pg 1 of xx agi orbit lifetime prediction jim woodburn
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Pg 1 of xxAGI www.agiuc.com
Orbit Lifetime Prediction
Jim Woodburn
Pg 2 of 46AGI www.agiuc.com
Orbit Lifetime Prediction Methods
• Interactively determine the “right answer”
• Employ the services of a mystic
• Astrology
• Try to compute it…
Pg 3 of 46AGI www.agiuc.com
History
• Research motivated by questions from STK users
• Extension of work presented at the AAS/AIAA Astrodynamics Specialists Conference in Lake Tahoe, August 2005– Coauthor, AGI Application Support Engineer, Shannon
Lynch
• Community benefit– Extensions to STK/Lifetime capabilities– Public presentation of results
Pg 4 of 46AGI www.agiuc.com
Agenda
• Orbit lifetime drivers
• Sources of uncertainty
• Solar weather characterization
• Atmospheric density model selection
• Numerical methods
• Wrap up
• What’s next
Pg 5 of 46AGI www.agiuc.com
What affects orbit lifetime?
• Orbit lifetime mainly driven by atmospheric drag– Removes energy from the orbit– Lowers the altitude of the orbit more drag
• Atmospheric drag depends on– Satellite area to mass ratio– Satellite velocity relative to the atmosphere – Atmospheric density
Atmospheric Density
Pg 6 of 46AGI www.agiuc.com
What affects atmospheric density?
• Solar weather
• Geomagnetic activity
• Selection of density model
• Satellite altitude
• Relative position of the Sun
• Time of the year
Pg 7 of 46AGI www.agiuc.com
Uncertainty Uncertainty Uncertainty…
• Solar weather– Cycle amplitude
– Daily variability
– Cycle timing
– Storms
• Geomagnetic activity
• A priori density models
• Initial conditions
• Projected area
• Numerical Methods
BLUE = Addressed in this study
We need to predict the future, but…
Pg 8 of 46AGI www.agiuc.com
Solar Weather Characterization
Pg 9 of 46AGI www.agiuc.com
How well can we predict F10.7?
from Schatten K.H., Solar Activity and the Solar Cycle
Pg 10 of 46AGI www.agiuc.com
Prediction appears difficult
• Uncertainty in the mean behavior
• Random looking variations on a daily basis
• Can we simulate it?
Pg 11 of 46AGI www.agiuc.com
Desire statistical similarity to historical data
• Separate into a mean behavior and variation about the mean
• Random deviations on amplitude of mean trajectory, assume no timing error
• Superimpose daily variations– Amplitude varies through solar cycle– Time correlation varies through solar cycle– Simulate with a stochastic sequence
Pg 12 of 46AGI www.agiuc.com
Another look at F10.7
from Schatten K.H., Solar Activity and the Solar Cycle
Pg 13 of 46AGI www.agiuc.com
2 Problems in 2 Parts
• Looking deep into the future– Unknown solar cycle behavior– Unknown daily variations
• Analysis for existing satellites– Average characteristics of cycle may be known– Daily variations still unknown
• Look at effects separately and combined
Pg 14 of 46AGI www.agiuc.com
Random deviation of mean
• Schatten predicts– Nominal– Plus/minus 2 sigma– Early/nominal/late timing
• Perform Monte-Carlo analyses– Draw a random sigma level– Generate associated solar flux trajectory– Compute an orbit lifetime prediction
Pg 15 of 46AGI www.agiuc.com
Lifetime distribution – Variations of Mean F10.7
Solar Max Solar Min
Jacchia 1970 Density Model
Alt0 = 375 Km, A/M = 0.02, Cd = 2.0
0
50
100
150
200
250
300
Days
Freq
uenc
y
Frequency
Mean = 34.476
StDev = 3.115306-2 Sigma +2 Sigma
Mean
0
50
100
150
200
250
300
Days
Freq
uenc
y
Frequency
Mean = 34.476
StDev = 3.115306-2 Sigma +2 Sigma
Mean
0
20
40
60
80
100
120
140
160
180
DaysFr
eque
ncy
Frequency
Mean = 181.798
StDev = 22.11045
-2 Sigma+2 Sigma
Mean
0
20
40
60
80
100
120
140
160
180
DaysFr
eque
ncy
Frequency
Mean = 181.798
StDev = 22.11045
-2 Sigma+2 Sigma
Mean
Pg 16 of 46AGI www.agiuc.com
Lifetime distribution – Variations of Mean F10.7
0
20
40
60
80
100
120
140
160
180
200
Days
Freq
uenc
y
Frequency
Mean = 263.8678
StDev = 43.52883
Solar Max Solar Min
Jacchia 1970 Density Model
Alt0 = 450 Km, A/M = 0.02, Cd = 2.0
+2 Sigma -2 Sigma
Mean
0
20
40
60
80
100
120
140
DaysFr
eque
ncy
Frequency
Mean = 1752.569
StDev = 626.8172+2 Sigma -2 Sigma
Mean
Pg 17 of 46AGI www.agiuc.com
Characterizing daily variations
• Generated functional fits to last 3 solar cycles– Emulate an accurate mean prediction– Schatten predictions had significant timing errors
• Divided each solar cycle into 8 segments
• Constructed sample variances and time correlations
• Fit data using simple functional forms
• Goal: Produce simple functions to drive our stochastic sequence
Pg 18 of 46AGI www.agiuc.com
Solar Cycle 21
0
50
100
150
200
250
1 286 571 856 1141 1426 1711 1996 2281 2566 2851 3136 3421 3706
Days
F1
0.7
cm
Flu
x
fit
obs
Pg 19 of 46AGI www.agiuc.com
Flux history revisited
Pg 20 of 46AGI www.agiuc.com
Sample Data & Functional Forms
Standard Deviation Time Correlation
0
20
40
60
80
100
120
0
0.06
0.13
0.19
0.25
0.31
0.38
0.44 0.
