agi revisiting spacetrack report #3 david a. vallado, paul crawford, richard hujsak, and t. s....

AGI www.centerforspace.com

Revisiting Spacetrack Report #3David A. Vallado, Paul Crawford, Richard Hujsak, and T. S. Kelso

Analytical Graphics Inc.

Center for Space Standards and Innovation

Paper Presented at the AIAA Astrodynamics Specialist Conference, Keystone, Colorado, 21-24 August 2006

Pg 2 of 30AGI www.centerforspace.com

Outline

• Introduction– Program History– Program Description

• Computer Code Development– STR#3 to GSFC– GSFC to revised

• Test Cases– Verification– Expected Code Updates– Suggested Technical Changes

• Comparison Analyses– Complete Catalog tests

• Availability

• Conclusions


History

• Theoretical basis– Brouwer / Kozai theory (1959)

• Development of SGP4 specific theory– 1960s

• Mathematical technique origination– Kozai– Brouwer– Lyddane– Other

– 1970s• Development / Modification for NORAD

– Cranford– Lane– Hujsak– Hoots– Other


History

• Distribution of the Theory– Hoots and Roehrich Spacetrack Report #3 (1980)

• Baseline the theory– Many versions existed– Equations, Source Code, and Test Cases

– Hoots Spacetrack Report #6 (1986)• HANDE• Often assumed to be correction of Deep Space

– 1997 GSFC release of updated code (1990 version)• Implementation updates

– Merge of SGP4 / SDP4– Re-look at resonances– Re-look at deep space– Many Others

– Hoots (1998, 2004)• Equations


History

• Since 1980– No official comprehensive update of STR#3 – STR#3 caveat:

• The most important point to be noted is that not just any prediction model will suffice… The NORAD element sets must be used with one of the models described in this report in order to retain maximum prediction accuracy

– AFSPC Instructions indicate multiple official versions within DoD

• Independent efforts using released code– Variety of applications– Many changes– Lack of documentation and configuration control

No common baseline exists today


Objectives

• Provide consolidated update– Make widely available – “Close” to official standalone version

• Closer than 1980 and other derivative versions

– Fully documented test cases– Modern computer code

• Structured programming• Multiple languages

– C++ – MATLAB– FORTRAN – Pascal


Primary References

• Original documentation (1980)– Hoots, Felix R., and Roehrich, R. L. 1980. Spacetrack Report #3, Models

for Propagation of the NORAD Element Sets. U.S. Air Force, CO.

• Updated Equations and History– Hoots, Felix R. “Spacetrack Report #6: Models for Propagation of Space

Command Element Sets.” Space Command, U. S. Air Force, CO. – Hoots, Felix R., P. W. Schumacher, and R. A. Glover. 2004. History of

Analytical Orbit Modeling in the U. S. Space Surveillance System. Journal of Guidance, Control, and Dynamics. 27(2):174-185.

• Updated source code (~1990)– http://seawifs.gsfc.nasa.gov/SEAWIFS/SOFTWARE/src/bobdays/sgp4sub.f

• Many other references– Listed in this paper, and in Hoots, et al. (2004)


Program Description

• SGP4 is an analytical theory – Must use proper mathematical technique– Using different mathematical technique adds significant error

• Part of original need for 1980 publication– Structure in STR#3

• (SGP4) Near Earth (Periods less than 225 min)• (SDP4) Deep Space (Periods greater than 225 min)

• Two-line element sets (TLE)– Data for use with SGP4– TLEs produced through Orbit Determination (OD) of satellite observations– TLE data released publicly for over 20 years– TLE accuracy is coarse

• Depends on orbit and OD, but in general– ~1 km accuracy at epoch– ~1-3 km per day error growth


Program Challenges

• Disconnect between available theories in 1980 and today– Coordinate System

• TEME and current IAU 2000 Resolutions• TEME “of date” vs. “of epoch”

– Time System• UTC, Sidereal Time

• Configuration Control– Implementation and documentation of changes


TEME details

• Frame in between TOD and PEF

• TEME of Date– Calculate nutation parameters at each propagation time– We assume as the default

• TEME of Epoch– Calculate nutation parameters at epoch– Use this value for all propagation times

TEMEGMSTPEF

PEFGMSTTEME

GMSTGASTPEFGASTTOD

rROTr

rROTr

EqeandrROTr

)(3

)(3

)(3

82

82

82828282


Configuration Control Challenges

• Items requiring configuration control– Data Formats have changed over time

• Checksum• Field widths• Other?

