Concise Track Characterization of Maneuvering TargetsProblem ContextResearch GoalsApproach - Segmenting Track Identifier (STI)Target modelsLinking coordinated turnsPosition and velocity continuityKnot Placement ApproachKnot placement flow diagramCost functionsCosts for joining segmentsTwo Segment ExampleEstimated weaving tracksTurn rate estimates for looping trackCumulative average RMS error for looping trackEstimation error vs. sample size and measurement noiseRemaining Tasks…February 2001 SUNY PlattsburghConcise Track Characterization of Maneuvering Targets Stephen LinderMatthew RyanRichard Quintin This material is based on work supported by Dr. Teresa McMullen through the Office of Naval Research underContract No. N00039-D-0042, Delivery Order No. D.O. 278.February 2001 SUNY PlattsburghProblem ContextA weaving target track constructed of linked coordinated turnsFebruary 2001 SUNY PlattsburghResearch Goals Improve instantaneous estimation of target velocity and acceleration for use by guidance law.Perform data compression on track data so that a succinct description of target track can be obtained “Target traveled at heading of 20° for 100 yards; Turned left at 10°/sec to heading of 100°”Use track characterization to dynamically select and tune guidance law parametersClassification of target from pattern of motion Computational feasibility for a real-time in-water systemFebruary 2001 SUNY PlattsburghApproach - Segmenting Track Identifier (STI)Support multiple localized nonlinear models of target motionMost current tracking techniques require linear motion models Use batch processing of dataDo not attempt to calculate globally optimal solution, ratherGenerate locally optimal track segments byminimizing mean square error of each track segment, and thenmatching the position and velocity of consecutive segments at the knots connecting the segmentsFebruary 2001 SUNY PlattsburghTarget modelsTarget models used by current trackersTurns (maneuvers) are modeled by the Singer maneuver modelManeuvers are time correlated with a specified time constant and acceleration varianceLocally linear models of coordinated models STI target modelTarget runs at only several discrete speedsTarget performs only coordinated turn maneuvers Continuity in position and velocity between segmentsFebruary 2001 SUNY PlattsburghLinking coordinated turnsknotsFebruary 2001 SUNY PlattsburghPosition and velocity continuityMatch positionMatch velocityFebruary 2001 SUNY PlattsburghKnot Placement ApproachPhase I – initial segmentationCalculate if knot is needed after every measurementPlace knot if RMSE error of current spline begins to increaseErr on the side of generating two many knots and then recombine knots in second phase of processingMake initial position, velocity and acceleration estimate Phase II – refine segmentationAfter second knot is placed go back and search for a knot position that optimizescontinuity conditions for position and velocity of the splines at knot, andminimize total least square fit of both splines to measured dataFebruary 2001 SUNY PlattsburghKnot placement flow diagram No YesAcquire new segment Optimize knot between Sn-2 and Sn-1Can segment Sn-1 and Sn-2 be merged?Merge successive segmentsSnSn-1Sn-2SnSn-1Sn-2SnSn-2Sn-1Sn-3SnSn-2Sn-1Sn-3SnSn-2Sn-1Sn-3Optimize knot between Sn-1 and SnFebruary 2001 SUNY PlattsburghCost functionsThe total least squares term for a line segment QL isThe total least squares term for circular arc segment QA is221 1pi iLiy mx bQm=� �- -=� �+� ��2122)(( )pcAi ciyyQ rx xi=� �-= + --� �� ��February 2001 SUNY PlattsburghCosts for joining segmentsThe C0 and C1 continuity condition is given by is the difference in position at the knot between the n and n+1 segment is the difference in heading at the knot between the n and n+1 segment kp is a proportionality constant based on the length of the diagonal of the spline’s bounding box ( )1, , 1 1, , 1( )C p n n n n n n n nQ n k f- + - += D +D +D +DR R, 1n n+DR, 1n nf+DFebruary 2001 SUNY PlattsburghTwo Segment Example-5-30 -20 -10 010-15-1051015-30-25-200X - positionX - position-30 -20 -10 0 1020-30-25-20-15-10-5051015X - positionY - positionSingle Trial 20 TrialsMeasurement Noise STD = 2.0truthKalman filter tracksKalman filter tracktruthSTI trackSTI tracksFebruary 2001 SUNY PlattsburghEstimated weaving tracksNoisy MeasurementsTrack EstimatesKalman Filter TrackSTI TrackFebruary 2001 SUNY PlattsburghTurn rate estimates for looping track0 10 20 30 40 50 60 70-40-35-30-25-20-15-10-50510X- positionY- position0 5 10 15 20 25 30-1-0.8-0.6-0.4-0.200.20.40.60.81Time (seconds)Turn rateTruthSTIKalman filterEstimated TracksEstimated Turn RatesFebruary 2001 SUNY PlattsburghCumulative average RMS error for looping trackRMS ErrorKalman filter-based tracker STI Trackerposition 1.56 0.64velocity 2.79 0.91acceleration 3.41 1.52900 trials of the five-maneuver track for a combination •measurement noise STD: 0.5, 1.0 and 2.0•sample sizes: 60, 120 and 180.February 2001 SUNY PlattsburghEstimation error vs. sample size and measurement noise0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 Measurement Error Velocity Error STI Algorithm 60 samples 120 samples 180 samples 180 samples 60s samples 120 samples Baseline Algorithm Diameter of the circle represents the RMS acceleration estimation errorKalman Filter Tracker with Singer Maneuver ModelSegmenting Track Identifier (STI)RMS error from 100 trials with looping tracksFebruary 2001 SUNY PlattsburghRemaining Tasks…Continue to refine algorithm Develop cost functions for range/bearing measurements.Support fusion of passive, active and Doppler processed active sonar data.Develop multiple track version of the tracker.Compare performance with Kalman filter-based trackerCharacterize lags in detecting maneuvers and performance with very sparse data.Extract track properties and integrate with guidance law and use track characterization to improve guidance
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