A Hybrid Tracker and Smoother for Highly Maneuvering Targets

April 2004 Dartmouth College 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.


Problem Context

A weaving target track constructed of linked

coordinated turns


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


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


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


Linking coordinated turns

knots


Position and velocity continuity

Match position

Match velocity


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


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


Selecting Track Model Selection of model affects effectiveness

of optimization

Arc Centric Target CentricCenter of Arc – x Starting Position – x

Center of Arc – y Starting Position – y

Angle to Start Heading

Radius Turn Rate

Length Speed


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


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

, 1 , 1( )C p n n n nQ n k R

, 1n nR

, 1n n


Example weaving track

Noisy Measurements

Track Estimates

Kalman Filter Track

STI Track


Benchmark comparison

1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 x 10 4

2.5

3

3.5

4

4.5

5

5.5

6 x 10 4

meters

met

ers

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.


Turn rate estimates

0 10 20 30 40 50 -40

-20

0

20

40

Tu

rn R

ate

(d

eg

rees/s

ec)

Time(sec)

0 10 20 30 40 50 -40

-20

0

20

40

Tu

rn R

ate

(d

eg

rees/s

ec)

Time(sec)

0 10 20 30 40 50 -40

-20

0

20

40

Tu

rn R

ate

(d

eg

rees/s

ec)

Time(sec)

0 10 20 30 40 50 -40

-20

0

20

40

Tu

rn R

ate

(d

eg

rees/s

ec)

Time(sec)

0 10 20 30 40 50 -30

-20

-10

0

10

20

30

40

Turn

Rate

(degre

es/s

ec)

Time(sec)

VS – AIMM Tracker

AGIMM Tracker

STI Tracker , τ = 0

Kalman Smoother

STI Smoother, τ = L

20 trials superimposed


Median Absolute Deviation in Turn Rate Estimates

N = 200 N = 400

VS-AIMM 1.041 0.203AG IMM 0.952 1.509

STI (τ = 0) 0.229 0.268STI (τ = 1) 0.193 0.243STI (τ = 2) 0.166 0.223STI (τ = 4) 0.152 0.198Smoother 1.098 0.868STI (τ = L) 0.022 0.018

100 trials


CDF of turn rate estimation error

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Pro

babi

lity

0 5 10 15 20 25 30 35 40 45 50 Cumulative Turn Rate Errors (Degrees)

VS-AIMM AGIMM STI τ = 0 STI τ = 1 STI τ = 2 STI τ = 4 CV Smoother STI τ = L

100 trials


Second Scenario – highly maneuverable target

0 50 100 150 200

-30 -20 -10

0 10 20 30 40 50 60 70

meters

met

ers

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


Turn rate estimates

0 10 20 30 40 50 -40

-20

0

20

40

Tu

rn R

ate

(d

eg

rees/s

ec)

Time(sec)

0 10 20 30 40 50 -40

-20

0

20

40

Tu

rn R

ate

(d

eg

rees/s

ec)

Time(sec)

0 10 20 30 40 50 -40

-20

0

20

40

Tu

rn R

ate

(d

eg

rees/s

ec)

Time(sec)

0 10 20 30 40 50 -40

-20

0

20

40

Tu

rn R

ate

(d

eg

rees/s

ec)

Time(sec)

0 10 20 30 40 50 -30

-20

-10

0

10

20

30

40

Turn

Rate

(degre

es/s

ec)

Time(sec)

VS – AIMM Tracker

AGIMM Tracker

STI Tracker , τ = 0

Kalman Smoother

STI Smoother, τ = L

20 trials superimposed


Median Absolute Deviation in Turn Rate Estimates

N = 100 N = 200

VS-AIMM 10.000 8.376

AG IMM 11.884 23.577

STI (τ = 0) 2.412 1.916

STI (τ = 1) 1.817 1.649

STI (τ = 2) 1.575 1.445

STI (τ = 4) 1.055 1.235

Smoother 7.497 6.166

STI (τ = L) 0.259 0.200

100 trials


CDF of turn rate estimation error

0 5 10 15 20 25 30 35 40 45 50 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Cumulative Turn Rate Errors (Degrees)

Pro

babi

lity

VS-AIMM AGIMM STI τ = 0 STI τ = 1 STI τ = 2 STI τ = 4 CV Smoother STI τ = L

100 trials


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


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.


Sensitivity analysis: worse case results for horizontal motion

AlgorithmSpeedRMSE(cm/s)

SpeedKS

Prob.

Turn RateMAD(°/s)

TurnRateKS

Prob.

PositionRMSE(cm/s)

Point-wiseDifferentiation

10.58 6.5 *10-8 63.29 2.9 *10-18 3.04

KalmanFilter

12.90 4.2*10-13 52.49 4.5 *10-51 9.31

Fixed-LagSmoother

9.50 1.9 *10-6 29.47 2.4 *10-30 5.92

Fixed-Interval

Smoother9.56 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

Lower values are better for RMSE and MAD, higher values are better for KS Probabilities.


One Track Simulation


Multiple target tracking


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

A Hybrid Tracker and Smoother for Highly Maneuvering Targets

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