

∑∑∞

= =

⊕⊕ +∇=0 0

)sincos)((sinn

n

mnmnmnmn

n

mSmCPr

Rr

GM λλφaɺɺ

Cunningham L. E.; „On the Computation of the Spherical HarmonicTerms needed during the Numerical Integration of the Orbital Motion of an Artificial Satellite“; Celestial Mechanics 2, 207–216 (1970).


Non-Gravitational Accelerations

Air DragNo r/t access to solar flux & geomagnetic indices

Simple desity model (Harris Priester)

Adjustable drag coefficient

Solar Radiation PressureCannon-ball model

Cyclindrical shadow model

Adjustable rad. pressure coefficient

Maneuvers

Empirical AccelerationsAdjustable parameters

Compensation of force model deficiencies

va ⋅⋅−= vmA

CD ρ21

ɺɺ

23Sun AU⋅⋅⋅=

s

sa

mA

CP Rɺɺ

nnttrr aaa eeea ⋅+⋅+⋅=ɺɺ


Numerical Integration

Real-time navigation systemsFrequent measurement updates

Short propagation intervals (0.001 to 0.01 revs)

Limited resources

Use low order Runge-Kutta methods

RK4 with Richardson ExtrapolationCombines two RK4 steps of size h with one step of size H=2h

Gives 5th order at 6 function calls per h

Hermite interpolation5th order polynomial for y(t)=(r,v) from y0, y1 , y2 , y´0, y´1 , y´2

Gill E., Montenbruck O., Kayal H.; “The BIRD Satellite Mission as a Milestone Towards GPS-based Autonomous Navigation”; Navigation - Journal of the Institute of Navigation 48/2, 69-75 (2001).

Montenbruck O., Gill E.; „State Interpolation for On-board Navigation Systems“; Aerospace Science and Technology 5, 209-220 (2001). DOI 10.1016/S1270-9638(01)01096-3).

t0 t2t1t

yh

h

2h


Measurement Model

Ionosphere-free measurementsDual-frequency pseudorange (P12)

Dual-frequency pseudorange and carrier phase (P12 & L12)

GRAPHIC (GRoup and PHase Ionospheric Calibration) (C/A+L1)

Average of code and carrier phase measurement

Biased measurement

Noise reduced by 50%

Requires only C/A code tracking (better signal-to-noise ratio)

Broadcast ephemeridesSignal-In-Space-Range-Error ~ 1-1.5 m

ICD-GPS-200 models for GPS position, velocity, clock


Filter State Vector and Process Noise Model

NCH

1

3

1

1

33

DimState Vector

White noiseClock Offset

NoneDrag coefficient

Maneuver-free arcs: none

Maneuvers: white noise

PositionVelocity

(White noise)Biases

Expon. Correlated Random Vars.Empirical accelerations

NoneRadiation pressure coeff.

Process NoiseParameter

=

B

a

v

r

Y

tc

C

C

D

R

δemp


Update Scheme

Time Update

Data Screening

State Reconfiguration

Measurement Update

Time Update

Data Screening

State Reconfiguration

Measurement Update

Trajectory Integration

Trajectory Integration

High-Rate Processing Low-Rate Processing

Interpolation


Phoenix-XNS

Extension of DLR‘s Phoenix GPS receiver32-bit ARMTDMI microprocessor @30 MHz12 Channels L1 tracking

Real-time Kalman filtering of GPS rawmeasurements

Ionosphere-free C1+L1 combination

Code noise ~ 0.4 m, carrier phase <1 mm

Complements Phoenix standard software forGPS tracking and navigation

C++ software extension

40x40 gravity model

30s filter update rate

First in-flight demonstration on PROBA-2Montenbruck O., Markgraf M., Santandrea S., Naudet J., Gantois K., Vuilleumier P.; „Autonomous and Precise Navigation of the PROBA-2 Spacecraft“; AIAA-2008-7086; AIAA Astrodynamics Specialist Conference, 18-21 Aug. 2008, Honolulu, Hawaii (2008).


Phoenix-XNS Signal Simulator Test (PROBA-2)


RTNav Software

DLR analysis and development tool for trade-off and design studies

Offline implementation of real-time navigation filterRINEX observation interface

SP3 or RINEX ephemeris interface

Gravity model interface

User configurable processing parameters

Close match with XNS designSame core models and filtering scheme

Simple RK4 integrator (no need for interpolation)

Add on‘sAttitude and antenna offset modeling

Data editing

Maneuver handling


RTNav with Broadcast Ephemerides (GRAS)

55 cm3D rms


GRAS Preformance Study

0.81 m

1.08 m

0.55 m

3D rms

+0.01 ± 0.21-0.23 ± 0.69-0.05 ± 0.27 1F PR & CP

+0.01 ± 0.67+0.31 ± 0.69-0.06 ± 0.36 2F PR

-0.01 ± 0.21-0.05 ± 0.44-0.01 ± 0.24 2F CP (& PR)

Cross [m]Along [m]Radial [m]Data Type

Broadcast ephemerides, 70x70 gravity field

0.14 m

0.35 m

0.55 m

3D rms

+0.01 ± 0.05+0.03 ± 0.08+0.04 ± 0.08 JPL R/T

+0.01 ± 0.10-0.03 ± 0.28+0.00 ± 0.18 IGU predicted

-0.01 ± 0.21-0.05 ± 0.44-0.01 ± 0.24 Broadcast

Cross [m]Along [m]Radial [m]Ephemeris

0.14 m

0.35 m

0.55 m

3D rms

+0.01 ± 0.05+0.03 ± 0.08+0.04 ± 0.08 JPL R/T

+0.01 ± 0.10-0.03 ± 0.28+0.00 ± 0.18 IGU predicted

-0.01 ± 0.21-0.05 ± 0.44-0.01 ± 0.24 Broadcast

Cross [m]Along [m]Radial [m]Ephemeris

Dual Frequency Carrier Phase, 70 x 70 gravity field


Outlook

GalileoTargeted SISRE 0.8 m

Improved clocks (H-Maser)

Needs to demonstrate competetivness

TDRSS Augmentation Satellite System (TASS)Real-time transmission of precise GPS orbit and clock information via geostationary satellite

Enables real-time navigation at the 10 cm level

Future usersRadio-occultation missions ?

SAR imaging ?

Are we too good?


Summary

Dynamical filtering of GPS measurements offers improvedAccuracy

Robustness

Predictability

Reference algorithms definedCompatible with low power microprocessors

Real-time capability demonstrated (Phoenix)

Proper accuracy (0.5 m 3D rms) demonstratedBroadcast ephemerides sufficient for current applications

Even single-frequency GPS can provide excellent performance

Next stepsImplementation in Sentinel-3 GPS receiver (RUAG)

XNS flight demonstration on PROBA-2

colloquium montenbruck slides

Documents

leo compatible

modeling of gps orbits

standard positioning

spacemission needs

accurate itrf position

n vel rms

n pos rms

mission operations