An interval-based target tracking approach for range-only ...

IntroductionProblem description

TIBANumerical results

Conclusions

An interval-based target tracking approach forrange-only multistatic radar

G.L. Soares?†, A. Arnold-Bos?, L. Jaulin?,J.A. Vasconcelos† and C.A. Maia†

† UFMG - Belo Horizonte-MG, CEP 31270-010, Brazil? ENSIETA - 29806 Brest Cedex 9 - France

GT MEA Meeting, July 2007

Soares, Arnold-Bos, Jaulin, Vasconcelos and Maia Interval Evolutionary Algorithms



Conclusions

Main objective

WhatPresentation of TIBA, an interval approach to solve the problem ofmaneuvering target tracking, using range-only multistatic radar.

WhyThe radar process is plagued by several uncertainty sources thataffect directly the receivers’ measures. As a result, the radarsystem can be both imprecise and unreliable. Usually, intervalmethods handle uncertainty easily . . .

HowBy computation of the all feasible configurations for the targetwhich are consistent with the measures.




Conclusions

Summary

1 Introduction

2 Problem description

3 TIBA

4 Numerical results

5 Conclusions




Conclusions

Scenario

Radar applications

airspace monitoring, marine surveillance

weather prediction, ground imaging

Radar systems can face

noise in measurements

outliers, missing measures

. . . thus, the radar system can be unprecise and unreliable.

. . . then, we present TIBA as an alternative to traditional trackingalgorithms.




Conclusions

Scenario

Radar applications











Conclusions

Scenario

Radar applications











Conclusions

Scenario

Radar applications











Conclusions

Problem description

Multistatic radar example

x position (km)

y po

sitio

n (k

m)

E=R1

R2

R3

T

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

Xn

Xn+1

Xn+2

target trajectory

Details

multistatic radar

range-only measures

one transmitter, threereceivers

monotarget

state: Xn = [xn, yn, xn, yn]t

evolution: Xn+1 = f(Xn) + Vn




Conclusions

Problem description

evolution: Xn+1 = AXn︸︷︷︸f(Xn)

+BNn︸︷︷︸Vn

,

where matrices A and B are given by:

A =

1 0 ∆t 00 1 0 ∆t0 0 1 00 0 0 1

B =

∆t2

2 0

0 ∆t2

2∆t 00 ∆t




Conclusions

Tracking using an Interval-Based Approach (TIBA)

(SIVIA)

-1

(*)

(*) used if incoherent observations

,1




Conclusions

SIVIA

SIVIA to solve [r in − ε, r i

n + ε] = [d ]E [z] + [d ][z]Ri

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

x position (km)

y po

sitio

n (k

m)

Target position with SIVIA

E=R1

R2

R3




Conclusions

Zoom on the region where the solution lies.

3.97 3.98 3.99 4 4.01 4.02 4.03

3.97

3.98

3.99

4

4.01

4.02

4.03

x position (km)

y po

sitio

n (k

m)

Target position with SIVIA (datail on solution boxes)

wrapper box

boundary boxes

solution boxes

3.97 3.98 3.99 4 4.01 4.02 4.03

3.97

3.98

3.99

4

4.01

4.02

4.03

x position (km)

y po

sitio

n (k

m)

Target position with SIVIA (datail on solution boxes)

solution boxes

boundary boxes

wrapper box

(CPU time= 0.7s; [z] = [0, 25]km × [0, 10]km; ε = 2m, ε = 12m)




Conclusions


(SIVIA)

-1

(*)


,1

[X]n+1|n = A[X]n + B[N]n�

��

��

[Y]n+1 = [d ]E [z] + [d ][z]Ri

��

[Y]n+1 = [d ]E [z] + [d ][z]Ri

��




Conclusions


(SIVIA)

-1

(*)


,1

[X]n+1|n = A[X]n + B[N]n�

��

��

[Y]n+1 = [d ]E [z] + [d ][z]Ri

��

[Y]n+1 = [d ]E [z] + [d ][z]Ri

��




Conclusions


(SIVIA)

-1

(*)


,1

[X]n+1|n = A[X]n + B[N]n�

��

��

[Y]n+1 = [d ]E [z] + [d ][z]Ri

��

[Y]n+1 = [d ]E [z] + [d ][z]Ri

��




Conclusions


(SIVIA)

-1

(*)


,1

[X]n+1|n = A[X]n + B[N]n�

��

��

[Y]n+1 = [d ]E [z] + [d ][z]Ri

��

[Y]n+1 = [d ]E [z] + [d ][z]Ri

��




Conclusions

Experiments - simulation details

Trajectory generation

Yn = AXn + BWn,

Yn is Gaussian, mean 0 and σY = 4mWn is Gaussian, mean 0 and σW = 100m.s−2

delay between the observations: ∆t = 0.1

outliers and missing measures: 10%

sample: 1000 observations




Conclusions

Experiments - approaches details

TIBA

radar range: [0, 25]km × [0, 10]km

maximal error in measurements: ε = 12m

SIVIA’s accuracy: ε = 2m

interval noise: Nn = [−90, 90]

Particle filtering

particles: 1000

Regularization noise: [10, 10, 10, 10];




Conclusions

Experiments - Trajectory

0 5 10 15 20 250

1

2

3

4

5

6

7

8

9

X position (km)

Y p

ositi

on (

km)

Target trajectory

E=R1

R2

R3




Conclusions

Experiments - Observation example

0 100 200 300 400 500 600 700 800 900 100010

15

20

25

30

35

Iteration number

Dis

tanc

e (k

m)

Measured distance for receiver 3




Conclusions

Experiments - TIBA’s output




Conclusions

Experiments - TIBA’s output

0 0.5 1 1.5 2 2.5

x 104

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500Valid measurement

x position (km)

y po

sitio

n (m

)




Conclusions

Experiments - PF’s output

0 0.5 1 1.5 2 2.5

x 104

4000

4500

5000

5500

6000

6500

7000

7500

8000Iteration 1000/1000 after resampling

x position (km)

y po

sitio

n (m

)




Conclusions

Experiments - TIBA’s estimation




Conclusions

Experiments - TIBA x Particle filtering

100 200 300 400 500 600 700 800 900 10000

1000

2000

3000

4000

Tracking performance for the particle filtering

Iteration number

Mete

rs (

m)

Error between reckoned and true positionEstimated error on the reckoned position (3!

e)

100 200 300 400 500 600 700 800 900 10000

1000

2000

3000

4000

Tracking performance for TIBA

Iteration number

Mete

rs (

m)

Error between reckoned and true position

Estimated error on the reckoned position (distance from center to farthest side)




Conclusions

Experiments - Error difference TIBA x PF

0 100 200 300 400 500 600 700 800 900 1000−400

−300

−200

−100

0

100

200

300

Difference of the estimations: |errorpf|−|errorTIBA|

Iteration number

Met

ers

(m)




Conclusions

Conclusions

TIBA is a deterministic, interval-based technique while particlefiltering is a stochastic method. The experiments provide thefollowing comparison:

Criteria TIBA PFfast cpu time Xno parameter tuning Xconvergence X not guaranteedsmall maximal error Xgood estimation X X


An interval-based target tracking approach for range-only ...

Documents