Reverse Engineering Maneuvers
R Hujsak
Oct 13, 2005
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The problem
Pre-maneuver tracking
Unknown
maneuver event
Post-maneuver tracking
Normal OD
AGI
Predict thru unknown maneuver
Pg 2 of 89
Reject data
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The usual approach
Unknown
maneuver event
Pre-maneuver tracking
Normal OD
Normal OD
Post-maneuver tracking
Predict thru unknown maneuver
Stop OD process during maneuver
Reject data
Restart OD
process with postmaneuver data
Predict forward
Reconstruction depends on
post-maneuver accuracy
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Pg 3 of 89
Predict backward
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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?
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Pg 4 of 89
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Filters provide other options
Pre-maneuver tracking
Normal OD
Unknown
impulsive event
Post-maneuver tracking
Predict thru unknown maneuver
Reject data
Use the filter
covariance
inflate the covariance
Adding data refines estimate
Postulate various
maneuver hypotheses
Smoothed ephemeris is predicted backward.
Intersection defines maneuver.
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Pg 5 of 89
Filter accepts new data
& covariance collapses
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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
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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
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Pg 7 of 89
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GOE EW stationkeeping
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Pg 8 of 89
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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
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Pg 9 of 89
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The usual approach
Unknown
maneuver event
Pre-maneuver tracking
Normal OD
Normal OD
Post-maneuver tracking
Predict thru unknown maneuver
Stop OD process during maneuver
Reject data
Restart OD
process with postmaneuver data
Predict forward
Reconstruction depends on
post-maneuver accuracy
AGI
Pg 10 of 89
Predict backward
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Maneuver detection is easy…
Maneuver
But residual trends do not
indicate maneuver time
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Pg 11 of 89
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Post-maneuver tracks (enlarged)
Residual trends do not
indicate maneuver time ..
2 hours < 1/3 rev
.. so perform IOD and 3track least squares
(standard orbit analysis).
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Pg 12 of 89
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Least-squares fit & back predict
Satellite-Pred - 10 Oct 2005 11:25:13
100
2 Jun 2004 00:00:00.000
1 Jun 2004 00:00:00.000
100
90
80
70
60
50
40
30
20
10
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
12:00
90
80
70
60
50
40
Solution = 1 Jun 2004 15:00:00
30
Truth = 1 Jun 2004 00:00:00
20
10
0
18:00
00:00
06:00
12:00
18:00
00:00
06:00
12:00
31 May 2004 12:00:00.000 to 2 Jun 2004 14:05:00.000 (UTCG)
Radial (km)
In-Track (km)
Cross-Track (km)
Range (km)
LS fit to 3 tracks, less than 1 rev of sampling
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Pg 13 of 89
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Least-squares fit & back predict
2 Jun 2004 00:00:00.000
2
1 Jun 2004 00:00:00.000
Satellite-Pred - 10 Oct 2005 11:16:59
3
1.90
1.80
1.70
1.60
Rdot = 0.1 m/sec
1
1.50
Idot = 0.99 m/sec
1.40
1.30
0
1.20
1.10
-1
1.00
0.90
Solution = 1 Jun 2004 15:00:00
0.80
Truth = 1 Jun 2004 00:00:00
0.70
-2
0.60
-3
12:00
0.50
18:00
00:00
06:00
12:00
18:00
00:00
06:00
12:00
31 May 2004 12:00:00.000 to 2 Jun 2004 14:05:00.000 (UTCG)
Radial Vel Diff (m/sec)
Cross-Track Vel Diff (m/sec)
AGI
In-Track Vel Diff (m/sec)
SpeedRelToRICFrame (m/sec)
Pg 14 of 89
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Add another day of tracking data …
60
30
0
-30
440
420
400
380
360
340
320
300
280
260
240
220
200
180
160
140
120
100
80
60
40
20
0
2 Jun 2004 00:00:00.000
90
1 Jun 2004 00:00:00.000
Satellite-Pred - 10 Oct 2005 10:13:42
-60
-90
-120
-150
-180
-210
-240
Solves the problem:
Solution = 1 Jun 2004 00:01
-270
-300
-330
-360
-390
-420
12:00
Radial (km)
18:00
00:00
06:00
12:00
18:00
00:00
(UTCG)
31 May 2004 12:00:00.000 to 2 Jun 2004 14:05:00.000
In-Track (km)
Cross-Track (km)
06:00
12:00
Range (km)
LS fit to 3 tracks, less than 2 revs of sampling
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Pg 15 of 89
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… gives the right answer
4
3
2
2 Jun 2004 00:00:00.000
5
1 Jun 2004 00:00:00.000
Satellite-Pred - 10 Oct 2005 10:53:13
1.90
1.80
1.70
1.60
1.50
1
1.40
1.30
0
1.20
-1
1.10
1.00
-2
0.90
-3
0.80
0.70
-4
-5
12:00
0.60
0.50
18:00
00:00
12:00
18:00
00:00
(UTCG)
31 May 2004 12:00:00.000 to 2 Jun 2004 14:05:00.000
Radial Vel Diff (m/sec)
Cross-Track Vel Diff (m/sec)
AGI
06:00
06:00
12:00
In-Track Vel Diff (m/sec)
SpeedRelToRICFrame (m/sec)
Pg 16 of 89
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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
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Pg 17 of 89
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Questions on GEO EW
Reconstruction?
