0. Brandon A. Jones University of Colorado / CCAR
Statistical Orbit Determination: Software Packages and Previous Research
Brandon A. Jones
University of Colorado / CCAR

1. Brandon A. Jones

2. Brandon A. Jones

3. The Orbit Determination Tool Kit (ODTK)
Brandon A. Jones
University of Colorado / CCAR

4. Introduction Summary of ODTK Scenario Setup Process Data Processing
Data Output
Sample Results
Brandon A. Jones

5. ODTK Description Provides OD and orbit analysis support
Estimates satellite state
Estimates environment parameters
Profile equipment characteristics
Covariance analysis
Integrated with Satellite Tool Kit (STK)
Primary Tools:
Tracking Data Simulator
Filter Capabilities
Least Squares Estimator
Sequential filter
Filter Smoother
Graph/Report Generator
Brandon A. Jones

6. ODTK Description Residual editing
Combines multiple observation sources to provide state estimate
Includes vehicle attitude variations
Advertises realistic covariance
CCAR studies have shown this varies from satellite to satellite
Brandon A. Jones

7. Scenario Setup Object Oriented Implementation
Satellites
Sensors: GPS Receiver/Antenna pair
Filters/Smoother
Etc.
Object Browser and Properties window provide primary interface
Brandon A. Jones

8. Satellite Filter Properties
Brandon A. Jones

9. Data Processing Two Primary Data Sources:
Simulation Data
External Data
Several external data formats recognized:
RINEX
More…
Data analysis automation through scripting
Monte Carlo Analysis
Brandon A. Jones

10. Data Processing
Data simulation tool is capable of generating all data sources processed by ODTK
Used for preliminary analysis and performance evaluation
Assists in satellite and ground station design phase
Helps determine operations requirements
Brandon A. Jones

11. Characterize filter & smoother
Filter Processing Direction
Filter (Current time process)
Smoother (Post-fit process)
Smoother Processing Direction
Prediction Error
Growth
Filter Correction
at Tracking Data
Data Gap
Smoother
Post-Fit
Solution

12. Data Output Smoother and Filter output as a STK ephemeris file
Can output state and covariance information
Brandon A. Jones

13. Data Output Easy import of ODTK output to STK
Allows for analysis utilizing other STK tools
Visual comparisons to another ephemeris
Brandon A. Jones

14. STK can be used to visualize OD Tool Kit process

15. Data Output Static/Dynamic Product Builder
Charts for visual output
Reports for data output
Multiple data formats: MS Word, PDF, Text
Reports allow for post-processing of ODTK results
Brandon A. Jones

16. Summary ODTK provides most OD software required for data analysis
Includes state estimate and covariance analysis capabilities
Data export capabilities provide increased flexibility during data analysis process
Questions?
Brandon A. Jones

17. Brandon A. Jones University of Colorado / CCAR
GIPSY-OASIS (GOA)
Brandon A. Jones
University of Colorado / CCAR

18. GOA Overview
GPS-Inferred Positioning SYstem and Orbit Analysis Simulation Software (GIPSY-OASIS)
Product of JPL/NASA
Square-Root Information Filter (SRIF)
SRIF Smoother
Advertises 1-2 cm level accuracy: on-orbit and terrestrial scenarios
Brandon A. Jones

19. GOA Uses Primarily processes GPS observations
Aids in mission design process
Provides capabilities to generate and process simulated observations
Aids in operational OD
Brandon A. Jones

20. GOA vs. STK/ODTK Advantages: Disadvantages Pedigree
Various modules/utilities have uses outside of GOA data processing
GOA provides increased scenario customization
Disadvantages
Requires increased understanding of OD process
Unix command line interface reduces user friendliness
GUI is provided, but reduces user control of OD processing
Brandon A. Jones

21. GOA Flowchart
Source: GOA Tutorial Course Notes
Brandon A. Jones

22. GOA Input Function inputs provided by FORTRAN namelist files
Processes simulated and recorded GPS observations
Recorded observation format: RINEX
Brandon A. Jones

23. GOA Output Outputs filter state in FORTRAN binary file
Includes utilities to convert output to text output in a variety of formats
.sp3, .jpltext, .sp1, etc.
Outputs covariance in similar binary file
Includes some graphical output capabilities
CCAR studies utilize MATLAB to customize graphical output
Brandon A. Jones

24. Brandon Jones University of Colorado - CCAR
Expected OD Accuracy for High Altitude, Highly Inclinated Satellites Using GPS
Brandon Jones
University of Colorado - CCAR

25. Outline Simulation development Summary of previous tests Results
Future work
Brandon A. Jones

26. GPS and OD (1) Continuous measurement coverage High accuracy (1-2 cm)
Range (CA and Phase)
Range-rate
High accuracy (1-2 cm)
Reduction in operation costs (Earth based tracking not required)
Pedigree
Brandon A. Jones

