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An Analysis of State Vector Propagation Using Differing Flight Dynamics ProgramsPowerPoint Presentation

An Analysis of State Vector Propagation Using Differing Flight Dynamics Programs

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### An Analysis of State Vector Propagation Using Differing Flight Dynamics Programs

David A Vallado

Analytical Graphics Inc.

Center for Space Standards and Innovation

Paper AAS-05-199, Presented at the AAS/AIAA Space Flight Mechanics Conference, Copper Mountain Colorado, January 23-27, 2005

Overview Flight Dynamics Programs

- Introduction
- Standards
- Objective
- Potential Error Sources
- Initial State Vectors
- Programs

- Input Data Sources
- Using the Input Data
- Interpolation, timing, etc
- State vector format

- Study Process
- Build up the force models

Overview (continued) Flight Dynamics Programs

- Results
- Force Model Sensitivity Analysis
- Individual Force Model Contributions
- Gravity
- Atmospheric Drag
- Solar Radiation Pressure

- Ephemeris Comparison Results
- Gravity
- Third Body
- Solar Radiation Pressure
- Atmospheric Drag
- Combined Forces

- POE Comparison Results

- Force Model Sensitivity Analysis
- Community Standard Ephemeris Baseline
- Conclusions

Introduction Flight Dynamics Programs

- Numerically derived state vectors
- Not new to astrodynamics
- Navy 1st full numerical catalog in 1997

- Answer fundamental question
- What observations and processing are needed to achieve a certain level of accuracy on a particular satellite, now, and at a future time?
- Requires
- Orbit Determination
- Propagation*
- Standards
- Other

Objectives Flight Dynamics Programs

- Demonstrate the inconsistencies of AFSPC Instructions
- 33-105 and 60-102

- Standards are useful when properly applied
- Computer code is not a standard
- Mathematical theory is a standard
- Historically
- SGP4 vs. PPT
- Mathematical theory differences

- Bad example of a need for standards
- WGS-72 vs WGS-84

- Good examples of a need for standards
- 1950 Nutation theory and 1980 IAU nutation theory

- Example of need for a recommended practice
- 1980 IAU Nutation sum terms from 1-106 vs. 106 to 1

- Historically

Potential Error Sources Flight Dynamics Programs

- Inaccurate models
- Measurement errors
- Truncation error
- Round-off
- Mathematical simplifications
- Human error
- Tracking all input parameters*
- Treatment of input data*
* indicates important outcome from the paper

Tracking All Input Data Flight Dynamics Programs

- Critical to provide adequate information
- Proposed format at end of paper and on web
- Detail treatment of
- Satellite positional information
- Forces included
- Sizes, coefficients, etc.

- Satellite characteristics
- BC, mass, area, attitude, etc.

- Source and use of data
- Solar weather data, EOP, other

- Integrator information
- Covariance information
Current formats simply not adequate

Programs Flight Dynamics Programs

- Legacy Programs
- GEODYN
- GTDS
- Raytheon TRACE
- Special-K
- STK/HPOP

Input Data Flight Dynamics Programs

- Need correct constants and data
- Coordinate system
- Mean equator Mean equinox of J2000

- Integrator
- Gravitational Model / Constants
- EGM-96 Rotational vel 0.0743668531687138 rad/min
- EGM-96 Radius earth 6378.137 km
- EGM-96 Gravitational param 398600.4418 km3/s2

- EOP Timing coefficients from actual (EOPC04 or USNO)
- Solar flux from actual (NGDC) measurements

- Coordinate system

Test Conditions Flight Dynamics Programs

- Best approach built up force models incrementally
- Two-body
- Numerical integrators, Coordinate and Time Systems

- Gravity Field
- Checks mu, re, gravitational coefficients

- Two-body plus Atmospheric Drag
- Atmospheric density model, solar weather data handling

- Two-Body plus Third-body
- JPL DE/LE file incorporation, constants

- Two-body plus Solar Radiation Pressure
- Earth shadow model, solar constants

- Two-body

Sensitivity Results Flight Dynamics Programs

- Force model contributions
- Determine which forces contribute the largest effects
- 12x12 gravity field is the baseline

- Note
- Gravity and Drag are largest contributors
- 3rd body ~km effect for higher altitudes

- Point to take away:
- Trying to get the last cm from solid earth tides no good unless all other forces are at least that precise

- Determine which forces contribute the largest effects

Force Model Contributions Flight Dynamics Programs

Sensitivity Results Flight Dynamics Programs

- Gravitational modeling
- Typically square gravity field truncations
- Appears the zonals contribute more

- Point to take away:
- Use “complete” field
- Any truncations should include additional, if not all, zonals