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Pg 18 of 89
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HEO unknown “perigee” burn
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Pg 19 of 89
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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
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Pg 20 of 89
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Process overview – HEO impulse
Pre-maneuver tracking
Normal OD (filter)
Unknown
maneuver event
Post-maneuver tracking
Predict thru unknown maneuver
Filter rejects tracking data
Add “shotgun” V’s
Filter accepts
tracking data
Predict Backward
Smooth
backward
Difference ephemerides in STK
GUESS
Filter & Smooth – Solve for correction to GUESS
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Pg 21 of 89
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Dense tracking schedule
• Single ground station (Boston)
• Dense tracking 1 ob / 10 minutes
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Pg 22 of 89
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Nominal performance without
maneuver
Two Sigmas (m)
Position Uncertainty (0.95P)
480
450
420
390
360
330
300
270
240
210
180
150
120
90
60
30
0
0.5
5 hour data gap
1.0
Satellite1 2-Sigmas Radial
AGI
1.5
2.0
Days since 01 Jun 2004 00:00:00.00
Satellite1 2-Sigmas Intrack
Pg 23 of 89
2.5
3.0
Satellite1 2-Sigmas Crosstrack
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Nominal range residuals without
maneuver
Insert maneuver in 5 hr gap
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Pg 24 of 89
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Simulated maneuver
• Tracking gap 3 Jun (7:20 – 12:20)
• Simulated delta-v intrack = 0.5 m/sec
• Maneuver time = 3 Jun 10:20
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Pg 25 of 89
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Maneuver detection is easy
AGI
Pg 26 of 89
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Process overview – HEO impulse
Pre-maneuver tracking
Normal OD (filter)
Unknown
maneuver event
Predict thru unknown maneuver
Post-maneuver tracking
Filter rejects tracking data
Add “shotgun” V’s
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Pg 27 of 89
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“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
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Pg 28 of 89
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Process overview – HEO impulse
Pre-maneuver tracking
Normal OD (filter)
AGI
Unknown
maneuver event
Post-maneuver tracking
Predict thru unknown maneuver
Filter rejects tracking data
Add “shotgun” V’s
Filter accepts
tracking data
Pg 29 of 89
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Filter processes through maneuver
First post-maneuver
track (at ~ 2.6 d)
Maneuver
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Pg 30 of 89
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Covariance inflated by delta-V’s
Almost 80 km
First post-maneuver
track (at ~ 2.6 d)
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Pg 31 of 89
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Process overview – HEO impulse
Pre-maneuver tracking
Normal OD (filter)
Unknown
maneuver event
Post-maneuver tracking
Predict thru unknown maneuver
Filter rejects tracking data
Add “shotgun” V’s
Filter accepts
tracking data
Smooth backward
Show why this does not identify maneuver time
AGI
Pg 32 of 89
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Smoother covariance is much better
Significantly reduced from 80 km
First post-maneuver
track (at ~ 2.6 d)
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Pg 33 of 89
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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
•
•
•
•
•
07:30:00.000
08:40:00.000
09:50:00.000
11:00:00.000
12:10:00.000
impulses m/s
sigmas m/s
-.03, .07, .0008
.05, .10, -.0009
-.05, .13, -.002
-.05, .15, -.003
.06, -.06, .001
.27, .33, .29
.44, .41, .41
.46, .43, .40
.45, .37, .34
.42, .13, .47
– Can’t tell where maneuver is, but there is no crosstrack
component
– Rerun with CDOT = 0
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Pg 34 of 89
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Performance with subsets is similar
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Pg 35 of 89
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Systematic search
• (True maneuver at 10:20)
• Postulate 3 maneuvers with CDOT = 0
– Case 1
• 07:30:00.000
• 08:40:00.000
• 09:50:00.000
.10, -.16, 0
-.07, .14, 0
-.11, .48, 0
.19, .21, 0
.42, .40, 0
.19, .21, 0
-.02, .05, 0
-.03, .20, 0
.10, .27, 0
.18, .22, 0
.44, .39, 0
.17, .22, 0
-.04, .32, 0
.005, .19, 0
.03, -.01, 0
.19, .23, 0
.43, .35, 0
.30, .07, 0
– Case 2
• 08:40:00.000
• 09:50:00.000
• 11:00:00.000
– Case 3
• 09:50:00.000
• 11:00:00.000
• 12:10:00.000
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Pg 36 of 89
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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?