– Operational SGP4 code has changed over time• 1980 – Spacetrack Report Number 3• 1990s – Spacetrack Report Number 6 and GSFC Code• Other?


Open Issues

• Time, coordinate systems, etc.– How to interface modern programs to older concepts?

• Existing historical database of TLE data– When did data formats change?– How to synchronize each TLE to the operational version

used to create it? – What was the precise mathematical description of each

former version?• Includes current operational version

– What accuracy can be expected with each version?


Code Development

• STR#3 to GSFC Changes– Merge SGP4 and SDP4 routines– Double Precision (FORTRAN)– Update of Deep space variables– Frequency of Lunar-Solar term computation – Lunar-Solar perturbation applications

• “Lyddane bug” (see following chart)

– Kepler’s equation (see following chart)– When to apply Lunar-Solar modifications

• Lyddane choice (see following chart)

– Many Others


Code Development

• Lunar-Solar Modifications (23599)– Incorrect update of lunar-solar perturbations

– Need to update quadrants in periodic calculations

274.5

275.0

275.5

276.0

276.5

277.0

277.5

278.0

278.5

250 300 350 400 450 500 550 600 650 700 750

Min from Epoch

Arg

umen

t of P

erig

ee (d

eg)

Corrected

STR#3

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

30000

250 300 350 400 450 500 550 600 650 700 750

Min from Epoch

Pos

itio

n C

ompo

nent

s (k

m)

Corrected

STR#3

x-component

z-component

y-component


Code Development

• Kepler’s Iteration (23333)– Note the dramatic

jumps in inclination

– Choppy behavior before 200 min is from update interval of LS terms

30.18

30.20

30.22

30.24

30.26

30.28

30.30

30.32

0 200 400 600 800 1000 1200 1400 1600

Min from Epoch

Incl

inat

ion

(deg

)

Corrected

STR#3


Code Development

• Lyddane Choice (14128)– Decision on applying

Lyddane modifications

– Based on inclination value (perturbed or original)

– Small magnitude difference

• Best to determine a better crossover point

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0

Min from Epoch

Pos

itio

n C

ompo

nent

Dif

fere

nce

(km

)

z-component

y-component


Code Modernization

• Highlights– GOTOs eliminated– Structures

• Permit multiple satellite use at one time• Better organization of the code

– Initialization• Consolidate functions in one routine• Call once

– Variable names• Consistent names

– No limit of 8 characters• No implicit typing

– Use of intrinsic functions


Structural Organization (existing - GSFC)

SGP4

DPPER

SREZ

DSCOM

INITL

if meth

od

if meth

od

if init

if <225

if init

DPPER

SREZ

DSCOM

if init

if initd

s

DSPACE

SREZ

if initds

DSPACE

SREZ

Deep Space

Near Earth

One call each time

Initialization integrated


Structural Organization (Revised)

SGP4init

INITL if meth

od

if <225

Deep Space

Near Earth

One initialization call

Routine calls toSGP4

SGP4

if meth

od

DSPACE

DPPERDSCOM

DPPER

DSINIT


Program Code Structure START

TwoLine2RVSGP4

Days2DMYHMS

SGP4Loop

Loop to read

input file of TLE data

SGP4init

Loop to propagate each tle

Loop

JDay

Function Locations

if

if

DSPACE

DPPER

GETGRAVCONST

INITL GETGRAVCONST

GSTIME

if

if

DPPER

DSINIT

if

DSCOM

GETGRAVCONST

SGP4GETGRAVCONST

DSPACEDPPER

SGP4Ext

SGP4IO

SGP4Unit

Output


Test Case Overview

• Verification test cases– Use actual satellites where possible– Test each “path” through the code

• High eccentricity• Data formats• Other

• Expected Code Updates– Error checking– Constants

• WGS-72, WGS-84, other?– Negative Inclination– Integrator problems

• Backwards propagation– Kepler’s equation

• Limit amount of corrections per step


Constants

• WGS-72 stated– We use as default

• WGS-84 possible

Symbol Calculation Value 398,600.8 km3/s2RK 6378.135 kmJ2 0.001 082 616J3 –0.000 002 538 81J4 –0.000 001 655 97

XKE 60/sqrt(RK3/) 0.074 366 916 133 17 /min

TUMin sqrt(RK3 /)/60 13.446 839 696 959 31 min

Symbol Calculation Value 398,600.5 km3/s2RK 6378.137 kmJ2 C2,0 = –0.000 484 166 850 00 0.001 082 629 989 05J3 C3,0 = 0.000 000 957 063 90 –0.000 002 532 153 06J4 C4,0 = 0.000 000 536 995 87 –0.000 001 610 987 61

