Pg 1 of 89 AGI Reverse Engineering Maneuvers R Hujsak Oct 13, 2005.
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Transcript of Pg 1 of 89 AGI Reverse Engineering Maneuvers R Hujsak Oct 13, 2005.
Pg 1 of 89AGI www.agiuc.com
Reverse Engineering ManeuversR Hujsak
Oct 13, 2005
Pg 2 of 89AGI www.agiuc.com
The problem
Pre-maneuver trackingUnknown
maneuver event
Post-maneuver tracking
Predict thru unknown maneuverNormal OD Reject data
Pg 3 of 89AGI www.agiuc.com
The usual approach
Pre-maneuver trackingUnknown
maneuver event Post-maneuver tracking
Predict thru unknown maneuverNormal OD Reject data
Normal OD Stop OD process during maneuver
Predict backward
Predict forward
Restart OD process with post-
maneuver data
Reconstruction depends on post-maneuver accuracy
Pg 4 of 89AGI www.agiuc.com
Limitations with the usual approach
• Accuracy is a function of tracking data– Density & distribution
• Timeliness is a function of– Tracking system response to maneuver detection
• Assumes impulsive maneuvers– Does not work for longer duration burns
• ANIK-F2 thrusting 8 hrs/days• MEXSAT thrusts for 5 days ON, 1 day OFF, 6 days ON• PANAMSAT D4S thrusts for 15 hrs/day• GEO transfer thrust 1 hour
Is there a way to handle finite maneuvers?
Pg 5 of 89AGI www.agiuc.com
Filter accepts new data & covariance collapses
Filters provide other options
Predict thru unknown maneuverNormal OD Reject data
Pre-maneuver trackingUnknown
impulsive event Post-maneuver tracking
Use the filter covariance
Postulate various maneuver hypotheses
inflate the covariance
Smoothed ephemeris is predicted backward. Intersection defines maneuver.
Adding data refines estimate
Pg 6 of 89AGI www.agiuc.com
This presentation
• Examine alternatives to classical approach
• Examine various maneuvers– Simple impulsive burns– Complex duration thrusting
• Examine various methods– “Shot-gun” approach– IOD and reverse prediction– Brute force & iterated analysis approach
Pg 7 of 89AGI www.agiuc.com
Concrete examples
• Classical method, unknown impulse– GEO unknown EW stationkeeping
• HEO unknown impulse perigee burn
• XIPS finite maneuvers– Boeing 702 (ANIK-F2 insertion)
• DSCS perigee raising finite maneuver
• Backups (if there’s time)– LEO single large impulse
Pg 8 of 89AGI www.agiuc.com
GOE EW stationkeeping
Pg 9 of 89AGI www.agiuc.com
GEO unknown EW stationkeeping
• Assume 3 tracking stations– Track once per day, each– 5 minute track, range, az, el
• Unknown intrack maneuver 1 m/sec– 15 minute track after maneuver
• Objectives: Use IOD to help identify maneuver time– Use IOD solution to process through maneuver
Pg 10 of 89AGI www.agiuc.com
The usual approach
Pre-maneuver trackingUnknown
maneuver event Post-maneuver tracking
Predict thru unknown maneuverNormal OD Reject data
Normal OD Stop OD process during maneuver
Predict backward
Predict forward
Restart OD process with post-
maneuver data
Reconstruction depends on post-maneuver accuracy
Pg 11 of 89AGI www.agiuc.com
Maneuver detection is easy…
A COOK-B Meas Residuals A HULA-B Meas Residuals A PIKE-A Meas ResidualsRE COOK-B Meas Residuals RE HULA-B Meas Residuals RE PIKE-A Meas Residuals
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
-20000
-40000
-60000
-80000
-1000000.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0
Mea
sure
men
t Res
idu
al (m
)
Measurement ResidualMeasurement Residual
Days since 26 May 2004 00:00:00.00
Maneuver
But residual trends do not indicate maneuver time
Pg 12 of 89AGI www.agiuc.com
A COOK-B Meas Residuals A HULA-B Meas Residuals A PIKE-A Meas ResidualsRE PIKE-A Meas Residuals RE COOK-B Meas Residuals RE HULA-B Meas Residuals
0
10000
20000
30000
40000
50000
60000
70000
157.0 158.0 159.0 160.0 161.0 162.0 163.0 164.0 165.0 166.0 167.0
Me
as
ure
me
nt
Re
sid
ua
l (m
)
Range ResidualRange Residual
Hours since 26 May 2004 00:00:00.00
Post-maneuver tracks (enlarged)
Residual trends do not indicate maneuver time ..
.. so perform IOD and 3-track least squares (standard orbit analysis).
2 hours < 1/3 rev
Pg 13 of 89AGI www.agiuc.com
Radial (km) In-Track (km) Cross-Track (km) Range (km)
0
10
20
30
40
5060
70
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100
-10
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-100 0
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12:00 18:00 00:00 06:00 12:00 18:00 00:00 06:00 12:00
Satel l i te-Pred - 10 Oct 2005 11:25:13Satel l i te-Pred - 10 Oct 2005 11:25:13
31 May 2004 12:00:00.000 to 2 Jun 2004 14:05:00.000 (UTCG)
1 Ju
n 20
04 0
0:00
:00.
000
2 Ju
n 20
04 0
0:00
:00.