AGI
Pg 37 of 89
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Process overview – HEO impulse
Pre-maneuver tracking
Normal OD (filter)
Unknown
maneuver event
Post-maneuver tracking
Predict thru unknown maneuver
Filter rejects tracking data
Add “shotgun” V’s
Filter accepts
tracking data
Predict Backward
Smooth
backward
Difference ephemerides in STK
How much post-maneuver data is required and what is the maneuver reconstruction?
AGI
Pg 38 of 89
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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?
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Pg 39 of 89
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Position differences forward vs
backward predictions
Zero at 10:42
Truth at 10:20
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Pg 40 of 89
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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.)
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Pg 41 of 89
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Improve on maneuver time?
What if we filter one hour of tracking and predict
backward – and compare to forward prediction?
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Pg 42 of 89
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With one hour post-maneuver track
Zero at 09:49
Truth at 10:20
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Pg 43 of 89
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With one hour post-maneuver track
At 09:49, Rdot = -0.17, Idot = 0.43
These values will also cause residual rejection in
filter since the time is not well-determined
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Pg 44 of 89
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With four hour post-maneuver track?
What if we filter four hours of tracking and predict
backward – and compare to forward prediction?
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Pg 45 of 89
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With four hour post-maneuver track
Zero at 10:22
Truth at 10:20
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Pg 46 of 89
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With four hour post-maneuver track
At 09:49, Rdot = .01, Idot = 0.508
These values work well in the filter
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Pg 47 of 89
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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
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Pg 48 of 89
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Do we need 4 hours of dedicated tracking?
NO !
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Pg 49 of 89
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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
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Pg 50 of 89
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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
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Pg 51 of 89
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Questions on HEO “Shotgun”?
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Pg 52 of 89
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Continuous thrusting - XIPS
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Pg 53 of 89
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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
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Pg 54 of 89
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ANIK-F2 Maneuvers
TLE History of Apogee and Perigee Passages
Altitude (km)
40000
Apogee
Perigee
30000
20000
10000
XIPS-Circularization
0
0
10
20
30
40
50
60
Days since insertion into transfer orbit
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Pg 55 of 89
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Simulated thrust sequence
• XIPS ISP = 3800
–
–
–
–
–
–
–
AGI
9 Aug
11 Aug
13 Aug
18 Aug
22 Aug
25 Aug
27 Aug
35.8 hours
44.9 hours
96.7 hours
91.2 hours
59.2 hours
34.2 hours
0.5 hours
Pg 56 of 89
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The method of attack
• When commanded maneuver is not known
–
–
–
–
AGI
Brute force fit to data
Determine approximate thrust magnitude
Solve for actual thrust
Iterate to refine fit to data
Pg 57 of 89
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Process overview – XIPS
Pre-maneuver tracking
Unknown maneuver sequence
Post-maneuver tracking
With tracking during thrust
Normal OD
Use high frequency “shotgun”
Brute force fit to data – accept all
Post-maneuver
orbit
Normal OD
Iterate “shotgun” and brute force fit
seeking statistical consistency
Post-maneuver
orbit
GUESS bounded continuous thrusting
Filter & Smooth – Solve for correction to GUESS
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Pg 58 of 89
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Detect the maneuver
Measurement Residuals
Measurement Residuals (km)
200
100
0
-100
-200
-300
-400
0.5
AGI
1.0
1.5
2.0
2.5
3.0
Days since 08 Aug 2004 00:00:00.00
Pg 59 of 89
3.5
4.0
