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Slide 1Satellite Navigation Colloquium > TUM > 13 Jan 2009
Real-Time Onboard Navigation of LEO Satellitesusing GPSO. Montenbruck, DLR/GSOC
Slide 2Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
Slide 3Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
Slide 4Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
Slide 5Satellite Navigation Colloquium > TUM > 13 Jan 2009
... 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
Slide 6Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
Slide 7Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
Slide 8Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
Slide 9Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
Slide 10Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
Slide 11Satellite Navigation Colloquium > TUM > 13 Jan 2009
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).
Slide 12Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
Slide 13Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
Slide 14Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
Slide 15Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
Slide 16Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
Slide 17Satellite Navigation Colloquium > TUM > 13 Jan 2009
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).
Slide 18Satellite Navigation Colloquium > TUM > 13 Jan 2009
Phoenix-XNS Signal Simulator Test (PROBA-2)
Slide 19Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
Slide 20Satellite Navigation Colloquium > TUM > 13 Jan 2009
RTNav with Broadcast Ephemerides (GRAS)
55 cm3D rms
Slide 21Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
Slide 22Satellite Navigation Colloquium > TUM > 13 Jan 2009
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?
Slide 23Satellite Navigation Colloquium > TUM > 13 Jan 2009
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
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