000
Least-squares fit & back predict
Solution = 1 Jun 2004 15:00:00
Truth = 1 Jun 2004 00:00:00
LS fit to 3 tracks, less than 1 rev of sampling
Pg 14 of 89AGI www.agiuc.com
Radial Vel Diff (m/sec) In-Track Vel Diff (m/sec)Cross-Track Vel Diff (m/sec) SpeedRelToRICFrame (m/sec)
0
1
2
3
-1
-2
-3 0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
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1.50
1.60
1.70
1.80
1.90
12:00 18:00 00:00 06:00 12:00 18:00 00:00 06:00 12:00
Satel l i te-Pred - 10 Oct 2005 11:16:59Satel l i te-Pred - 10 Oct 2005 11:16:59
31 May 2004 12:00:00.000 to 2 Jun 2004 14:05:00.000 (UTCG)
1 Ju
n 20
04 0
0:00
:00.
000
2 Ju
n 20
04 0
0:00
:00.
000
Rdot = 0.1 m/sec
Idot = 0.99 m/sec
Least-squares fit & back predict
Solution = 1 Jun 2004 15:00:00
Truth = 1 Jun 2004 00:00:00
Pg 15 of 89AGI www.agiuc.com
Add another day of tracking data …
Radial (km) In-Track (km) Cross-Track (km) Range (km)
0
30
60
90
-30
-60
-90
-120
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-4200
20406080
100120140160180200220240260280300320340360380400420440
12:00 18:00 00:00 06:00 12:00 18:00 00:00 06:00 12:00
Satellite-Pred - 10 Oct 2005 10:13:42Satellite-Pred - 10 Oct 2005 10:13:42
(UTCG) 31 May 2004 12:00:00.000 to 2 Jun 2004 14:05:00.000
1 Ju
n 20
04 0
0:00
:00.
000
2 Ju
n 20
04 0
0:00
:00.
000
Solves the problem:
Solution = 1 Jun 2004 00:01
LS fit to 3 tracks, less than 2 revs of sampling
Pg 16 of 89AGI www.agiuc.com
… gives the right answer
Radial Vel Diff (m/sec) In-Track Vel Diff (m/sec)Cross-Track Vel Diff (m/sec) SpeedRelToRICFrame (m/sec)
0
1
2
3
4
5
-1
-2
-3
-4
-5 0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
12:00 18:00 00:00 06:00 12:00 18:00 00:00 06:00 12:00
Satel l i te-Pred - 10 Oct 2005 10:53:13Satel l i te-Pred - 10 Oct 2005 10:53:13
(UTCG) 31 May 2004 12:00:00.000 to 2 Jun 2004 14:05:00.000
1 Ju
n 20
04 0
0:00
:00.
000
2 Ju
n 20
04 0
0:00
:00.
000
Pg 17 of 89AGI www.agiuc.com
General remarks
• Classical approach works well– For single impulse– No tracking during thrust
• The accuracy of maneuver reconstruction– Depends on the tracking data density– Depends on sampling post-maneuver orbit
• Rules of thumb– Can be developed through parametric analyses
• Using a simulator, IOD, and Least Squares
Pg 18 of 89AGI www.agiuc.com
Questions on GEO EW Reconstruction?
Pg 19 of 89AGI www.agiuc.com
HEO unknown “perigee” burn
Pg 20 of 89AGI www.agiuc.com
The HEO problem
• Tracking during apogee
• No tracking through perigee
• Small maneuvers at perigee spoil the fit to tracking data– Find a way to “fit through” maneuvers– Then reverse engineer maneuver
Pg 21 of 89AGI www.agiuc.com
Process overview – HEO impulse
Pre-maneuver trackingUnknown
maneuver event Post-maneuver tracking
Filter accepts tracking data
Smooth backwardPredict Backward
Filter & Smooth – Solve for correction to GUESS
GUESS
Normal OD (filter) Predict thru unknown maneuver Filter rejects tracking data
Add “shotgun” V’s
Difference ephemerides in STK
Pg 22 of 89AGI www.agiuc.com
Dense tracking schedule
• Single ground station (Boston)
• Dense tracking 1 ob / 10 minutes
0.5 1.0 1.5 2.0 2.5 3.0
Measurement File TimesMeasurement File Times
Days since 01 Jun 2004 00:00:00.00
Pg 23 of 89AGI www.agiuc.com
Nominal performance without maneuver
Satellite1 2-Sigmas Radial Satellite1 2-Sigmas Intrack Satellite1 2-Sigmas Crosstrack
0306090
120150180210240270300
330360390420450480
0.5 1.0 1.5 2.0 2.5 3.0
Tw
o S
igm
as
(m
)
Position Uncertainty (0.95P)Position Uncertainty (0.95P)
Days since 01 Jun 2004 00:00:00.00
5 hour data gap
Pg 24 of 89AGI www.agiuc.com
Nominal range residuals without maneuver
0
10
20
30
-10
-20
-30
-40
-500.5 1.0 1.5 2.0 2.5 3.0
Me
as
ure
me
nt
Re
sid
ua
l (m
)
Measurement ResidualMeasurement Residual
Days since 01 Jun 2004 00:00:00.00
Insert maneuver in 5 hr gap
Pg 25 of 89AGI www.agiuc.com
Simulated maneuver
• Tracking gap 3 Jun (7:20 – 12:20)
• Simulated delta-v intrack = 0.5 m/sec
• Maneuver time = 3 Jun 10:20
Pg 26 of 89AGI www.agiuc.com
Maneuver detection is easy
A Tracker Meas Residuals RE Tracker Meas Residuals
0
3000
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9000
12000
15000
18000
21000
24000
27000
30000
33000
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-3000
