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Pg 1 of 89 AGI www.agiuc.com Reverse Engineering Maneuvers R Hujsak Oct 13, 2005

Reverse Engineering Maneuvers

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Reverse Engineering Maneuvers. R Hujsak Oct 13, 2005. Unknown maneuver event. Pre-maneuver tracking. Post-maneuver tracking. Predict thru unknown maneuver. Normal OD. Reject data. The problem. Predict thru unknown maneuver. Normal OD. Reject data. - PowerPoint PPT Presentation

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Page 1: Reverse Engineering Maneuvers

Pg 1 of 89AGI www.agiuc.com

Reverse Engineering ManeuversR Hujsak

Oct 13, 2005

Page 2: Reverse Engineering Maneuvers

Pg 2 of 89AGI www.agiuc.com

The problem

Pre-maneuver trackingUnknown

maneuver event

Post-maneuver tracking

Predict thru unknown maneuverNormal OD Reject data

Page 3: Reverse Engineering Maneuvers

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

Page 4: Reverse Engineering Maneuvers

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?

Page 5: Reverse Engineering 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

Page 6: Reverse Engineering Maneuvers

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

Page 7: Reverse Engineering Maneuvers

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

Page 8: Reverse Engineering Maneuvers

Pg 8 of 89AGI www.agiuc.com

GOE EW stationkeeping

Page 9: Reverse Engineering Maneuvers

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

Page 10: Reverse Engineering Maneuvers

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

Page 11: Reverse Engineering Maneuvers

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

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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

Page 12: Reverse Engineering Maneuvers

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

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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

Page 13: Reverse Engineering Maneuvers

Pg 13 of 89AGI www.agiuc.com

Radial (km) In-Track (km) Cross-Track (km) Range (km)

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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

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n 20

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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

Page 14: Reverse Engineering Maneuvers

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)

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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

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:00.

000

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n 20

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: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

Page 15: Reverse Engineering Maneuvers

Pg 15 of 89AGI www.agiuc.com

Add another day of tracking data …

Radial (km) In-Track (km) Cross-Track (km) Range (km)

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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

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000

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:00.

000

Solves the problem:

Solution = 1 Jun 2004 00:01

LS fit to 3 tracks, less than 2 revs of sampling

Page 16: Reverse Engineering Maneuvers

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)

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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

Page 17: Reverse Engineering Maneuvers

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

Page 18: Reverse Engineering Maneuvers

Pg 18 of 89AGI www.agiuc.com

Questions on GEO EW Reconstruction?

Page 19: Reverse Engineering Maneuvers

Pg 19 of 89AGI www.agiuc.com

HEO unknown “perigee” burn

Page 20: Reverse Engineering Maneuvers

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

Page 21: Reverse Engineering Maneuvers

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

Page 22: Reverse Engineering Maneuvers

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

Page 23: Reverse Engineering Maneuvers

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

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igm

as

(m

)

Position Uncertainty (0.95P)Position Uncertainty (0.95P)

Days since 01 Jun 2004 00:00:00.00

5 hour data gap

Page 24: Reverse Engineering Maneuvers

Pg 24 of 89AGI www.agiuc.com

Nominal range residuals without maneuver

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Measurement ResidualMeasurement Residual

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Insert maneuver in 5 hr gap

Page 25: Reverse Engineering Maneuvers

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

Page 26: Reverse Engineering Maneuvers

Pg 26 of 89AGI www.agiuc.com

Maneuver detection is easy

A Tracker Meas Residuals RE Tracker Meas Residuals

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Range ResidualsRange Residuals

Days since 01 Jun 2004 00:00:00.00

Page 27: Reverse Engineering Maneuvers

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

Page 28: Reverse Engineering Maneuvers

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

Page 29: Reverse Engineering Maneuvers

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

Page 30: Reverse Engineering Maneuvers

Pg 30 of 89AGI www.agiuc.com

Filter processes through maneuver

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Measurement ResidualMeasurement Residual

Days since 01 Jun 2004 00:00:00.00

Maneuver

First post-maneuver track (at ~ 2.6 d)

Page 31: Reverse Engineering Maneuvers

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

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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

Page 32: Reverse Engineering Maneuvers

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

Page 33: Reverse Engineering Maneuvers

Pg 33 of 89AGI www.agiuc.com

Smoother covariance is much better

Satellite1 2-Sigmas Radial Satellite1 2-Sigmas Intrack Satellite1 2-Sigmas Crosstrack