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Step 1: Brute force – accept all residuals
Forced Acceptance - Zero Random Noise
200
Measurement Residuals (km)
150
Poor residuals
3 tracks per day x 3 stns
100
50
0
-50
-100
-150
-200
Filter states:
6 x orbit
1 x solar pressure
3 x time varying range bias
-250
-300
0.5
1.0
1.5
2.0
2.5
3.0
Days since 08 Aug 2004 00:00:00.00
BOSS-A Range Meas Residuals
HULA-A Range Meas Residuals
AGI
3.5
4.0
COOK-A Range Meas Residuals
Pg 60 of 89
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Brute force = poor fit & prediction
Force Acceptance - Zero Random Noise
Position Difference vs Simulated Truth (km)
8000
7000
5000
Tracking Data
Intrack
4000
3000
2000
Poor fit
Crosstrack
1000
0
-1000
-2000
0.5
AGI
Maneuver Schedule
6000
Radial
1.5
2.5
3.5
4.5
5.5
6.5
Days Since 08 Aug 2004 00:00:00.00
Pg 61 of 89
7.5
8.5
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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
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Step 2: Best delta-V selection
Force Acceptance - 0.6 cm/sec Random Noise
Measurement Residuals (km)
10
5
Better residuals
0
-5
-10
-15
0.5
1.0
3.0
2.5
2.0
1.5
Days since 08 Aug 2004 00:00:00.00
BOSS-A Range Meas Residuals
HULA-A Range Meas Residuals
AGI
3.5
4.0
COOK-A Range Meas Residuals
Pg 63 of 89
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Step 2: Add random process noise
Force Acceptance - 0.6 cm/sec Random Noise
Position Difference vs Simulated Truth (km)
2000
1500
Maneuver Schedule
1000
500
Intrack
Tracking Data
0
-500
Good fit
-1000
Crosstrack
-1500
-2000
0.5
AGI
Radial
1.5
2.5
3.5
4.5
5.5
6.5
Days Since 08 Aug 2004 00:00:00.00
Pg 64 of 89
7.5
8.5
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Good fit enlarged
Force Acceptance - 0.6 cm/sec Random Noise
Position Difference vs Simulated Truth (km)
50
25
0
-25
-50
0.5
AGI
2.5
1.5
Days Since 08 Aug 2004 00:00:00.00
Pg 65 of 89
3.5
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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
•
•
•
•
AGI
6 x orbit
1 x solar pressure
3 x time varying range biases
3 x thrust accelerations
Pg 66 of 89
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Recall Step 2 residuals
Force Acceptance - 0.6 cm/sec Random Noise
Measurement Residuals (km)
10
5
Better residuals
0
-5
-10
-15
0.5
1.0
3.0
2.5
2.0
1.5
Days since 08 Aug 2004 00:00:00.00
BOSS-A Range Meas Residuals
HULA-A Range Meas Residuals
AGI
3.5
4.0
COOK-A Range Meas Residuals
Pg 67 of 89
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Step 3 – much smaller residuals
Force Acceptance - Estimate Thrust Parameters
Measurement Residuals (m)
1000
500
0
-500
-1000
0
2
4
6
8
10
12
14
16
Days since 08 Aug 2004 00:00:00.00
BOSS-A Range Meas Residuals
HULA-A Range Meas Residuals
AGI
18
20
22
24
COOK-A Range Meas Residuals
Pg 68 of 89
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Recall thrust sequence
• XIPS ISP = 3800
–
–
–
–
–
–
–
AGI
9 Aug
11 Aug
13 Aug
18 Aug
22 Aug
25 Aug
27 Aug
35.8 hours
44.9 hours
96.7 hours
91.2 hours
59.2 hours
34.2 hours
0.5 hours
Pg 69 of 89
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Step 3 – orbit error < 1 km
Except for where real thrust
is zero
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Pg 70 of 89
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Step 3 - detects thrust acceleration
Force Acceptance - Estimate Maneuver Parameters
Estimate recovers thrust magnitude and
detects gaps in thrusting
0.00004
Accel Magnitude m/sec**2
0.00002
0.00000
-0.00002
-0.00004
-0.00006
-0.00008
-0.00010
0
2
4
Reverse Eng Mnvr X DelAccel
AGI
6
8
10
12
14
Days since 09 Aug 2004 00:00:00.00
Reverse Eng Mnvr Y DelAccel
Pg 71 of 89
16
18
20
Reverse Eng Mnvr Z DelAccel
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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
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DSCS perigee raising burn
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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
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Process overview – DSCS
Pre-maneuver tracking
Unknown maneuver sequence
Post-maneuver tracking
With tracking during thrust
Normal OD
Normal OD
Detect start of burn with residuals
Solve for continuous thrust in Intrack
and Crosstrack directions at apogee
Iterate on end of
burn until postburn residuals are
accepted
Iterate on thrust uncertainties
Filter & Smooth – Solve for correction to GUESS
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Maneuver detection is easy
Range Residual
700
600
Range Residual (km)
500
400
300
200
100
0
0
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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
Hours since 20 Oct 2000 00:00:00.00
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Enlarged
Range Residual (km)
Range Residual
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4.8
4.5
4.2
3.9
3.6
3.3
3.0
2.7
2.4
2.1
1.8
1.5
1.2
0.9
0.6
0.3
0.0
-0.3
-0.6
-0.9
2820
Ignition = 21 Oct 2000 23:28:00.000 UTCG
~2853.5
2825
2830
2835
2840
2845
2850
2855
2860
Minutes since 20 Oct 2000 00:00:00.00
