February 2001SUNY Plattsburgh Concise Track Characterization of Maneuvering Targets Stephen Linder Matthew Ryan Richard Quintin This material is based on work supported by Dr. Teresa McMullen through the Office of Naval Research under Contract No. N00039-D-0042, Delivery Order No. D.O. 278.

February 2001SUNY Plattsburgh Problem Context A weaving target track constructed of linked coordinated turns

February 2001SUNY Plattsburgh Research 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 parameters Classification of target from pattern of motion Computational feasibility for a real-time in-water system

February 2001SUNY Plattsburgh Approach - Segmenting Track Identifier (STI) Support multiple localized nonlinear models of target motion Most current tracking techniques require linear motion models Use batch processing of data Do not attempt to calculate globally optimal solution, rather Generate locally optimal track segments by minimizing mean square error of each track segment, and then matching the position and velocity of consecutive segments at the knots connecting the segments

February 2001SUNY Plattsburgh Target models Target models used by current trackers Turns (maneuvers) are modeled by the Singer maneuver model Maneuvers are time correlated with a specified time constant and acceleration variance Locally linear models of coordinated models STI target model Target runs at only several discrete speeds Target performs only coordinated turn maneuvers Continuity in position and velocity between segments

February 2001SUNY Plattsburgh Linking coordinated turns knots

February 2001SUNY Plattsburgh Position and velocity continuity Match position Match velocity

February 2001SUNY Plattsburgh Knot Placement Approach Phase I – initial segmentation Calculate if knot is needed after every measurement Place knot if RMSE error of current spline begins to increase Err on the side of generating two many knots and then recombine knots in second phase of processing Make initial position, velocity and acceleration estimate Phase II – refine segmentation After second knot is placed go back and search for a knot position that optimizes continuity conditions for position and velocity of the splines at knot, and minimize total least square fit of both splines to measured data

February 2001SUNY Plattsburgh Knot placement flow diagram No Yes Acquire new segment Optimize knot between S n-2 and S n-1 Can segmen t S n-1 and S n-2 be merged ? Merge successive segments   SnSn S n-1 S n-2 SnSn S n-1   S n-2 SnSn S n-1 S n-3    SnSn S n-2 S n-1 S n-3    SnSn S n-2 S n-1 S n-3    Optimize knot between S n-1 and S n

February 2001SUNY Plattsburgh Cost functions The total least squares term for a line segment Q L is The total least squares term for circular arc segment Q A is

February 2001SUNY Plattsburgh Costs for joining segments The C 0 and C 1 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 k p is a proportionality constant based on the length of the diagonal of the spline’s bounding box

February 2001SUNY Plattsburgh Two Segment Example X - position X - position Y - position Single Trial20 Trials Measurement Noise STD = 2.0 truth Kalman filter tracks Kalman filter track truth STI track STI tracks

February 2001SUNY Plattsburgh Example weaving target track

February 2001SUNY Plattsburgh Estimated weaving tracks Noisy Measurements Track Estimates Kalman Filter Track STI Track

February 2001SUNY Plattsburgh Turn rate estimates for looping track X- position Y- position Time (seconds) Turn rate Truth STI Kalman filter Estimated Tracks Estimated Turn Rates

February 2001SUNY Plattsburgh Cumulative average RMS error for looping track RMS Error Kalman filter- based trackerSTI Tracker position velocity acceleration 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 2001SUNY Plattsburgh Estimation error vs. sample size and measurement noise Diameter of the circle represents the RMS acceleration estimation error Kalman Filter Tracker with Singer Maneuver Model Segmenting Track Identifier (STI) RMS error from 100 trials with looping tracks

February 2001SUNY Plattsburgh Remaining 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 tracker Characterize 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 performance