XKE 60/sqrt(RK3/) 0.074 366 853 168 71 /min

TUMin sqrt(RK3 /)/60 13.446 851 082 044 98 min


Expected Code Updates

• Application of Negative Inclination (25954)– Deep space resonance, low inclination

– Note the z-axis jump

0.0140

0.0145

0.0150

0.0155

0.0160

0.0165

0.0170

0.0175

0.0180

0.0185

0.0190

-1440 -1200 -960 -720 -480 -240 0 240 480 720 960 1200 1440

Min from Epoch

Incl

ina

tio

n (

de

g)

Corrected

GSFC

-20

-15

-10

-5

0

5

10

15

20

-1440 -1200 -960 -720 -480 -240 0 240 480 720 960 1200 1440

Min from Epoch

z-P

os

itio

n C

om

po

ne

nts

(k

m)

Corrected

GSFC


Expected Code Updates

• Integrator problems– Backwards or negative propagation– Appears to have been in the computer code– Note the small magnitudes of the differences

38221.5

38221.52

38221.54

38221.56

38221.58

38221.6

38221.62

38221.64

38221.66

38221.68

38221.7

-1440 -1320 -1200 -1080 -960 -840 -720 -600

Min from Epoch

Se

mim

ajo

r A

xis

(k

m)

corrected

gsfc

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

-1440 -1320 -1200 -1080 -960 -840 -720 -600

Min from Epoch

Pos

itio

n C

ompo

nent

Dif

fere

nce

(km

)

y-component

z-component

x-component


Version Comparisons

• Several code versions exist– Original 1980

• http://celestrak.com/NORAD/documentation/spacetrk.zip

– GSFC ~ 1997 (code dated 1990)• http://seawifs.gsfc.nasa.gov/SEAWIFS/SOFTWARE/src/bobdays/sgp4sub.f • No longer available, current file is Brouwer theory, but with same name

– JPL – • ftp://naif.jpl.nasa.gov/pub/naif/toolkit/FORTRAN/PC_Linux/packages/toolkit.tar.Z • Modified starting from 1980 version

• Test versions to establish performance envelope– Scales are all the same


Computer Language Comparisons

• Test FORTRAN/CPP/PASCAL– Sample entire catalog ~9000 satellites– Pascal uses Extended type (10-bytes) CPP and FOR used double (8-byte)

CPP vs. FOR CPP vs. PAS

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

100000

0 200 400 600 800 1000 1200 1400 1600

Period (min)

Del

ta r

(m

)

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

100000

0 200 400 600 800 1000 1200 1400 1600

Period (min)

Del

ta r

(m

)


Alternate versions

• Test of GSFC version– Sample entire catalog ~9000 satellites– GSFC code differences very small if no negative propagations (right)– Much larger variations if negative times (left)

CPP vs. GSFC CPP vs. GSFC positive only

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

100000

0 200 400 600 800 1000 1200 1400 1600

Period (min)

Delt

a r

(m

)

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

100000

0 200 400 600 800 1000 1200 1400 1600

Period (min)

Del

ta r

(m

)


Alternate versions

• Test 1980 versions– Sample entire catalog ~9000 satellites

CPP vs. AF80 single CPP vs. AF80 double

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

100000

0 200 400 600 800 1000 1200 1400 1600

Period (min)

Del

ta r

(m

)

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

100000

0 200 400 600 800 1000 1200 1400 1600

Period (min)

Del

ta r

(m

)


Alternate versions

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

100000

0 200 400 600 800 1000 1200 1400 1600

Period (min)

Del

ta r

(m

)

• Test of JPL version– Sample entire catalog ~9000 satellites– JPL code improved dramatically for > 225-minute orbits with change of DOPERT variable (control of

Lunar-Solar zeroing at epoch)

CPP vs. JPL original CPP vs. JPL modified

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

100000

0 200 400 600 800 1000 1200 1400 1600

Period (min)

De

lta

r (

m)


Conclusions

• Updated version of SGP4– Incorporates all known changes and updates– Documented

• Technical equations in the literature• Code in several languages• Test cases and results

– Widely available• Hardcopy in this paper• Softcopy: http://www.centerforspace.com/downloads/

agi revisiting spacetrack report #3 david a. vallado, paul crawford, richard hujsak, and t. s....

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