27. GPS and OD (2)
Satellite positions are known, thus range measurements are used to triangulate the satellite position
For real-time position estimation, four satellites must be visible for position estimation
Requires at least four equations for the four unknown values
X, Y, and Z
Time
Brandon A. Jones

28. GPS Visibility GPS satellites orbit at ~20,200 km altitude
Primary signals broadcast in 27.8 deg cone
Side lobes provide weakened signal
Limits satellite altitudes for optimal visibility
Acceptable for most LEO satellites
Brandon A. Jones

29. MEO/GEO and GPS Low elevation satellites provide measurements
Close to limb of Earth
Reduced signal power
Reduced satellite visibility
Brandon A. Jones

30. GPS S/V Inclination GPS Satellite inclination: 55 deg
Reduced visibility above poles
Low elevation satellites still visible
Brandon A. Jones

31. How do we determine accuracy and visibility?

32. Gipsy-Oasis Software package developed by NASA-JPL for POD studies
Specialized in GPS data processing
Implements a Sequential Square Root Information Filter (SRIF) with data smoothing
Provides capabilities for data simulation
Brandon A. Jones

33. Simulation Design Other error Sources (ionosphere, relativity, etc.)
Antenna Characteristics
Multipath Characteristics
Gravity Models:
GGM, EGM, etc.
Atmospheric Drag
Models
Brandon A. Jones

34. Gipsy-Oasis Simulation Design
Orbit
Integrator(oi)
High fidelity models
Gravity - JGM-03 70x70
Ocean Tides
Earth Tides
Atmo. Drag - DTM94
Relativistic Forces
Etc.
Low fidelity models
Gravity - JGM-03 70x70 True/Clone
Atmo. Drag - DTM79
True State File
Measurement generator (qregres)
Measurement Selector (C)
Add measurement noise (qm_noise)
Prepare data for filter (qregres)
Measurement File
“Wash Cycle”
preprefilter
prefilter
filter
smapper
Estimated State Files
Measurement Generation
State Estimation
True GPS S/V File
Estimate GPS S/V File
Brandon A. Jones

35. Previous Tests Case C: Case B: Case D: Case A: Eccentric orbit
Circular orbit
550 km altitude
96 deg inclination
Case C:
Eccentric orbit
622 x km altitude
55 deg inclination
Case B:
Eccentric orbit
520 x 7800 km altitude
deg inclination
Case D:
Molniya orbit
1600 x km altitude
63.4 deg inclination
Brandon A. Jones

36. Simulation Details Run for 3 orbital periods
GPS transmission EIRP: 28.2 dBW
Signal power strengths of at least 35 dB-Hz
12 Channel receiver modeled
Measurement types: DF M-code (Range and Phase)
Measurement noise:  = 1.72 m (Logan, 2005)
Filter noise (simulation dependent)
Brandon A. Jones

37. Results - Case D
Brandon A. Jones

38. Test Expansion Expand tests for many sun-synchronous orbits
Used software batch processing and Python to automate processing
Eccentricity between 0.0 and 0.5, increments of 0.2
Altitude of periapsis between 800 and 6300 km, increments of 250 km
Processed CA and Phase (DF, Single differenced measurements)
Filter and smoother
Gravity clones
Brandon A. Jones

39. Gravity Clone?
When gravity models determined, there is a corresponding covariance matrix
A gravity clone is a similar model that satisfies the covariance matrix
Used 6, 1- gravity clones of the JGM-3 model for reference trajectory
Allows for processing with gravity errors
Characterize impact on gravity error on state estimation
Brandon A. Jones

40. Distribution Satellite Inclination Average Number of Satellites
Brandon A. Jones

41. Smoothed Position
Brandon A. Jones

42. Smoothed Position Increased error with reduced number of satellites.
Inclination changes vs. accuracy
Brandon A. Jones

43. Filter vs. Smoother Small impact for CA and phase processing
RSS 1.334
RSS 1.159
Small impact for CA and phase processing
Has bigger impact with CA only processing (factor of 2)
Brandon A. Jones

44. Smoothed Position Gravity errors have an impact
True JGM-3
JGM-3 Gravity Clones
RSS = 1.159
RSS = 1.180
Gravity errors have an impact
Principal error source is measurement noise (~94%)
Brandon A. Jones

45. Other Tests Critically inclined orbits
Both prograde and retrograde
Eccentricities between 0.0 and 0.7, increments of 0.02
Altitude of periapsis between 800 and 20,200 km, increments of 500 km
Maximum altitude at apoapsis of 20,200 km (semi-synchronous orbit)
Recommended future tests include major transfer orbits
Increase model fidelity
Brandon A. Jones

46. Questions?