5
0.56
0.63
0.69
0.75
0.81
0.88
0.94
1
Fraction of CycleH
alf l
ife (d
ays)
Half life
Half life Data
0
5
10
15
20
25
30
0.00
0.06
0.13
0.19
0.25
0.31
0.38
0.44
0.50
0.56
0.63
0.69
0.75
0.81
0.88
0.94
1.00
Fraction of Cycle
F10.
7 St
d. D
ev Sigma
Sigma Data
Pg 21 of 46AGI www.agiuc.com
0
50
100
150
200
250
1 216 431 646 861 1076 1291 1506 1721 1936 2151 2366 2581 2796 3011 3226 3441 3656
Days
F1
0.7
cm
Flu
x
Nominal
Sim
Simulated solar flux
0
50
100
150
200
250
1 208 415 622 829 1036 1243 1450 1657 1864 2071 2278 2485 2692 2899 3106 3313 3520
Days
F10
.7 c
m F
lux
Nominal
+1 Sigma
Sim
0
50
100
150
200
250
1 286 571 856 1141 1426 1711 1996 2281 2566 2851 3136 3421 3706
Days
F10.
7 cm
Flu
x
fit
obs
Pg 22 of 46AGI www.agiuc.com
Daily variation simulations
• Daily variations only– Select a single mean solar flux trajectory– Monte-Carlo analyses of daily variations– Appropriate for near term studies
• Daily and mean variations– Monte-Carlo analyses vary both the mean trajectory and
daily variations about the mean– Appropriate for studies in future solar cycles
Pg 23 of 46AGI www.agiuc.com
Effects of Daily Variations on Orbit Lifetime – 375 Km Alt
0
20
40
60
80
100
120
140
160
180
Days
Fre
qu
ency
Frequency
Mean = 181.798
StDev = 22.11045
0
50
100
150
200
250
300
350
400
450
Days
Fre
qu
en
cy
Frequency
Mean = 34.354
StDev = 2.065175
0
50
100
150
200
250
300
350
Days
Fre
qu
en
cy
Frequency
Mean = 179.625
StDev = 10.20669
0
50
100
150
200
250
300
Days
Fre
qu
ency
Frequency
Mean = 34.476
StDev = 3.115306
Daily Variation Only Daily Variation Only
Mean Variation Only Mean Variation Only
Solar Max Solar Min
Pg 24 of 46AGI www.agiuc.com
Mean and daily variations – 375 Km
0
20
40
60
80
100
120
140
160
Days
Fre
qu
ency
Frequency
Mean = 35.617
StDev = 7.555753
0
20
40
60
80
100
120
140
Days
Fre
qu
ency
Frequency
Mean = 181.944
StDev = 27.66413
Solar Max
Solar Min
Vary Only Mean FluxMean = 34.476StDev = 3.115
Vary Only Mean FluxMean = 181.798StDev = 22.11
Pg 25 of 46AGI www.agiuc.com
Effects of Daily Variations on Orbit Lifetime – 450 Km Alt
0
20
40
60
80
100
120
140
Days
Fre
qu
en
cy
Frequency
Mean = 267.0768
StDev = 60.83151
0
20
40
60
80
100
120
140
Days
Fre
qu
en
cy
Frequency
Mean = 1605.912
StDev = 73.50759
Daily Variation OnlyDaily Variation Only
0
20
40
60
80
100
120
140
160
180
200
Days
Fre
qu
en
cy
Frequency
Mean = 263.8678
StDev = 43.52883
Mean Variation Only
Solar Max Solar Min
0
20
40
60
80
100
120
140
Days
Fre
qu
en
cy
Frequency
Mean = 1752.569
StDev = 626.8172
Mean Variation Only
Pg 26 of 46AGI www.agiuc.com
0
20
40
60
80
100
120
140
160
180
Days
Fre
qu
en
cy
Frequency
Mean = 1711.944
StDev = 482.0397
Mean and daily variations – 450 Km
0
20
40
60
80
100
120
140
Days
Fre
qu
en
cy
Frequency
Mean = 272.5578
StDev = 79.1795
Solar Max
Solar Min
Vary Only Mean FluxMean = 263.8StDev = 43.5
Vary Only Mean FluxMean = 1752.6StDev = 626.8
Pg 27 of 46AGI www.agiuc.com
How do I do that in STK?
