agi an analysis of state vector propagation using differing flight dynamics programs david a vallado...

AGI

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

Pg 2 of 30 www.centerforspace.comAGI

Overview

• 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)

• 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

• Community Standard Ephemeris Baseline

• Conclusions


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 • Orbit Determination• Propagation*• Standards• Other


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


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


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


Programs

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


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


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


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


Force Model Contributions

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Time, min from Epoch

Dif

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nc

e (

m)

vs Two-Body

vs EGM-96 70x70

vs DragMSIS 00

vs DragJrob

vs ThirdBody

vs SRP

vs SolidTides

vsOceanTides

21867

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vs Two-Body

vs EGM-96 70x70

vs DragMSIS 00

vs DragJrob

vs ThirdBody

vs SRP

vs SolidTides

vsOceanTides

25054


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


Gravitational Modeling

• Satellite JERS (21867)– Note the dynamic variability over time

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22x22

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70x22

70x20

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70x16

70x14


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)


Sensitivity Results

• 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 -50.000

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01-Jan-87 31-Dec-88 01-Jan-91 31-Dec-92 01-Jan-95 31-Dec-96 01-Jan-99 31-Dec-00 01-Jan-03 31-Dec-04

D Ap

Dlast-Avg

Trend

LastF107


Atmospheric Drag

• 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

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Dif

fere

nce

(m

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vs MSIS86

vs MSIS90

vs MSIS00

vs J60

vs J70

vs J71

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Dif

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vsF107DayCon

vsF107AvgCon

vsF107AllCon

vs Last 81d

vs Last 81d2000

vs 3 hourly

vs Daily

vs ConAll


Sensitivity Results

• Solar Radiation Pressure– Several variations shown

– Notice maximum is only about 100m

– Point to take away• Relatively small effect• Some variations

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Dif

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nce

(m

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cylindrical

none

80.000

app to true

true

noboundary


Ephemeris Comparisons

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

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Dif

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nce

(m

)

218672x0

266902x0

2669012x12

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Dif

fere

nce

(m

)

76460x0

764641x41

250540x0

2505441x41

218670x0

2186741x41



• Third-Body– GTDS (left) and Ray TRACE (right) examples

– Generally a few cm

GTDS vs STK HPOP

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Dif

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nce

(m

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2186741x413b

2669012x123b

218673b sub

266903b sub

Ray TRACE vs STK HPOP

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Dif

fere

nce

(m

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7646 3b

250543b

218673b



• Solar Radiation Pressure– GTDS (left) and Ray TRACE (right) examples

– Generally a few m

Ray TRACE vs STK HPOP

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Dif

fere

nce

(m

)

7646 sr

25054sr

21867sr

GTDS vs STK HPOP

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Dif

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nce

(m

)

2669012x123b SR



• 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 - DragRay TRACE vs STK HPOP

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Dif

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7646m90

25054m90

21867m90

Summary Position Comparison 21867GTDS vs STK HPOP

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Dif

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(m

)

41x41jrob 3b

41x41m90 3b



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



• GEODYN tests– Starlette (7646)– Note plot on right

• Difference of 2 GEODYN runs with different models• Nearly identical to sensitivity tests run for 7646

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Dif

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e (

m) MSIS-86

J71

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Dif

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GEODYNJ71-MSIS86

GEODYNDTM-MSIS86



• GEODYN (cont)– TDRS comparison (4 days and 1 month)

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Dif

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tdrs-4

tdrs-6

tdrs-616

tdrs-616 nosrp

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Dif

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(m

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tdrs-616 nosrp



• Special-K Comparisons

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Dif

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25054-40x40j70 3bsrp

21867-40x40j70

21867-40x40j70 3b

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Dif

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nce

(m

)

7646-40x40j70 3bsrp

7646-40x40j70 3b

21867-40x40


POE Ephemeris Comparisons

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

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Dif

fere

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all forces

1m , 1m m /s

26997 Jason

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Dif

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1m, 1mm/s

GPS


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


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”


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• 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

agi an analysis of state vector propagation using differing flight dynamics programs david a vallado...

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