1. April 2004Dartmouth College 1 A Hybrid Tracker and Smoother for 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.

2. April 2004Dartmouth College2 Problem Context A weaving target track constructed of linked coordinated turns

3. April 2004Dartmouth College3 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

4. April 2004Dartmouth College4 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

5. April 2004Dartmouth College5 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

6. April 2004Dartmouth College6 Linking coordinated turns knots

7. April 2004Dartmouth College7 Position and velocity continuity Match position Match velocity

8. April 2004Dartmouth College8 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

9. April 2004Dartmouth College9 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

10. April 2004Dartmouth College10 Selecting Track Model Selection of model affects effectiveness of optimization Arc CentricTarget Centric Center of Arc – xStarting Position – x Center of Arc – yStarting Position – y Angle to StartHeading RadiusTurn Rate LengthSpeed

11. April 2004Dartmouth College11 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

12. April 2004Dartmouth College12 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 number points in the segments

13. April 2004Dartmouth College13 Example weaving track Noisy Measurements Track Estimates Kalman Filter Track STI Track

14. April 2004Dartmouth College14 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.

15. April 2004Dartmouth College15 Turn rate estimates VS – AIMM Tracker AGIMM Tracker STI Tracker, τ = 0 Kalman Smoother STI Smoother, τ = L 20 trials superimposed

16. April 2004Dartmouth College16 Median Absolute Deviation in Turn Rate Estimates N = 200N = 400 VS-AIMM 1.0410.203 AG IMM 0.9521.509 STI (τ = 0) 0.2290.268 STI (τ = 1) 0.1930.243 STI (τ = 2) 0.1660.223 STI (τ = 4) 0.1520.198 Smoother 1.0980.868 STI (τ = L) 0.0220.018 100 trials

17. April 2004Dartmouth College17 CDF of turn rate estimation error 100 trials

18. April 2004Dartmouth College18 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

19. April 2004Dartmouth College19 Turn rate estimates VS – AIMM Tracker AGIMM Tracker STI Tracker, τ = 0 Kalman Smoother STI Smoother, τ = L 20 trials superimposed

20. April 2004Dartmouth College20 Median Absolute Deviation in Turn Rate Estimates N = 100N = 200 VS-AIMM 10.0008.376 AG IMM 11.88423.577 STI (τ = 0) 2.4121.916 STI (τ = 1) 1.8171.649 STI (τ = 2) 1.5751.445 STI (τ = 4) 1.0551.235 Smoother 7.4976.166 STI (τ = L) 0.2590.200 100 trials

21. April 2004Dartmouth College21 CDF of turn rate estimation error 100 trials

22. April 2004Dartmouth College22 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

23. April 2004Dartmouth College23 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.

24. April 2004Dartmouth College24 Sensitivity analysis: worse case results for horizontal motion Algorithm Speed RMSE (cm/s) Speed KS Prob. Turn Rate MAD (°/s) Turn Rate KS Prob. Position RMSE (cm/s) Point-wise Differentiation 10.586.5 *10 -8 63.292.9 *10 -18 3.04 Kalman Filter 12.904.2*10 -13 52.494.5 *10 -51 9.31 Fixed-Lag Smoother 9.501.9 *10 -6 29.472.4 *10 -30 5.92 Fixed- Interval Smoother 9.562.6 *10 -11 28.162.9*10 -142 9.04 EKF12.633.0 *10-841.786.6 *10 -20 4.49 STI6.250.01232.243.4 *10 -15 3.10 Lower values are better for RMSE and MAD, higher values are better for KS Probabilities.

25. April 2004Dartmouth College25 One Track Simulation

26. April 2004Dartmouth College26 Multiple target tracking

27. April 2004Dartmouth College27 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