A Hybrid Tracker and Smoother for Highly Maneuvering Targets

1. A Hybrid Tracker and Smootherfor Highly Maneuvering Targets Stephen Linder 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. Dartmouth College

2. Problem Context A weaving target track constructed of linked coordinated turns Dartmouth College

3. Research Goals • Develop and algorithm that tracks highly maneuverable targets with sparse measurements. • 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°” • Classification of target and target behavior Dartmouth College

4. Approach – Segmenting Track Identifier (STI) • Use batch processing of data rather than recursive Kalman filter approach • Segment track into discrete segments with each segment have only one mode of motion • support multiple localized nonlinear models of target motion • most tracking techniques require either linearized models or use of Extended Kalman Filters that have stability problems • Avoid statistical mixing of models as with the IMM approach • Generate locally optimal track by • minimizing mean square error of each track segment, and • minimizing discontinuity of segments at the knots connecting the segments Dartmouth College

5. Maneuvering Target Models • Target models used by Bayesian trackers • Constant Velocity • Coordinate Turns – sustained turn rate at constant speed • Statistical Models • Singer maneuver model • Maneuvers are modeled as zero-mean, time-correlated accelerations • STI target models • Any model for which a cost function can be written • Continuity condition at knots • Position • Direction Dartmouth College

6. Linking coordinated turns knots Dartmouth College

7. Position and velocity continuity Match position Match velocity Dartmouth College

8. Knot Placement Approach (1) • Phase I – initial segmentation • Add data to current segment keeping continuity with previous segment • Fit model • Determine if the new measurements are a good fit to model • Place knot if residuals of new measurements is greater than for the older measurements • Err on the side of generating two many knots and then recombine knots in second phase of processing • Estimate current position, velocity and acceleration Dartmouth College

9. Knot Placement Approach (2) • Phase II – optimize knots • Recursively optimize previous knot placement if • positions and velocity are not continuous at knot, or • a new knot has been place • Combine segments that reduce cost of track • Refine current position, velocity and acceleration estimates Dartmouth College

10. Selecting Track Model • Selection of model affects effectiveness of optimization Dartmouth College

11. Affect of Model on Optimization • Difference in Two Arcs • Arc Centric • large change in location of arc center • Target Centric • Small change in • starting location and • turn rate Dartmouth College

12. Costs for joining segments • The 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 number points in the segments Dartmouth College

13. Example weaving track Kalman Filter Track Noisy Measurements Track Estimates STI Track Dartmouth College

14. Benchmark comparison Semerdjiev, Emil, Ludmila Mihaylova and X. Rong Li (2000). Variable- and Fixed-Structure Augmented IMM Algorithms Using Coordinated Turn Model. International Conference on Information Fusion (Fusion' 2000), Paris, France. Dartmouth College

15. Turn rate estimates 20 trials superimposed VS – AIMM Tracker Kalman Smoother AGIMM Tracker STI Smoother, τ = L STI Tracker , τ = 0 Dartmouth College

16. Median Absolute Deviation in Turn Rate Estimates 100 trials Dartmouth College

17. CDF of turn rate estimation error 100 trials Dartmouth College

18. Second Scenario – highly maneuverable target 200 measurements with σ = 1 linked turns of 10, -25, 35, 10, -25, and 35/sec for duration of 7, 10, 6, 6, 10, 6 and 5 seconds respectively Dartmouth College

19. Turn rate estimates 20 trials superimposed VS – AIMM Tracker Kalman Smoother AGIMM Tracker STI Smoother, τ = L STI Tracker , τ = 0 Dartmouth College

20. Median Absolute Deviation in Turn Rate Estimates 100 trials Dartmouth College

21. CDF of turn rate estimation error 100 trials Dartmouth College

22. Characterizing Fish Tracks • Characterize motion of fish • Estimate energy expenditure of salmon below fish ladders • Work done in collaboration with Chad Schell • Graduate student at University of California at San Diego and • Scripts Oceanographic Institute • Results compared to • Kalman Filter with Singer Maneuver model • Kalman Smoother with no maneuver model Dartmouth College

23. Fish Tracks • There is no good model of fish motion • Tracker can not be tuned reliably Composite video image showing 14 fish tracks recorded at ~3.75 Hz during a 25 second sequence of video data. All tracks were successfully tracked using the STIJPDAF. Dartmouth College

24. Algorithm Speed RMSE (cm/s) Speed KS Prob. Turn Rate MAD (°/s) Turn Rate KS Prob. Position RMSE (cm/s) Point-wise Differentiation 10.58 6.5 *10-8 63.29 2.9 *10-18 3.04 Kalman Filter 12.90 4.2*10-13 52.49 4.5 *10-51 9.31 Fixed-Lag Smoother 9.50 1.9 *10-6 29.47 2.4 *10-30 5.92 Fixed- Interval Smoother 9.56 2.6 *10-11 28.16 2.9*10-142 9.04 EKF 12.63 3.0 *10-8 41.78 6.6 *10-20 4.49 STI 6.25 0.012 32.24 3.4 *10-15 3.10 Sensitivity analysis: worse case results for horizontal motion Lower values are better for RMSE and MAD, higher values are better for KS Probabilities. Dartmouth College

25. One Track Simulation Dartmouth College

26. Multiple target tracking Dartmouth College

27. Remaining Research … • Track and catch Ping-Pong balls using a single video camera • Segmenting pulse-oximeter data to extract individual cardiac cycles • Characterize effect of breathing on cardiac events • Characterize heart dynamics in response to physical activity • Predict exhaustion/volitional fatigue to help prevent injury to first responders • Detect and characterize disease • Track cells Dartmouth College