0.5 1.0 1.5 2.0 2.5 3.0
Me
as
ure
me
nt
Re
sid
ua
l (m
)
Range ResidualsRange Residuals
Days since 01 Jun 2004 00:00:00.00
Pg 27 of 89AGI www.agiuc.com
Process overview – HEO impulse
Pre-maneuver trackingUnknown
maneuver event Post-maneuver tracking
Normal OD (filter) Predict thru unknown maneuver Filter rejects tracking data
Add “shotgun” V’s
Pg 28 of 89AGI www.agiuc.com
“Shotgun” maneuver process noise over 5 hours
• Over data gap (true maneuver at 10:20)– Insert 5 V impulses at:
• 3 Jun 2004 07:30:00.000 UTCG• 3 Jun 2004 08:40:00.000 UTCG• 3 Jun 2004 09:50:00.000 UTCG• 3 Jun 2004 11:00:00.000 UTCG• 3 Jun 2004 12:10:00.000 UTCG
– Set VR = VI = VC = 0– Set process noise magnitude
RDOT = 0.5 m/sec IDOT = 0.5 m/sec CDOT = 0.5 m/sec
– Run filter and smoother
Pg 29 of 89AGI www.agiuc.com
Process overview – HEO impulse
Pre-maneuver trackingUnknown
maneuver event Post-maneuver tracking
Filter accepts tracking data
Normal OD (filter) Predict thru unknown maneuver Filter rejects tracking data
Add “shotgun” V’s
Pg 30 of 89AGI www.agiuc.com
Filter processes through maneuver
0
10
20
30
-10
-20
-30
-40
-500.5 1.0 1.5 2.0 2.5 3.0
Me
as
ure
me
nt
Re
sid
ua
l (m
)
Measurement ResidualMeasurement Residual
Days since 01 Jun 2004 00:00:00.00
Maneuver
First post-maneuver track (at ~ 2.6 d)
Pg 31 of 89AGI www.agiuc.com
Covariance inflated by delta-V’s
Satellite1 2-Sigmas Radial Satellite1 2-Sigmas Intrack Satellite1 2-Sigmas Crosstrack
0
10000
20000
30000
40000
50000
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80000
0.5 1.0 1.5 2.0 2.5 3.0
Tw
o S
igm
as
(m
)
Position Uncertainty (0.95P)Position Uncertainty (0.95P)
Days since 01 Jun 2004 00:00:00.00
First post-maneuver track (at ~ 2.6 d)
Almost 80 km
Pg 32 of 89AGI www.agiuc.com
Process overview – HEO impulse
Pre-maneuver trackingUnknown
maneuver event Post-maneuver tracking
Filter accepts tracking data
Normal OD (filter) Predict thru unknown maneuver Filter rejects tracking data
Add “shotgun” V’s
Smooth backward
Show why this does not identify maneuver time
Pg 33 of 89AGI www.agiuc.com
Smoother covariance is much better
Satellite1 2-Sigmas Radial Satellite1 2-Sigmas Intrack Satellite1 2-Sigmas Crosstrack
0
300600
9001200
1500
18002100
2400
27003000
33003600
3900
42004500
4800
0.5 1.0 1.5 2.0 2.5 3.0
Tw
o S
igm
as
(m
)
Position Uncertainty (0.95P)Position Uncertainty (0.95P)
Days since 01 Jun 2004 00:00:00.00
First post-maneuver track (at ~ 2.6 d)
Significantly reduced from 80 km
Pg 34 of 89AGI www.agiuc.com
Smoother estimates Rdot, Idot, Cdot
• (true maneuver at 10:20 with 0.0, 0.5, 0.0 m/s)
• Solves for Rdot, Idot, Cdot:– 5 times impulses m/s sigmas m/s
• 07:30:00.000 -.03, .07, .0008 .27, .33, .29• 08:40:00.000 .05, .10, -.0009 .44, .41, .41• 09:50:00.000 -.05, .13, -.002 .46, .43, .40• 11:00:00.000 -.05, .15, -.003 .45, .37, .34• 12:10:00.000 .06, -.06, .001 .42, .13, .47
– Can’t tell where maneuver is, but there is no crosstrack component
– Rerun with CDOT = 0
Pg 35 of 89AGI www.agiuc.com
Performance with subsets is similar
Satellite1 2-Sigmas Radial Satellite1 2-Sigmas Intrack Satellite1 2-Sigmas Crosstrack
0
200
400
600
800
1000
1200
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1600
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2200
0.5 1.0 1.5 2.0 2.5 3.0
Tw
o S
igm
as
(m
)
Position Uncertainty (0.95P)Position Uncertainty (0.95P)
Days since 01 Jun 2004 00:00:00.00
Pg 36 of 89AGI www.agiuc.com
Systematic search
• (True maneuver at 10:20)
• Postulate 3 maneuvers with CDOT = 0– Case 1
• 07:30:00.000 .10, -.16, 0 .19, .21, 0• 08:40:00.000 -.07, .14, 0 .42, .40, 0• 09:50:00.000 -.11, .48, 0 .19, .21, 0
– Case 2• 08:40:00.000 -.02, .05, 0 .18, .22, 0• 09:50:00.000 -.03, .20, 0 .44, .39, 0• 11:00:00.000 .10, .27, 0 .17, .22, 0
– Case 3• 09:50:00.000 -.04, .32, 0 .19, .23, 0• 11:00:00.000 .005, .19, 0 .43, .35, 0• 12:10:00.000 .03, -.01, 0 .30, .07, 0
Pg 37 of 89AGI www.agiuc.com
Remarks – HEO “shotgun”
• Disadvantage of V “shotgun”– Can’t really find the time of maneuver with shotgun
approach– Can’t reverse engineer maneuver without time of
maneuver
• Advantages of V “shotgun”– Allows continued operations through maneuver– Rapid return to operational accuracy
• So how can we leverage the solution to find the maneuver?