- Typically square gravity field truncations

Gravitational Modeling Flight Dynamics Programs

- Satellite JERS (21867)
- Note the dynamic variability over time

Sensitivity Results Flight Dynamics Programs

- Atmospheric Drag
- Large variations
- Several sources
- Using predicted values of F10.7, kp, ap for real-time operations
- Not using the actual measurement time for the values (particularly F10.7 at 2000 UTC)
- Using step functions for the atmospheric parameters vs interpolation
- Using the last 81-day average F10.7 vs. the central 81-day average
- Using undocumented differences from the original atmospheric model definition
- Not accounting for [possibly] known dynamic effects – changing attitude, molecular interaction with the satellite materials, etc.
- Inherent limitations of the atmospheric models
- Use of differing interpolation techniques for the atmospheric parameters
- Using approximations for the satellite altitude, solar position, etc.
- Using ap or kpand converting between these values
- Use of F10.7 vs E10.7 in the atmospheric models (not well characterized yet)

Sensitivity Results Flight Dynamics Programs

- Plot
- Note Dap almost as large as ap values
- Note Last - Ctrd 81 day, 30-50 SFU

- Factors examined
- Daily
- 3-Hourly
- 3-Hourly interp
- Last 81 day
- Last 81 day, 2000
- F10.7 Day Con
- F10.7 Avg Con
- F10.7 All Con
- All Con

Atmospheric Drag Flight Dynamics Programs

- Differing models (left)
- Note grouping of similar models
- “transient” effects only for first day or so

- Options for processing data (right)
- Note 10-100km effect

Sensitivity Results Flight Dynamics Programs

- Solar Radiation Pressure
- Several variations shown
- Notice maximum is only about 100m
- Point to take away
- Relatively small effect
- Some variations

Ephemeris Comparisons Flight Dynamics Programs

- Gravitational
- GTDS (left) and Ray TRACE (right) examples
- Generally cm and mm-level comparisons
- Regularized time not explored

Ephemeris Comparisons Flight Dynamics Programs

- Third-Body
- GTDS (left) and Ray TRACE (right) examples
- Generally a few cm

Ephemeris Comparisons Flight Dynamics Programs

- Solar Radiation Pressure
- GTDS (left) and Ray TRACE (right) examples
- Generally a few m

Ephemeris Comparisons Flight Dynamics Programs

- Atmospheric Drag
- GTDS (left) and Ray TRACE (right) examples
- A few km to many km
- Recall sensitivity results which were even higher

Ephemeris Comparisons Flight Dynamics Programs

- Combined forces
- Several runs made without detailed build-up of forces
- Included drag

Ephemeris Comparisons Flight Dynamics Programs

- GEODYN tests
- Starlette (7646)
- Note plot on right
- Difference of 2 GEODYN runs with different models
- Nearly identical to sensitivity tests run for 7646

Ephemeris Comparisons Flight Dynamics Programs

- GEODYN (cont)
- TDRS comparison (4 days and 1 month)

Ephemeris Comparisons Flight Dynamics Programs

- Special-K Comparisons

POE Ephemeris Comparisons Flight Dynamics Programs

- POE Comparisons
- Initial state taken and propagated
- No coordination, estimate of drag and solar radiation pressure
- Perturbed initial state results

Community Ephemeris Baseline Flight Dynamics Programs

- Need to provide standard ephemeris comparison data
- Provide community baseline on the web
- Interactive forum for cooperative comparisons

- Initial release designed to stimulate community involvement
- NOT intended to force compliance
- CSSI clearinghouse for this innovation
- Data hosted under CenterForSpace website
- www.centerforspace.com/EphemerisBaseline

- Scenarios available for use in STK

- Data hosted under CenterForSpace website
- CSSI available for consultation, analysis, inputs, questions

Conclusions Flight Dynamics Programs

- Numerous conclusions in topical areas
- Standards, Code, Instructions
- Recommended Practice needed

- Data Formats
- Proposed format of additional information

- Force model contributions
- Summary for a particular satellite
- Identify which are important

- Results for comparisons
- Conservative, cm-level
- Non Conservative, km-level
- Tremendous variability just with input data

- Summary for a particular satellite
- Sensitivity studies
- Tremendous variation

- POE “analyses”
- No propagation perfectly matches “truth”

- Standards, Code, Instructions

Conclusions Flight Dynamics Programs

- Bottom line
- With variability on treatment of input data,
- What does exact agreement mean?
- Nothing
- Right and wrong are indistinguishable!

- What does exact agreement mean?
- Identical code is not needed to align programs
- Attention to detail is
- Adequate data formats is
- Standardized approach for treating input data is
- Cooperation is
- Organizations involved in this study were tremendously helpful and cordial

- With variability on treatment of input data,

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