• New scenario level connect command to generate randomly deviated solar flux histories from Schatten predict files. Written out as .fxm files.
• STK/Lifetime has been enhanced to accept solar flux input from .fxm files– Supported through STK/Connect interface
• STK/Connect based scripts used to perform Monte-Carlo analyses
Pg 28 of 46AGI www.agiuc.com
Atmospheric Density Model Selection
Pg 29 of 46AGI www.agiuc.com
Which density model should I use???
Models Considered
• Jacchia 1970
• Jacchia 1971
• MSIS 1986
• MSISE 1990
• NRL MSISE 2000
• Harris Priester
• F10.7 uncertainty is larger effect mean < 0.5 at solar max mean < 1.0 at solar min
• MSIS models consistent– Lower density predictions at solar
min than Jacchia models
– Longer solar min lifetimes with larger standard deviations
• Harris Priester did not perform well
Survey says…
Pg 30 of 46AGI www.agiuc.com
Different density models – same results – 375 Km
0
20
40
60
80
100
120
140
160
Days
Fre
qu
ency
Frequency
Mean = 35.617
StDev = 7.555753
0
50
100
150
200
250
Days
Fre
qu
ency
Frequency
Mean = 32.769
StDev = 7.037696
Solar max
0
50
100
150
200
250
Days
Fre
qu
ency
Frequency
Mean = 32.769
StDev = 7.037696
Solar max
0
20
40
60
80
100
120
140
160
180
200
Days
Fre
qu
ency
Frequency
Mean = 33.835
StDev = 8.080041
Solar max
0
20
40
60
80
100
120
140
160
180
200
Days
Fre
qu
ency
Frequency
Mean = 33.835
StDev = 8.080041
Solar max
0
20
40
60
80
100
120
140
160
180
Days
Fre
qu
ency
Frequency
Mean = 34.381
StDev = 8.095763
Solar max
0
20
40
60
80
100
120
140
160
180
Days
Fre
qu
ency
Frequency
Mean = 34.381
StDev = 8.095763
Solar max
Jacchia 70
Jacchia 71
MSIS 86
MSISE 90
Solar max
Pg 31 of 46AGI www.agiuc.com
Different density models – same results – 450 km
Jacchia 70
Jacchia 71
MSIS 86
MSISE 90
0
20
40
60
80
100
120
Days
Fre
qu
en
cy
Frequency
Mean = 253.2752
StDev = 76.50432
Solar max
0
20
40
60
80
100
120
Days
Fre
qu
en
cy
Frequency
Mean = 252.672
StDev = 76.31497
0
20
40
60
80
100
120
140
160
Days
Fre
qu
en
cy
Frequency
Mean = 236.5036
StDev = 68.47013
0
20
40
60
80
100
120
140
Days
Fre
qu
en
cy
Frequency
Mean = 272.5578
StDev = 79.1795
Solar maxSolar max
Solar max
Pg 32 of 46AGI www.agiuc.com
How do I do that in STK?
• STK/Lifetime has been enhanced to allow for selection of various atmospheric density models– Supported through STK/Connect interface
• STK/Connect based scripts used to perform Monte-Carlo analyses
Pg 33 of 46AGI www.agiuc.com
Selection of a Numerical Method
Pg 34 of 46AGI www.agiuc.com
Numerical method selection
• How much time do you have?
• How long do you expect your orbit to last?
• What method do you trust?
