Statistical Orbit Determination: Software Packages and Previous Research

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Statistical Orbit DeterminationSoftware
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

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Introduction

• Summary of ODTK
• Scenario Setup Process
• Data Processing
• Data Output
• Sample Results

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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

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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
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
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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
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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

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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

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Outline

• 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?
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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

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Simulation Design
Other error Sources (ionosphere, relativity, etc.)
Antenna Characteristics
Multipath Characteristics
Gravity Models GGM, EGM, etc.
Atmospheric Drag Models
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Gipsy-Oasis Simulation Design
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Previous Tests

• Case A
• Circular orbit
• 550 km altitude
• 96 deg inclination

• Case C
• Eccentric orbit
• 622 x 20200 km altitude
• 55 deg inclination

• Case B
• Eccentric orbit
• 520 x 7800 km altitude
• 116.57 deg inclination

• Case D
• Molniya orbit
• 1600 x 38900 km altitude
• 63.4 deg inclination

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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)

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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 1.334
RSS 1.159

• 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

• 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
  (semi-synchronous orbit)
• Recommended future tests include major transfer
  orbits
• Increase model fidelity

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Questions?