Pg 38 of 89AGI www.agiuc.com
Process overview – HEO impulse
Pre-maneuver trackingUnknown
maneuver event Post-maneuver tracking
Filter accepts tracking data
Smooth backwardPredict Backward
Normal OD (filter) Predict thru unknown maneuver Filter rejects tracking data
Add “shotgun” V’s
Difference ephemerides in STK
How much post-maneuver data is required and what is the maneuver reconstruction?
Pg 39 of 89AGI www.agiuc.com
Satellite1 2-Sigmas Radial Satellite1 2-Sigmas Intrack Satellite1 2-Sigmas Crosstrack
0
2000
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6000
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55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
Tw
o S
igm
as
(m
)
Position Uncertainty (0.95P)Position Uncertainty (0.95P)
Hours since 01 Jun 2004 00:00:00.00
Closely examine filter response
Single measurement eliminates a lot of the orbit error.
What if we filter one measurement and predict backward – and compare to forward prediction?
Pg 40 of 89AGI www.agiuc.com
Position differences forward vs backward predictions
Zero at 10:42
Truth at 10:20
Pg 41 of 89AGI www.agiuc.com
Velocity differences forward vs backward predictions
At 10:42, Rdot = 0.22, Idot = 0.57
These values will cause residual rejection in filter. (A litmus test for good maneuver reconstruction.)
Pg 42 of 89AGI www.agiuc.com
Satellite1 2-Sigmas Radial Satellite1 2-Sigmas Intrack Satellite1 2-Sigmas Crosstrack
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igm
as
(m
)
Position Uncertainty (0.95P)Position Uncertainty (0.95P)
Hours since 01 Jun 2004 00:00:00.00
Improve on maneuver time?
What if we filter one hour of tracking and predict backward – and compare to forward prediction?
Pg 43 of 89AGI www.agiuc.com
With one hour post-maneuver track
Zero at 09:49
Truth at 10:20
Pg 44 of 89AGI www.agiuc.com
At 09:49, Rdot = -0.17, Idot = 0.43
With one hour post-maneuver track
These values will also cause residual rejection in filter since the time is not well-determined
Pg 45 of 89AGI www.agiuc.com
Satellite1 2-Sigmas Radial Satellite1 2-Sigmas Intrack Satellite1 2-Sigmas Crosstrack
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Tw
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igm
as
(m
)
Position Uncertainty (0.95P)Position Uncertainty (0.95P)
Hours since 01 Jun 2004 00:00:00.00
What if we filter four hours of tracking and predict backward – and compare to forward prediction?
With four hour post-maneuver track?
Pg 46 of 89AGI www.agiuc.com
Zero at 10:22
Truth at 10:20
With four hour post-maneuver track
Pg 47 of 89AGI www.agiuc.com
At 09:49, Rdot = .01, Idot = 0.508
With four hour post-maneuver track
These values work well in the filter
Pg 48 of 89AGI www.agiuc.com
Resolution of maneuver time
Post-maneuver track length Estimated time of maneuver
1 observation 10:42
1 hour 09:49
2 hours 10:04
3 hours 10:09
4 hours (1/3 rev) 10:20
Pg 49 of 89AGI www.agiuc.com
Do we need 4 hours of dedicated tracking?
NO !
Pg 50 of 89AGI www.agiuc.com
Reduce tracking schedule
• Thinned tracking yields maneuver time of 10:22 – Short track at “rise”– Short track “at apogee”– Short track at “set”
• Sparse tracking yields maneuver time of 10:11 – Short track at “rise”– Short track at “set”
• Rule of Thumb– 3 tracks over a 1/3 rev is better than 2 tracks
Pg 51 of 89AGI www.agiuc.com
Summary HEO perigee impulse
• “Shotgun” allows filter to process through maneuver when time of maneuver is unknown
• Post-maneuver filter– Rapidly converges– Can be used to form backward prediction– Compare to forward filter– And find an approximate maneuver time and magnitude
• Accuracy of maneuver estimate depends on– Duration of post-maneuver track– Quality of post-maneuver data
Pg 52 of 89AGI www.agiuc.com
Questions on HEO “Shotgun”?