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2865
2870
2875
2880
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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
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First attempt, duration = 30 min
Ignition = 21 Oct 2000 23:28:00.000 UTCG
 2853.5
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2nd attempt, duration = 60 min
Ignition = 21 Oct 2000 23:28:00.000 UTCG
 2853.5
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3rd guess = 65 minutes
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
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Best guess start & end times
Duration = 62:02 minutes
Filter another 17 hrs
And smooth back
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Filter corrections to maneuver
Best guess: constant thrust
Initial acceleration  0.356 m/sec**2
Final acceleration  0.632 m/sec**2
Filter correction
Initial acceleration  0.000 m/sec**2
Final acceleration  -0.009 m/sec**2
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Smoother corrections to maneuver
Best guess: constant thrust
Initial acceleration  0.356 m/sec**2
Final acceleration  0.632 m/sec**2
Most of correction probably due to increased
yaw error through long burn
Smoother correction
Initial acceleration  -0.007 m/sec**2
Final acceleration  -0.054 m/sec**2
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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
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Tools used in this analysis
• ODTK for orbit determination
–
–
–
–
IOD
Least squares
Filter
Smoother
• STK for ephemeris comparisons
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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
–
–
–
–
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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
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Additional topic (if there’s time)
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LEO Single Impulse
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This approach
Pre-maneuver tracking
Unknown
maneuver event
Post-maneuver tracking
Normal OD
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Predict thru unknown maneuver
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Reject data
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Establish normal orbit accuracy
INITALIZATION = 2 Hrs (< 2 revs)
• “Normal” real-time
accuracy
CONVERGED
– ~ 30 m over radar sites (2)
• Gaussian residuals
• Next:
– Insert maneuver
– 20 m/sec at 84 hours
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Simulation & tracking schedule
(radar only)
Simulated Maneuver
• Insert maneuver:
– Impulsive delta-V
• 20 m/s Intrack
– 78 min gap in tracking data
Tracking Data Gap = 78 min
Simulated Maneuver
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Maneuver detection
• Detection is easy
Maneuver + 35 min
– Range residuals  200 km
– Expected target is “missing”
• Radar response
– Collect a longer track
• Challenge to determine
– Time of maneuver
Maneuver + 41 min
– Direction of maneuver
• Rapidly recover orbit accuracy
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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
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Lambert’s problem
At each time over gap in
tracking data
Find the delta-v that
passes through
the detected radar
observation
position
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Find likely maneuver times
Search For Maneuver Time
UseUsing
Gooding's
solution to
Lambert's
problem
Hill's Equations
and
Two Radar
OBS
Delta-V Magnitude (m/sec)
OB at 5100 sec
OB at 5160 sec
30
Very Large Delta-V’s
Are Unlikely
What delta-v is required
to rendezvous with 2 Eglin
OBS ?
Find times where
hypotheses agree
Last Good Track
Most likely hypotheses are
smaller delta-v’s
Solutions Disagree
Discard Hypotheses
20
truth = 20 m/sec
at t = 3060 sec
Most Likely Hypothesis
Hypotheses Agree &
Minimum Delta-V
10
0
1000
2000
3000
Seconds Since Last Good Track
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Find maneuver components
Probable Delta V Components
Using Hill's
Equations
and Two Radar
OBS& two OBS
Use Gooding's
solution
to Lambert's
problem
OB at 5100 sec
OB at 5160 sec
30
Delta-V Components (m/sec)
Choose most likely
hypothesis
Set filter a priori value:
• RDOT = 2 m/sec
• IDOT = 20 m/sec
• CDOT = 0 m/sec
INTRACK
20
10
Set maneuver covariance:
CROSSTRACK
0
RDOT = IDOT = CDOT = (10%
V) = 2 m/sec
-10
Most likely hypothesis
Hypotheses agree &
Minimum delta-v
Solutions disagree
Discard hypotheses
-20
RADIAL
0
1000
2000
Seconds Since Last Good Track
(Covariance accounts for errors
in tracking data, hill’s
equations, & pre-maneuver
orbit estimate)
3000
Algorithm requires 2 OBS, T = 1 min
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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 !!!
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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
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