Transcript AGI conference presentation

An Analysis of State Vector Propagation
Using Differing Flight Dynamics Programs
David A Vallado
Analytical Graphics Inc.
Center for Space Standards and Innovation
AGI
Paper AAS-05-199, Presented at the AAS/AIAA Space Flight Mechanics Conference, Copper Mountain Colorado, January 23-27, 2005
Overview
• Introduction
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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
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Overview (continued)
• Results
– Force Model Sensitivity Analysis
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Individual Force Model Contributions
Gravity
Atmospheric Drag
Solar Radiation Pressure
– Ephemeris Comparison Results
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Gravity
Third Body
Solar Radiation Pressure
Atmospheric Drag
Combined Forces
– POE Comparison Results
• Community Standard Ephemeris Baseline
• Conclusions
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Introduction
• 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
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Orbit Determination
Propagation*
Standards
Other
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Objectives
• 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
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Potential Error Sources
• 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
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Tracking All Input Data
• 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
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Programs
• Legacy Programs
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GEODYN
GTDS
Raytheon TRACE
Special-K
STK/HPOP
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Input Data
• 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
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Test Conditions
• 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
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Sensitivity Results
• 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
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Force Model Contributions
21867
25054
1000000.0
1000000.0
vs TwoBody
100000.0
vs EGM96 70x70
vs Drag
Jrob
100.0
vs Third
Body
Difference (m)
Difference (m)
1000.0
vs EGM96 70x70
10000.0
10000.0
vs Drag
MSIS 00
vs TwoBody
100000.0
vs Drag
MSIS 00
1000.0
vs Drag
Jrob
vs Third
Body
100.0
vs SRP
vs Solid
Tides
1.0
vs
Ocean
Tides
0.1
0
1440
2880
4320
vs Solid
Tides
1.0
vs
Ocean
Tides
0.1
5760
0
Time, min from Epoch
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vs SRP
10.0
10.0
1440
2880
4320
5760
Time, min from Epoch
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Sensitivity Results
• 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
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Gravitational Modeling
• Satellite JERS (21867)
– Note the dynamic variability over time
400.0
400.0
350.0
350.0
300.0
22x22
250.0
20x20
200.0
18x18
150.0
16x16
100.0
14x14
50.0
70x22
Difference (m)
Difference (m)
300.0
250.0
70x20
200.0
70x18
150.0
70x16
100.0
70x14
50.0
0.0
0.0
0.0
1440.0
2880.0
4320.0
5760.0
0.0
Time, min from Epoch
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1440.0
2880.0
4320.0
5760.0
Time, min from Epoch
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Sensitivity Results
• 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 kp and converting between these values
• Use of F10.7 vs E10.7 in the atmospheric models (not well characterized yet)
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Sensitivity Results
• Plot
– Note Dap almost as large as ap
values
– Note Last - Ctrd 81 day, 30-50
SFU
250.000
• Factors examined
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–
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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
200.000
150.000
D Ap
Trend
LastF107
50.000
0.000
-50.000
01-Jan-87
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Dlast-Avg
100.000
31-Dec-88
01-Jan-91
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31-Dec-92
01-Jan-95
31-Dec-96
01-Jan-99
31-Dec-00
01-Jan-03
31-Dec-04
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Atmospheric Drag
•
Differing models (left)
– Note grouping of similar models
– “transient” effects only for first day or so
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Options for processing data (right)
– Note 10-100km effect
1000000.0
100000.0
vs
F107DayCon
100000.0
vs
F107AvgCon
10000.0
vs MSIS90
1000.0
vs MSIS00
vs J60
Difference (m)
Difference (m)
vs
F107AllCon
vs MSIS86
10000.0
1000.0
vs Last 81d
vs Last 81d
2000
100.0
vs 3 hourly
100.0
vs J70
vs Daily
vs J71
10.0
10.0
vs ConAll
1.0
1.0
0
1440
2880
4320
5760
0
Tim e, m in from Epoch
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2880
4320
5760
Tim e, m in from Epoch
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Sensitivity Results
• Solar Radiation Pressure
• Relatively small effect
• Some variations
cylindrical
10.000
none
Difference (m)
– Several variations shown
– Notice maximum is only
about 100m
– Point to take away
100.000
1.000
80.000
app to true
0.100
true
0.010
no
boundary
0.001
0
1440
2880
4320
5760
Tim e, m in from Epoch
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Ephemeris Comparisons
• Gravitational
– GTDS (left) and Ray TRACE (right) examples
– Generally cm and mm-level comparisons
– Regularized time not explored
0.070
0.010
0.009
0.060
0.008
0.040
26690
2x0
0.030
7646
0x0
0.007
21867
2x0
Difference (m)
Difference (m)
0.050
7646
41x41
0.006
25054
0x0
0.005
0.004
25054