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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

Page 34: Reverse Engineering Maneuvers

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

Page 35: Reverse Engineering Maneuvers

Pg 35 of 89AGI www.agiuc.com

Performance with subsets is similar

Satellite1 2-Sigmas Radial Satellite1 2-Sigmas Intrack Satellite1 2-Sigmas Crosstrack

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Position Uncertainty (0.95P)Position Uncertainty (0.95P)

Days since 01 Jun 2004 00:00:00.00

Page 36: Reverse Engineering Maneuvers

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

Page 37: Reverse Engineering Maneuvers

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?

Page 38: Reverse Engineering Maneuvers

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?

Page 39: Reverse Engineering Maneuvers

Pg 39 of 89AGI www.agiuc.com

Satellite1 2-Sigmas Radial Satellite1 2-Sigmas Intrack Satellite1 2-Sigmas Crosstrack

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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?

Page 40: Reverse Engineering Maneuvers

Pg 40 of 89AGI www.agiuc.com

Position differences forward vs backward predictions

Zero at 10:42

Truth at 10:20

Page 41: Reverse Engineering Maneuvers

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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.)

Page 42: Reverse Engineering Maneuvers

Pg 42 of 89AGI www.agiuc.com

Satellite1 2-Sigmas Radial Satellite1 2-Sigmas Intrack Satellite1 2-Sigmas Crosstrack

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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?

Page 43: Reverse Engineering Maneuvers

Pg 43 of 89AGI www.agiuc.com

With one hour post-maneuver track

Zero at 09:49

Truth at 10:20

Page 44: Reverse Engineering Maneuvers

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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

Page 45: Reverse Engineering Maneuvers

Pg 45 of 89AGI www.agiuc.com

Satellite1 2-Sigmas Radial Satellite1 2-Sigmas Intrack Satellite1 2-Sigmas Crosstrack

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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?

Page 46: Reverse Engineering Maneuvers

Pg 46 of 89AGI www.agiuc.com

Zero at 10:22

Truth at 10:20

With four hour post-maneuver track

Page 47: Reverse Engineering Maneuvers

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

Page 48: Reverse Engineering Maneuvers

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

Page 49: Reverse Engineering Maneuvers

Pg 49 of 89AGI www.agiuc.com

Do we need 4 hours of dedicated tracking?

NO !

Page 50: Reverse Engineering Maneuvers

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

Page 51: Reverse Engineering Maneuvers

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

Page 52: Reverse Engineering Maneuvers

Pg 52 of 89AGI www.agiuc.com

Questions on HEO “Shotgun”?

Page 53: Reverse Engineering Maneuvers

Pg 53 of 89AGI www.agiuc.com

Continuous thrusting - XIPS

Page 54: Reverse Engineering Maneuvers

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

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ANIK-F2 Maneuvers

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Days since insertion into transfer orbit

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(km

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ApogeePerigee

XIPS-Circularization

Page 56: Reverse Engineering Maneuvers

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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

Page 57: Reverse Engineering Maneuvers

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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

Page 58: Reverse Engineering Maneuvers

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

Page 59: Reverse Engineering Maneuvers

Pg 59 of 89AGI www.agiuc.com

Detect the maneuver

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Days since 08 Aug 2004 00:00:00.00

Page 60: Reverse Engineering Maneuvers

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Step 1: Brute force – accept all residuals

BOSS-A Range Meas Residuals COOK-A Range Meas ResidualsHULA-A Range Meas Residuals

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-50

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0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

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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

Page 61: Reverse Engineering Maneuvers

Pg 61 of 89AGI www.agiuc.com

Brute force = poor fit & prediction

-2000

-1000

0

1000

2000

3000

4000

5000

6000

7000

8000

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5

Po

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late

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m)

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

Page 62: Reverse Engineering Maneuvers

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

Page 63: Reverse Engineering Maneuvers

Pg 63 of 89AGI www.agiuc.com

BOSS-A Range Meas Residuals COOK-A Range Meas ResidualsHULA-A Range Meas Residuals

-15

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-5

0

5

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0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

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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

Page 64: Reverse Engineering Maneuvers

Pg 64 of 89AGI www.agiuc.com

Step 2: Add random process noise

-2000

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-500

0

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2000

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5

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(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

