Statistical Orbit Determination:
Software Packages and Previous
Research
Brandon A. Jones
University of Colorado / CCAR
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The Orbit Determination Tool Kit
(ODTK)
Brandon A. Jones
University of Colorado / CCAR
Introduction
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Summary of ODTK
Scenario Setup Process
Data Processing
Data Output
Sample Results
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ODTK Description
• Provides OD and orbit analysis support
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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
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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
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Scenario Setup
• Object Oriented
Implementation
– Satellites
– Sensors: GPS
Receiver/Antenna pair
– Filters/Smoother
– Etc.
• Object Browser and
Properties window
provide primary
interface
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Satellite Filter Properties
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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
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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
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Characterize filter & smoother
Intrack Position Uncertainty (0.95P)
Two Sigmas (m)
1600
Filter Processing Direction
Filter (Current time process)
Smoother (Post-fit process)
Smoother Processing Direction
Prediction Error
Growth
1200
Filter Correction
at Tracking Data
Data Gap
800
Smoother
Post-Fit
Solution
400
0
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AGI
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Hours
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www.agi.com
Data Output
• Smoother and Filter
output as a STK
ephemeris file
• Can output state and
covariance
information
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Data Output
• Easy import of ODTK output to STK
– Allows for analysis utilizing other STK tools
– Visual comparisons to another ephemeris
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STK can be used to visualize OD Tool Kit
process
AGI
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www.agi.com
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
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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?
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GIPSY-OASIS (GOA)
Brandon A. Jones
University of Colorado / CCAR
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
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GOA Uses
• Primarily processes GPS observations
• Aids in mission design process
– Provides capabilities to generate and process
simulated observations
• Aids in operational OD
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GOA vs. STK/ODTK
• Advantages:
– 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
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GOA Flowchart
Source: GOA Tutorial Course Notes
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GOA Input
• Function inputs provided by FORTRAN
namelist files
• Processes simulated and recorded GPS
observations
– Recorded observation format: RINEX
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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
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Expected OD Accuracy for
High Altitude, Highly Inclinated
Satellites Using GPS
Brandon Jones
University of Colorado - CCAR
Outline
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Simulation development
Summary of previous tests
Results
Future work
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GPS and OD (1)
• Continuous
measurement coverage
– Range (CA and Phase)
– Range-rate
• High accuracy (1-2 cm)
• Reduction in operation
costs (Earth based
tracking not required)
• Pedigree
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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
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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
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MEO/GEO and GPS
• Low elevation
satellites provide
measurements
– Close to limb of Earth
• Reduced signal
power
• Reduced satellite
visibility
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GPS S/V Inclination
• GPS Satellite
inclination: 55 deg
• Reduced visibility
above poles
• Low elevation
satellites still visible
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How do we determine
accuracy and visibility?
Gipsy-Oasis
• Software package developed by NASAJPL for POD studies
– Specialized in GPS data processing
• Implements a Sequential Square Root
Information Filter (SRIF) with data
smoothing
• Provides capabilities for data simulation
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Simulation Design
X 
 
Y 
Z 
 
X  XÝ
YÝ
Ý
Z
 

 

Other error
Sources
(ionosphere,
relativity, etc.)
Antenna Characteristics
Multipath Characteristics
Gravity Models:
GGM, EGM, etc.
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Atmospheric Drag
Models
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Gipsy-Oasis Simulation Design
High fidelity models
Gravity - JGM-03 70x70
Ocean Tides
Earth Tides
Atmo. Drag - DTM94
Relativistic Forces
Etc.
True State File
Measurement
generator
(qregres)
Orbit
Integrator(oi)
Measurement
Selector (C)
Add measurement
noise (qm_noise)
Measurement Generation
True GPS S/V File
Measurement File
Estimated State Files
State Estimation
Low fidelity models
Gravity - JGM-03 70x70 True/Clone
Ocean Tides
Earth Tides
Atmo. Drag - DTM79
Relativistic Forces
Orbit
Integrator(oi)
Prepare data for
filter (qregres)
“Wash Cycle”
preprefilter
prefilter
filter
smapper
Estimate GPS S/V File
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Previous Tests
• Case A:
• Case C:
– Circular orbit
– 550 km altitude
– 96 deg inclination
– Eccentric orbit
– 622 x 20200 km
altitude
– 55 deg inclination
• Case B:
• Case D:
– Eccentric orbit
– 520 x 7800 km altitude
– 116.57 deg inclination
– Molniya orbit
– 1600 x 38900 km
altitude
– 63.4 deg inclination
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Simulation Details
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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)
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Results - Case D
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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
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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
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Distribution
Satellite Inclination
Average Number of Satellites
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Smoothed Position
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Smoothed Position
• Increased
error with
reduced
number of
satellites.
• Inclination
changes vs.
accuracy
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Filter vs. Smoother
Filter
Smoother
RSS 1.159
RSS 1.334
• Small impact for CA and phase processing
• Has bigger impact with CA only processing (factor of 2)
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Smoothed Position
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%)
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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 (semisynchronous orbit)
• Recommended future tests include major
transfer orbits
• Increase model fidelity
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Questions?