Pg 53 of 89AGI www.agiuc.com
Continuous thrusting - XIPS
Pg 54 of 89AGI www.agiuc.com
XIPS maneuvers
• Boeing 702 (ANIK-F2 insertion)– Nearly continuous thrusting for 18 days– Circularize GEO orbit– Low thrust XIPS (Xenon Ion Propulsion System)
• Assumption– Tracking = 3 tracks per day from 3 stations
Pg 55 of 89AGI www.agiuc.com
ANIK-F2 Maneuvers
0 10 20 30 40 50 60
Days since insertion into transfer orbit
0
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20000
30000
40000
Alt
itu
de
(km
)TLE History of Apogee and Perigee Passages
ApogeePerigee
XIPS-Circularization
Pg 56 of 89AGI www.agiuc.com
Simulated thrust sequence
• XIPS ISP = 3800– 9 Aug 35.8 hours– 11 Aug 44.9 hours– 13 Aug 96.7 hours– 18 Aug 91.2 hours– 22 Aug 59.2 hours– 25 Aug 34.2 hours– 27 Aug 0.5 hours
Pg 57 of 89AGI www.agiuc.com
The method of attack
• When commanded maneuver is not known– Brute force fit to data– Determine approximate thrust magnitude– Solve for actual thrust– Iterate to refine fit to data
Pg 58 of 89AGI www.agiuc.com
Process overview – XIPS
Pre-maneuver tracking Post-maneuver tracking
Filter & Smooth – Solve for correction to GUESS
GUESS bounded continuous thrusting
Unknown maneuver sequence
With tracking during thrust
Normal ODPost-maneuver
orbitUse high frequency “shotgun”
Brute force fit to data – accept all
Normal ODPost-maneuver
orbitIterate “shotgun” and brute force fit
seeking statistical consistency
Pg 59 of 89AGI www.agiuc.com
Detect the maneuver
0
100
200
-100
-200
-300
-4000.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Me
as
ure
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nt
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sid
ua
ls (
km
)
Measurement ResidualsMeasurement Residuals
Days since 08 Aug 2004 00:00:00.00
Pg 60 of 89AGI www.agiuc.com
Step 1: Brute force – accept all residuals
BOSS-A Range Meas Residuals COOK-A Range Meas ResidualsHULA-A Range Meas Residuals
-300
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ure
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ls (
km
)
Forced Acceptance - Zero Random NoiseForced Acceptance - Zero Random Noise
Days since 08 Aug 2004 00:00:00.00
Filter states: 6 x orbit1 x solar pressure3 x time varying range bias
3 tracks per day x 3 stnsPoor residuals
Pg 61 of 89AGI www.agiuc.com
Brute force = poor fit & prediction
-2000
-1000
0
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0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5
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imu
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Force Acceptance - Zero Random NoiseForce Acceptance - Zero Random Noise
Days Since 08 Aug 2004 00:00:00.00
Radial
Intrack
Crosstrack
Tracking Data
Maneuver Schedule
Poor fit
Pg 62 of 89AGI www.agiuc.com
Step 2: Shotgun delta-V process noise
• Brute force = poor fit
• Try brute force + process noise– Impulsive delta-V’s in each of RIC
• Parametric search– Vary process noise magnitude– Until accepted residuals within 3
Pg 63 of 89AGI www.agiuc.com
BOSS-A Range Meas Residuals COOK-A Range Meas ResidualsHULA-A Range Meas Residuals
-15
-10
-5
0
5
10
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Me
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ure
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nt
Re
sid
ua
ls (
km
)
Force Acceptance - 0.6 cm/sec Random NoiseForce Acceptance - 0.6 cm/sec Random Noise
Days since 08 Aug 2004 00:00:00.00
Step 2: Best delta-V selection
Better residuals
Pg 64 of 89AGI www.agiuc.com
Step 2: Add random process noise
-2000
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fere
nc
e v
s S
imu
late
d T
ruth
(k
m)
Force Acceptance - 0.6 cm/sec Random NoiseForce Acceptance - 0.6 cm/sec Random Noise
Days Since 08 Aug 2004 00:00:00.00
Radial
Intrack
Crosstrack
Tracking Data
Maneuver Schedule
Good fit
Pg 65 of 89AGI www.agiuc.com
Good fit enlarged
-50
-25
0
25
50
0.5 1.5 2.5 3.5
Po
sit
ion
Dif
fere
nc
e v
s S
imu
late
d T
ruth
(k
m)
Force Acceptance - 0.6 cm/sec Random NoiseForce Acceptance - 0.6 cm/sec Random Noise
Days Since 08 Aug 2004 00:00:00.00
Pg 66 of 89AGI www.agiuc.com
Step 2 result
• Parametric search - vary random velocity process until most residuals fall within 3 – 0.6 cm/sec – applied once per minute– Implies acceleration error < 0.01 cm/sec2
– Good fit to data + good bound for unknown accelerations
• Step 3:– Set filter acceleration state = 0.01 cm/sec2
• Correlation half-life to 20 days
– Filter states • 6 x orbit• 1 x solar pressure• 3 x time varying range biases• 3 x thrust accelerations