Page 65: Reverse Engineering Maneuvers

Pg 65 of 89AGI www.agiuc.com

Good fit enlarged

-50

-25

0

25

50

0.5 1.5 2.5 3.5

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imu

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(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

Page 66: Reverse Engineering Maneuvers

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

Page 67: Reverse Engineering Maneuvers

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

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ls (

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)

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

Page 68: Reverse Engineering Maneuvers

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

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Force Acceptance - Estimate Thrust ParametersForce Acceptance - Estimate Thrust Parameters

Days since 08 Aug 2004 00:00:00.00

Page 69: Reverse Engineering Maneuvers

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

Page 70: Reverse Engineering Maneuvers

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

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es

vs

Sim

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Tru

th (

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)

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

Page 71: Reverse Engineering Maneuvers

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

Page 72: Reverse Engineering Maneuvers

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

Page 73: Reverse Engineering Maneuvers

Pg 73 of 89AGI www.agiuc.com

Questions on “iterated brute force”?

Page 74: Reverse Engineering Maneuvers

Pg 74 of 89AGI www.agiuc.com

DSCS perigee raising burn

Page 75: Reverse Engineering Maneuvers

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

Page 76: Reverse Engineering Maneuvers

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

Page 77: Reverse Engineering Maneuvers

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

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es

idu

al (

km

)

Range ResidualRange Residual

Hours since 20 Oct 2000 00:00:00.00

Page 78: Reverse Engineering Maneuvers

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

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km

)

Range ResidualRange Residual

Minutes since 20 Oct 2000 00:00:00.00

Ignition = 21 Oct 2000 23:28:00.000 UTCG

~2853.5

Page 79: Reverse Engineering Maneuvers

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

Page 80: Reverse Engineering Maneuvers

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

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-0.60

-0.90

2820 2830 2840 2850 2860 2870 2880 2890 2900 2910

Ra

ng

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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

Page 81: Reverse Engineering Maneuvers

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

Page 82: Reverse Engineering Maneuvers

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

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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

Page 83: Reverse Engineering Maneuvers

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

Page 84: Reverse Engineering Maneuvers

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

Page 85: Reverse Engineering Maneuvers

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

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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

Page 86: Reverse Engineering Maneuvers

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

Page 87: Reverse Engineering Maneuvers

Pg 87 of 89AGI www.agiuc.com

Questions on DSCS transfer burn?

Page 88: Reverse Engineering Maneuvers

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

Page 89: Reverse Engineering Maneuvers

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

Page 90: Reverse Engineering Maneuvers

Pg 90 of 89AGI www.agiuc.com

Additional topic (if there’s time)

Page 91: Reverse Engineering Maneuvers

Pg 91 of 89AGI www.agiuc.com

LEO Single Impulse

Page 92: Reverse Engineering Maneuvers

Pg 92 of 89AGI www.agiuc.com

This approach

Pre-maneuver trackingUnknown

maneuver event

Post-maneuver tracking

Predict thru unknown maneuverNormal OD Reject data

Page 93: Reverse Engineering Maneuvers

Pg 93 of 89AGI www.agiuc.com

0

100

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400

500

12 24 36 48 60 72 84

Po

sit

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5P

Un

ce

rta

inty

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)

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

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-6

12 24 36 48 60 72 84

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(S

igm

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)

Measurement Residual / SigmaMeasurement Residual / Sigma

Hours

Page 94: Reverse Engineering Maneuvers

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

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390

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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

Page 95: Reverse Engineering Maneuvers

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

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180

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-60

-90

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5074 5075 5076 5077 5078 5079 5080 5081

Re

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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

Page 96: Reverse Engineering Maneuvers

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

Page 97: Reverse Engineering Maneuvers

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

Page 98: Reverse Engineering Maneuvers

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

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e (

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)

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

Page 99: Reverse Engineering Maneuvers

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

Page 100: Reverse Engineering Maneuvers

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

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500

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Po

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Un

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(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

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l R

ati

o (

Sig

ma

s)

Measurement Residual / SigmaMeasurement Residual / Sigma

Hours

Page 101: Reverse Engineering Maneuvers

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

Page 102: Reverse Engineering Maneuvers

Pg 102 of 89AGI www.agiuc.com

Questions on Lambert Problem approach?