Pg 35 of 46AGI www.agiuc.com
Numerical methods
• Simplified model (Lifetime)– Semi-analytic model– Earth gravity through J5– Solar and lunar 3rd body– Solar radiation pressure– Atmospheric drag via Gaussian quadrature
• Numerical integration– Complete force model– Gauss Jackson 12th order integrator
Pg 36 of 46AGI www.agiuc.com
Design of comparison experiment
• Generate a “Truth” solar flux trajectory
• Generate “Truth” ephemeris using “Truth” solar flux
• Perform Monte-Carlo analyses at several times between original initial conditions and predicted end of life– Each run is seeded from “Truth” solar and orbit
trajectories
• Compare results
Pg 37 of 46AGI www.agiuc.com
Comparison methodology
Time
Truth Solar Flux Trajectory
Truth Ephemeris
Initializationfrom truth
Solar Flux With Daily Random Variations Orbit Lifetime Estimate
Pg 38 of 46AGI www.agiuc.com
Comparison of approaches
0
10
20
30
40
50
60
70
Days
Fre
qu
en
cy
Frequency
Mean = 2.287685
StDev = 2.816856
Num Integ – Solar Max
0
10
20
30
40
50
60
70
Days
Fre
qu
en
cy
Frequency
Mean = 2.287685
StDev = 2.816856
Num Integ – Solar Max
0
10
20
30
40
50
60
70
80
90
Days
Fre
qu
en
cy
Frequency
Mean = 0.589775
StDev = 1.769449
Num Integ – Solar Max
0
10
20
30
40
50
60
70
80
90
Days
Fre
qu
en
cy
Frequency
Mean = 0.589775
StDev = 1.769449
Num Integ – Solar Max
4 weeks out
3 weeks out
Num Integ - Solar Max Lifetime - Solar Max
0
20
40
60
80
100
120
140
160
Days
Fre
qu
en
cy
Frequency
Mean = 1.014
StDev = 2.573
02040
6080
100120
140160
Days
Fre
qu
ency
Frequency
Mean = -0.480
StDev = 1.583
Lifetime - Solar Max
Lifetime - Solar Max
Pg 39 of 46AGI www.agiuc.com
Comparison of approachesNum Integ - Solar Min Lifetime - Solar Min
0
10
20
30
40
50
60
70
Days
Fre
qu
en
cy
Frequency
Mean = -2.7504
StDev = 8.986531
Num Integ – Solar Min
0
10
20
30
40
50
60
70
Days
Fre
qu
en
cy
Frequency
Mean = -2.7504
StDev = 8.986531
Num Integ – Solar Min
0
10
20
30
40
50
60
70
80
Days
Fre
qu
en
cy
Frequency
Mean = -3.55323
StDev = 5.259221
Num Integ – Solar Min
0
10
20
30
40
50
60
70
80
Days
Fre
qu
en
cy
Frequency
Mean = -3.55323
StDev = 5.259221
Num Integ – Solar Min
6 months out
4 months out
0
20
40
60
80
100
120
140
160
Days
Fre
qu
en
cy
Frequency
Mean = -17.3375
StDev = 9.730494
0
20
40
60
80
100
120
140
Days
Fre
qu
en
cy
Frequency
Mean = -13.7745
StDev = 4.777514
Lifetime – Solar Min
Lifetime – Solar Min
Pg 40 of 46AGI www.agiuc.com
Method comparison findings
• Additional study required for useful conclusions
• Results of numerical integration seem to follow expected behavior– Mean errors lie well with 1 sigma– Standard deviation decreases as end of life approaches
• Lifetime algorithm results varied– Look good for solar max test case– Errors are larger for solar min (consistently low)
Pg 41 of 46AGI www.agiuc.com
How do I do that in STK?
• STK/Connect based scripts used to perform Monte-Carlo analyses– Existing HPOP and Lifetime commands– New Lifetime commands
Pg 42 of 46AGI www.agiuc.com
STK/Lifetime enhancements
• Random solar flux history generation (Scenario)
• Atmospheric density model selection
• Duration stopping condition
• Reportable data after error conditions
• Enhanced documentation
Pg 43 of 46AGI www.agiuc.com
Conclusions…
• Monte-Carlo analyses are an effective tool in the prediction of orbit lifetime – There is a lot of uncertainty
• Solar flux daily variations important contributor in spread of orbit lifetime distributions– Who knows what’s going to happen tomorrow
• Atmospheric density model selection not primary importance – Statistically similar answers, all fairly uncertain
Pg 44 of 46AGI www.agiuc.com
Conclusions
• Similar accuracy was achieved using simplified lifetime prediction algorithms and numerical integration during solar max test case– Additional investigation is required for solar min test
case, uncertainty still exists
This much is certainAll analyses in this study were performed on orbits with short lifetimeActual results may vary
Disclaimer
Pg 45 of 46AGI www.agiuc.com
What’s Next
• Solar weather– Cycle amplitude
– Daily variability
– Cycle timing
– Storms
• Geomagnetic activity
• A priori density models
• Initial conditions
• Projected area
• Numerical methods
• Real data comparisons
BLUE = Addressed in this study
RED = To be addressed in next study
Pg 46 of 46AGI www.agiuc.com
Ultimate Recommendation
Compare results from 2 independent approaches
• Monte-Carlo
• Madame Zora