Pg 67 of 89AGI www.agiuc.com
BOSS-A Range Meas Residuals COOK-A Range Meas ResidualsHULA-A Range Meas Residuals
-15
-10
-5
0
5
10
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Me
as
ure
me
nt
Re
sid
ua
ls (
km
)
Force Acceptance - 0.6 cm/sec Random NoiseForce Acceptance - 0.6 cm/sec Random Noise
Days since 08 Aug 2004 00:00:00.00
Recall Step 2 residuals
Better residuals
Pg 68 of 89AGI www.agiuc.com
Step 3 – much smaller residuals
BOSS-A Range Meas Residuals COOK-A Range Meas ResidualsHULA-A Range Meas Residuals
0
500
1000
-500
-10000 2 4 6 8 10 12 14 16 18 20 22 24
Me
as
ure
me
nt
Re
sid
ua
ls (
m)
Force Acceptance - Estimate Thrust ParametersForce Acceptance - Estimate Thrust Parameters
Days since 08 Aug 2004 00:00:00.00
Pg 69 of 89AGI www.agiuc.com
Recall thrust sequence
• XIPS ISP = 3800– 9 Aug 35.8 hours– 11 Aug 44.9 hours– 13 Aug 96.7 hours– 18 Aug 91.2 hours– 22 Aug 59.2 hours– 25 Aug 34.2 hours– 27 Aug 0.5 hours
Pg 70 of 89AGI www.agiuc.com
Step 3 – orbit error < 1 km
Best_ANIK Radial Position Differences Best_ANIK Intrack Position DifferencesBest_ANIK Crosstrack Position Differences
0
5
10
-5
-10
-150 2 4 6 8 10 12 14 16 18 20 22 24
Po
sit
ion
Dif
fere
nc
es
vs
Sim
ula
ted
Tru
th (
km
)
Force Acceptance - Estimate Thrust ParametersForce Acceptance - Estimate Thrust Parameters
Days Since 08 Aug 2004 00:00:00.00
Except for where real thrust is zero
Pg 71 of 89AGI www.agiuc.com
Step 3 - detects thrust acceleration
Reverse Eng Mnvr X DelAccel Reverse Eng Mnvr Y DelAccel Reverse Eng Mnvr Z DelAccel
0.00000
0.00002
0.00004
-0.00002
-0.00004
-0.00006
-0.00008
-0.000100 2 4 6 8 10 12 14 16 18 20
Ac
ce
l Ma
gn
itu
de
m/s
ec
**2
Force Acceptance - Estimate Maneuver ParametersForce Acceptance - Estimate Maneuver Parameters
Days since 09 Aug 2004 00:00:00.00
Estimate recovers thrust magnitude and detects gaps in thrusting
Pg 72 of 89AGI www.agiuc.com
Review iteration method for continuous thrusting
• Detect maneuver by rejected residuals
• Step 1: Brute force accept residuals
• Step 2: Brute force + shotgun V– Iterate magnitude of V until residuals fall within 3– This defines process noise for continuous acceleration
• Step 3: postulate filter states for continuous thrusting– Set acceleration sigmas according to Step 2– Solve for accelerations as part of OD process
Pg 73 of 89AGI www.agiuc.com
Questions on “iterated brute force”?
Pg 74 of 89AGI www.agiuc.com
DSCS perigee raising burn
Pg 75 of 89AGI www.agiuc.com
DSCS event
• DSCS GEO transfer– Oct 21, 2000– Apogee burn – raising perigee – lower inclination– Tracking data during burn
• Times of maneuver unknown
• Thrust direction unknown
Pg 76 of 89AGI www.agiuc.com
Process overview – DSCS
Pre-maneuver tracking Post-maneuver tracking
Filter & Smooth – Solve for correction to GUESS
Iterate on thrust uncertainties
Normal OD Detect start of burn with residuals
Normal ODSolve for continuous thrust in Intrack and Crosstrack directions at apogee
Iterate on end of burn until post-
burn residuals are accepted
Unknown maneuver sequence
With tracking during thrust
Pg 77 of 89AGI www.agiuc.com
Maneuver detection is easy
0
100
200
300
400
500
600
700
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58
Ra
ng
e R
es
idu
al (
km
)
Range ResidualRange Residual
Hours since 20 Oct 2000 00:00:00.00
Pg 78 of 89AGI www.agiuc.com
Enlarged
0.0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
2.4
2.7
3.0
3.3
3.6
3.9
4.2
4.5
4.8
-0.3
-0.6
-0.9
2820 2825 2830 2835 2840 2845 2850 2855 2860 2865 2870 2875 2880
Ra
ng
e R
es
idu
al (
km
)
Range ResidualRange Residual
Minutes since 20 Oct 2000 00:00:00.00
Ignition = 21 Oct 2000 23:28:00.000 UTCG
~2853.5
Pg 79 of 89AGI www.agiuc.com
Educated guesswork
• Ignition at 21 Oct 2000 23:28:00.000 UTCG
• Perigee-raising maneuver– Radial thrust = 0– Intrack thrust 0, choose initial acceleration 0.25 m/sec2.
• Inclination change– Crosstrack thrust 0 , choose initial acceleration 0.25 m/sec2.
• Model as constant thrust (choose mass & ISP)
• Thrust uncertainty– Magnitude = 30%– Direction = 15
• Duration Parametric trial and error
Pg 80 of 89AGI www.agiuc.com
First attempt, duration = 30 min
0.00
0.30
0.60
0.90
1.20
1.50
1.80
2.10
2.40
2.70
3.00
3.30
3.60
3.90
4.20
4.50
-0.30
-0.60
-0.90
2820 2830 2840 2850 2860 2870 2880 2890 2900 2910
Ra
ng
e R
es
idu
al (
km
)
Measurement ResidualMeasurement Residual
Minutes past Midnight 20 Oct 2000 00:00:00.00
Ignition = 21 Oct 2000 23:28:00.000 UTCG
2853.5
Pg 81 of 89AGI www.agiuc.com