41x41
0.003
0.020
26690
12x12
0.010
0.000
0.002
21867
0x0
0.001
21867
41x41
0.000
0
720
1440
2160
2880
3600
4320
5040
5760
0
Time, min from Epoch
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1440
2160
2880
3600
4320
5040
5760
Time, min from Epoch
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Ephemeris Comparisons
• Third-Body
– GTDS (left) and Ray TRACE (right) examples
– Generally a few cm
GTDS vs STK HPOP
Ray TRACE vs STK HPOP
0.060
0.020
0.018
0.050
26690
12x12
3b
0.030
21867
3b sub
0.020
7646 3b
0.014
Difference (m)
0.040
Difference (m)
0.016
21867
41x41
3b
0.012
0.010
25054
3b
0.008
0.006
21867
3b
0.004
26690
3b sub
0.010
0.002
0.000
0.000
0
720
1440
2160
2880
3600
4320
5040
0
5760
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720
1440
2160
2880
3600
4320
5040
5760
Time, min from Epoch
Time, min from Epoch
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Ephemeris Comparisons
• Solar Radiation Pressure
– GTDS (left) and Ray TRACE (right) examples
– Generally a few m
Ray TRACE vs STK HPOP
4.000
3.500
3.500
3.000
3.000
2.500
2.500
2.000
26690
12x12
3b SR
1.500
Difference (m)
Difference (m)
GTDS vs STK HPOP
4.000
7646 sr
2.000
25054
sr
1.500
1.000
1.000
0.500
0.500
21867
sr
0.000
0.000
0
720
1440
2160
2880
3600
4320
5040
5760
0
Time, min from Epoch
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720
1440
2160
2880
3600
4320
5040
5760
Time, min from Epoch
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Ephemeris Comparisons
• Atmospheric Drag
– GTDS (left) and Ray TRACE (right) examples
– A few km to many km
• Recall sensitivity results which were even higher
Summary Position Comparison 21867
GTDS vs STK HPOP
Summary Position Comparison - Drag
Ray TRACE vs STK HPOP
50000.000
2000.000
45000.000
1800.000
40000.000
1600.000
41x41
jrob 3b
30000.000
25000.000
20000.000
15000.000
41x41
m90 3b
1200.000
1000.000
25054
m90
800.000
600.000
10000.000
400.000
5000.000
200.000
0.000
21867
m90
0.000
0
720
1440
2160
2880
3600
4320
5040
5760
0
Time, min from Epoch
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7646
m90
1400.000
Difference (m)
Difference (m)
35000.000
720
1440
2160
2880
3600
4320
5040
5760
Time, min from Epoch
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Ephemeris Comparisons
• Combined forces
– Several runs made without detailed build-up of forces
– Included drag
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Ephemeris Comparisons
• GEODYN tests
– Starlette (7646)
– Note plot on right
• Difference of 2 GEODYN runs with different models
• Nearly identical to sensitivity tests run for 7646
250.0
100.0
90.0
200.0
80.0
MSIS-86
60.0
50.0
40.0
J71
Difference (m)
Difference (m)
70.0
GEODYN
J71MSIS86
150.0
100.0
GEODYN
DTMMSIS86
30.0
50.0
20.0
10.0
0.0
0.0
0
480
960
1440
1920
2400
2880
3360
3840
4320
4800
5280
5760
0
Time, min from Epoch
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480
960
1440
1920
2400
2880
3360
3840
4320
4800
5280
5760
Time, min from Epoch
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Ephemeris Comparisons
• GEODYN (cont)
– TDRS comparison (4 days and 1 month)
2000.000
10000.000
1800.000
9000.000
1600.000
8000.000
tdrs-4
1200.000
tdrs-6
1000.000
800.000
tdrs-6
16
600.000
400.000
tdrs -6
5000.000
4000.000
tdrs -6
16
2000.000
tdrs -6
16 no
srp
1000.000
0.000
0.000
0
720
1440
2160
2880
3600
4320
5040
5760
0
Time, min from Epoch
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6000.000
3000.000
tdrs-6
16 no
srp
200.000
tdrs -4
7000.000
Difference (m)
Difference (m)
1400.000
5760
11520
17280
23040
28800
34560
40320
46080
51840
Time, min from Epoch
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Ephemeris Comparisons
• Special-K Comparisons
30.000
2000.000
1800.000
25.000
1600.000
Difference (m)
1200.000
1000.000
2186740x40
j70
800.000
764640x40
j70 3b
srp
20.000
Difference (m)
2505440x40
j70 3b
srp
1400.000
15.000
764640x40
j70 3b
10.000
600.000
2186740x40
j70 3b
400.000
2186740x40
5.000
200.000
0.000
0
720
1440
2160
0.000
2880
0
Time, min from Epoch
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720
1440
2160
2880
3600
4320
5040
5760
Time, min from Epoch
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POE Ephemeris Comparisons
• POE Comparisons
– Initial state taken and propagated
– No coordination, estimate of drag and solar radiation pressure
– Perturbed initial state results
GPS
26997 Jason
5000.0
2000.0
4500.0
1800.0
4000.0
1600.0
1400.0
all forces
all forces
Difference (m)
Difference (m )
3500.0
3000.0
2500.0
2000.0
1200.0
1000.0
1m , 1m m /s
1500.0
800.0
1000.0
400.0
500.0
200.0
0.0
0.0
0
1440
2880
4320
5760
7200
8640
10080 11520 12960 14400
0
Time, min from Epoch
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1m , 1m m /s
600.0
1440
2880
4320
5760
7200
8640
10080
11520
12960
Time, min from Epoch
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Community Ephemeris Baseline
• 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
– CSSI available for consultation, analysis, inputs, questions
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Conclusions
• 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
– Sensitivity studies
• Tremendous variation
– POE “analyses”
• No propagation perfectly matches “truth”
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Conclusions
• Bottom line
– With variability on treatment of input data,
• What does exact agreement mean?
– Nothing
– Right and wrong are indistinguishable!
– Identical code is not needed to align programs
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•
•
•
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
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