NASA Technical Reports Server (NTRS) 20150000800: Cauchy Drag Estimation For Low Earth Orbiters

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by  NASA Technical Reports Server (NTRS)

National Aeronautics and Space Administration
CAUCHY DRAG ESTIMATION FOR LOW
EARTH ORBITERS
5
9
J. Russell Carpenter
5
Alinda K. Mashiku

e
d
o
c
NAVIGATION & MISSION DESIGN BRANCH
GNL
NASA GSFC
www.nasa.gov
GPS-based Owner/Operator Predictions are
Sometimes Inferior to JSpOC’s
Initial JSpOC Initial JSpOC
prediction prediction
~2x closer to ~3x closer to
final final
consensus at consensus at
15 km
Time of TCA
closest
approach
(TCA)
185 186 187 188 189 190 191 192 193 194 195 213 213 214 215 216 217 218 219 220
Dayof Year–CARAReport Date Dayof Year–CARAReport Date
Initial
predictions Initial JSpOC
similar; GPS prediction
moving within 500 of
toward final
consensus consensus at
sooner TCA
242 243 244 245 246 247 218 276 277 278 279 280 281 282 283 284 258 286
Dayof Year–CARAReport Date Dayof Year–CARAReport Date
Ref:M.A. Vavrina, C.P. Newman, S.E. Slojkowski and J.R. Carpenter, “Improving Fermi Orbit Determination and Prediction in an Uncertain Atmospheric Drag Environment”
Proceedings of the 24thInternational Symposium on Space Flight Dynamics,www.issfd.org, 2014
NAVIGATION & MISSION DESIGN BRANCH, CODE 595
GNL 2
NASA GSFC
Tuning GPS EKF Yields Marginal Improvement
in Prediction Robustness to Density Variation
Ref:M.A. Vavrina, C.P. Newman, S.E. Slojkowski and J.R. Carpenter, “Improving Fermi Orbit Determination and Prediction in an Uncertain Atmospheric Drag Environment”
Proceedings of the 24thInternational Symposium on Space Flight Dynamics,www.issfd.org, 2014
NAVIGATION & MISSION DESIGN BRANCH, CODE 595
GNL 3
NASA GSFC
Solar Flux Variations During Higher Solar
Activity Intervals are Not Gaussian
Data Set: Observed F Flux when ISN > 75 Variations in Data Set: Time differences of
10.7
(Daily - Ctrd 81-day avg) - (Daily - Ctrd 81-day avg)
obs adj
F for ISN > 75
10.7
400
350
300
250
200
150
100
50
0
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
International Sunspot Number
400
350
300
250
200
150
100
50
0
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
NAVIGATION & MISSION DESIGN BRANCH, CODE 595
GNL 4
NASA GSFC
Drag Residuals from CHAMP are Not Gaussian
NAVIGATION & MISSION DESIGN BRANCH, CODE 595
GNL 5
NASA GSFC
Fits to Stable Distributions Suggest a Cauchy
Model
Fit PDFs for F Data Stable Distribution Fits
10.7
Data Concen- Asym-
tration* metry Scale
F 1.38 0.02 0.13
10.7
y
t A 1.03 0.0014 3.46
i
s p
n
e
CHAMP
D

y
t drag 1.34 0.6121 0.0001
i
l
i
b
a
b *Gaussian = 2.0, Cauchy = 1.0
o
r
P
Variation in F
10.7
NAVIGATION & MISSION DESIGN BRANCH, CODE 595
GNL 6
NASA GSFC
The Idan-Speyer Scalar Cauchy Estimator (ISCE)
(cid:131) Given a linear scalar system (cid:131) Posterior PDF
(cid:131) With Cauchy inputs and initial (cid:131) Has Finite Moments
condition
NAVIGATION & MISSION DESIGN BRANCH, CODE 595
GNL 7
NASA GSFC
The ISCE is Robust to Large Measurement &
Process Noise Disturbances
y
bilitsity
an
be
oD Measurement
r
P
Noise
Disturbance *
Process Noise
(cid:16187)
Measurement Noise *
Process Noise
Disturbance
(cid:16187)
NAVIGATION & MISSION DESIGN BRANCH, CODE 595
GNL 8
NASA GSFC
The ISCE May Be Embedded Within the EKF for
Density Estimation
GPS Receiver Drag Acceleration:
1 A (cid:167) (cid:71)(cid:85)(cid:183)
d (cid:32)(cid:16) C v2(cid:85)(cid:168)1(cid:14) (cid:184)
Gaussian Noise, v 2 D m r (cid:169) (cid:85)(cid:185)
(cid:92)i
GPS Pseudorange:
Cauchy Noise, v
(cid:92)(cid:32) r(cid:16)r (cid:14)v ,i(cid:32)1,2,...,n d
i SVi (cid:92)i SV
EKF Update Cauchy Filter Update
Gaussian Noise, w Cauchy Noise, w
g (cid:85)
EKF Dynamics: Cauchy Filter Dynamics:
ECI Velocity, v Id2 (cid:80) 1 A (cid:167) (cid:71)(cid:85)(cid:183) d (cid:167)(cid:71)(cid:85)(cid:183) 1(cid:167)(cid:71)(cid:85)(cid:183)
r(cid:32)(cid:16) r(cid:16) C (cid:85)(cid:168)1(cid:14) (cid:184)v v (cid:14)w (cid:168) (cid:184)(cid:32)(cid:16) (cid:168) (cid:184)(cid:14)w
dt2 r3 2 D m (cid:169) (cid:85)(cid:185) r r g dt(cid:169) (cid:85)(cid:185) (cid:87)(cid:169) (cid:85)(cid:185) (cid:85)
ECI Position, r
(cid:156)
Density Correction, (cid:71)(cid:85)(cid:18)(cid:85)
NAVIGATION & MISSION DESIGN BRANCH, CODE 595
GNL 9
NASA GSFC
Schmidt-Kalman Consider States Encapsulate
the ISCE Moments
Solve-For States:
Consider States:
NAVIGATION & MISSION DESIGN BRANCH, CODE 595
GNL 10
NASA GSFC