2nd attempt, duration = 60 min
0.00.3
0.6
0.91.2
1.5
1.82.1
2.4
2.73.0
3.3
3.6
3.94.2
4.5
-0.3
-0.6-0.9
2820 2830 2840 2850 2860 2870 2880 2890 2900 2910 2920 2930 2940
Ra
ng
e R
es
idu
al (
km
)
Range ResidualRange Residual
Minutes past Midnight 20 Oct 2000 00:00:00.00
Ignition = 21 Oct 2000 23:28:00.000 UTCG
2853.5
Pg 82 of 89AGI www.agiuc.com
3rd guess = 65 minutes
0.0
1.0
2.0
3.0
4.0
-1.0
-2.0
-3.0
-4.0
-5.01380 1390 1400 1410 1420 1430 1440 1450 1460 1470 1480 1490
Ra
ng
e R
es
idu
al (
km
)
Measurement ResidualMeasurement Residual
Minutes past Midnight 21 Oct 2000 00:00:00.00
Ignition = 21 Oct 2000 23:28:00.000 UTCG
1413.5
Sign reversal 1473
End burn 22 Oct 2000 00:32:00.000 UTCG
Total duration 64 minutes
Pg 83 of 89AGI www.agiuc.com
Best guess start & end times
A REEF-A Meas Residuals RE REEF-A Meas Residuals RE GUAM-A Meas Residuals A GUAM-A Meas ResidualsA LION-B Meas Residuals A BOSS-A Meas Residuals RE BOSS-A Meas Residuals A GUAM-B Meas Residuals
0.00
10.00
20.00
30.00
40.00
50.00
-10.00
-20.00
-30.00
-40.00
-50.000.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50
Ra
ng
e R
es
idu
al (
m)
Measurement ResidualMeasurement Residual
Days since 20 Oct 2000 00:00:00.00
Duration = 62:02 minutes
Filter another 17 hrs
And smooth back
Pg 84 of 89AGI www.agiuc.com
Filter corrections to maneuver
MEB planned X DelAccel MEB planned Y DelAccel MEB planned Z DelAccel
0.000.020.040.060.080.100.120.140.160.180.20
-0.02-0.04-0.06-0.08-0.10-0.12-0.14-0.16-0.18-0.20
1410 1414 1418 1422 1426 1430 1434 1438 1442 1446 1450 1454 1458 1462 1466 1470
Ac
ce
l Ma
gn
itu
de
m/s
ec
**2
Finite Maneuver Inertial Correction HistoryFinite Maneuver Inertial Correction History
Minutes since 21 Oct 2000 00:00:00.00
Best guess: constant thrust
Initial acceleration 0.356 m/sec**2Final acceleration 0.632 m/sec**2
Filter correction
Initial acceleration 0.000 m/sec**2Final acceleration -0.009 m/sec**2
Pg 85 of 89AGI www.agiuc.com
MEB planned X DelAccel MEB planned Y DelAccel MEB planned Z DelAccel
0.000.020.040.060.080.100.120.140.160.180.20
-0.02-0.04-0.06-0.08-0.10-0.12-0.14-0.16-0.18-0.20
1410 1414 1418 1422 1426 1430 1434 1438 1442 1446 1450 1454 1458 1462 1466 1470
Ac
ce
l Ma
gn
itu
de
m/s
ec
**2
Finite Maneuver Inertial Correction HistoryFinite Maneuver Inertial Correction History
Minutes since 21 Oct 2000 00:00:00.00
Smoother corrections to maneuver
Best guess: constant thrust
Initial acceleration 0.356 m/sec**2Final acceleration 0.632 m/sec**2
Smoother correction
Initial acceleration -0.007 m/sec**2Final acceleration -0.054 m/sec**2
Most of correction probably due to increased yaw error through long burn
Pg 86 of 89AGI www.agiuc.com
Remarks on DSCS transfer orbit
• This was a live data case– We had to also estimate biases and transponder biases– Truth is unknown
• The methodology – Developed for simulated maneuvers– Works for live maneuvers
• Data was thinned– Actual tracking data collected at 1 sec rate– Our analysis thinned data to 30 sec rate
Pg 87 of 89AGI www.agiuc.com
Questions on DSCS transfer burn?
Pg 88 of 89AGI www.agiuc.com
Tools used in this analysis
• ODTK for orbit determination– IOD– Least squares– Filter– Smoother
• STK for ephemeris comparisons
Pg 89 of 89AGI www.agiuc.com
Final Comments
• It is possible to reverse engineer maneuvers– A variety of techniques are explored and their strengths and weaknesses
are discussed– Accuracy depends on tracking frequency and post-maneuver orbit
coverage
• The classical approach works well for single impulses– Post maneuver IOD, least squares, and back prediction– Accuracy improves with more post-maneuver tracking
• The filter-smoother approach works well for finite maneuvers– With tracking data during the maneuver– Filter through maneuver & solve for thrust parameters– Refine thrust estimates by iterating filter & smoother– Accuracy depends on tracking frequency and coverage
Pg 90 of 89AGI www.agiuc.com
Additional topic (if there’s time)
Pg 91 of 89AGI www.agiuc.com
LEO Single Impulse
Pg 92 of 89AGI www.agiuc.com
This approach
Pre-maneuver trackingUnknown
maneuver event
Post-maneuver tracking
Predict thru unknown maneuverNormal OD Reject data
Pg 93 of 89AGI www.agiuc.com
0
100
200
300
400
500
12 24 36 48 60 72 84
Po
sit
ion
0.9
5P
Un
ce
rta
inty
(m
)
Normal Operational Orbit AccuracyNormal Operational Orbit Accuracy
Hours
Establish normal orbit accuracy
• “Normal” real-time accuracy– ~ 30 m over radar sites (2)
• Gaussian residuals
• Next: – Insert maneuver
– 20 m/sec at 84 hours
CONVERGED
INITALIZATION = 2 Hrs (< 2 revs)
0
3
6
-3
-6
12 24 36 48 60 72 84
Me
as
ure
me
nt
Re
sid
ua
l Ra
tio
(S
igm
as
)
Measurement Residual / SigmaMeasurement Residual / Sigma
Hours
Pg 94 of 89AGI www.agiuc.com
Simulation & tracking schedule (radar only)
• Insert maneuver:– Impulsive delta-V
• 20 m/s Intrack
– 78 min gap in tracking data
CC_SE Tracker ID FYL_A Tracker ID EGLI Tracker IDBE_S Tracker ID TH_N Tracker ID CDANE Tracker ID
330
340
350
360
370
380
390
400
410
80 82 84 86 88
Tra
ck
er
ID
M easurement Times - Radar OnlyM easurement Times - Radar Only
Hours Since 10 Jun 2003 00:00:00.00
Simulated Maneuver
Tracking Data Gap = 78 min
CC_SE Tracker ID FYL_A Tracker ID EGLI Tracker IDBE_S Tracker ID TH_N Tracker ID CDANE Tracker ID
330
340
350
360
370
380
390
400
410
12 24 36 48 60 72 84 96 108 120 132
Tra
ck
er
ID
Measurement Times - Radar OnlyMeasurement Times - Radar Only
Hours Since 10 Jun 2003 00:00:00.00
Simulated Maneuver
Pg 95 of 89AGI www.agiuc.com
Maneuver detection
• Detection is easy– Range residuals 200 km
– Expected target is “missing”
• Radar response– Collect a longer track
• Challenge to determine – Time of maneuver
– Direction of maneuver
• Rapidly recover orbit accuracy
0
30
60
90
120
150
180
-30
-60
-90
-120
-150
-180
5074 5075 5076 5077 5078 5079 5080 5081
Re
sid
ua
l (k
m)
Eglin Post-M aneuver Range Residual TrendEglin Post-M aneuver Range Residual Trend
Minutes
030
6090
120150180
210240
-30
-60-90
-120
-150-180
-210-240
5078 5079 5080 5081 5082 5083 5084 5085
Re
sid
ua
l (k
m)
Cape Cod Post-M aneuver Range Residual TrendCape Cod Post-M aneuver Range Residual Trend
Minutes
Maneuver + 35 min
Maneuver + 41 min
Pg 96 of 89AGI www.agiuc.com
Refine maneuver time
• SCC deduce maneuver magnitude:– Last good track = Fylingdales at 11:17– First post-maneuver track = Eglin at 12:35, as UCT– Possible maneuver times = 11:17 – 12:35
– Approach:• Use 2 Eglin OBS at 12:35 and 12:36• Solve rendezvous problem for each OB• Most likely maneuver = same as rendezvous solution
Pg 97 of 89AGI www.agiuc.com
At each time over gap intracking data
Find the delta-v thatpasses through
the detected radar observation
position
Lambert’s problem
Pg 98 of 89AGI www.agiuc.com
Find likely maneuver times
Last Good Track
Solutions DisagreeDiscard Hypotheses
Most Likely HypothesisHypotheses Agree &
Minimum Delta-V
What delta-v is requiredto rendezvous with 2 Eglin
OBS ?
Find times where hypotheses agree
Most likely hypotheses are smaller delta-v’s
truth = 20 m/sec at t = 3060 sec
Very Large Delta-V’sAre Unlikely
0 1000 2000 3000
Seconds Since Last Good Track
10
20
30
De
lta
-V M
ag
nit
ud
e (
m/s
ec
)
Search For Maneuver TimeUsing Hill's Equations and Two Radar OBS
OB at 5100 secOB at 5160 sec
Use Gooding's solution to Lambert's problem
Pg 99 of 89AGI www.agiuc.com
0 1000 2000 3000Seconds Since Last Good Track
-20
-10
0
10
20
30
De
lta
-V C
om
po
ne
nts
(m
/se
c)
Probable Delta V ComponentsUsing Hill's Equations and Two Radar OBS
OB at 5100 secOB at 5160 sec
INTRACK
RADIAL
CROSSTRACK
Solutions disagreeDiscard hypotheses
Most likely hypothesisHypotheses agree &
Minimum delta-v
Algorithm requires 2 OBS, T = 1 min
Find maneuver components
Choose most likely hypothesis
Set filter a priori value:• RDOT = 2 m/sec• IDOT = 20 m/sec• CDOT = 0 m/sec
Set maneuver covariance:
RDOT = IDOT = CDOT = (10% V) = 2 m/sec
(Covariance accounts for errors in tracking data, hill’s equations, & pre-maneuver orbit estimate)
Use Gooding's solution to Lambert's problem & two OBS
Pg 100 of 89AGI www.agiuc.com
Processes through maneuver
• Use restart feature– Restart before maneuver
• Use rendezvous maneuver components
– Process through maneuver• 20 m/sec
• Immediate convergence to new orbit– Recovery on one track
• Length = 1 minute
– No residuals rejected !!!
0
100
200
300
400
500
12 24 36 48 60 72 84 96 108 120 132 144
Po
sit
ion
0.9
5P
Un
ce
rta
inty
(m
)
Orbit Accuracy Thru 20 m/sec Maneuver EventOrbit Accuracy Thru 20 m/sec Maneuver Event
Hours
0
3
6
-3
-6
12 24 36 48 60 72 84 96 108 120 132 144
Me
as
ure
me
nt
Re
sid
ua
l R
ati
o (
Sig
ma
s)
Measurement Residual / SigmaMeasurement Residual / Sigma
Hours
Pg 101 of 89AGI www.agiuc.com
Remarks on Lambert’s Problem approach
• Advantages:– Rapidly identifies likely maneuver times
• Disadvantages– Utility diminishes as delta-V becomes smaller– Utility diminishes as data gap becomes longer
– Limitation is the two-body assumption
Pg 102 of 89AGI www.agiuc.com
Questions on Lambert Problem approach?