Target aided online sensor ... - SSPD Conference 2020 › sites › sspd.eng.ed.ac.uk › files › publicatio… · Sensor Signal Processing for Defence (SSPD) 2014 Problem De nition

University Defence Research Collaboration (UDRC)Sensor Signal Processing for Defence (SSPD) 2014

Target aided online sensor localisation in bearingonly clusters

Murat Uney1, Bernard Mulgrew1, Daniel Clark2

Edinburgh Research Partnership in Signal and Image Processing1 The University of Edinburgh

2 Heriot-Watt University

08/09/2014

1


Introduction

Bearing-only sensors detect objects and record theirline-of-sight (LOS) angles, in their sensor coordinate systems.

Fusion clusters filter target detections.

Sensor locations are needed for fusion and routing.

GPS denying environments, jamming,...

Target detections and Received Signal Strength (RSS) at thecommunication front-end are used.

2


Table of Contents

1 Introduction

2 Problem Definition

3 Conventional Approaches

4 Proposed Solution

5 Example

6 Conclusions and Future Work

3


Problem Definition

P2

P3

P1

PS

PS-1

C0

The cluster head C0

1 collects target detections Z 01:T in a

time window of T with its on-boardbearing only sensor,

2 receives Z i1:T from peripheral Pi .

3 The i th comm.s signal arrives at thereceiver with power R i (or ReceivedSignal Strength-RSS).

Find locations θ fi rθ1, θ2, ..., θS s given Z 01:T ,Z 1

1:T , ...,ZS1:T

and R1, ...,RS .

The uncertainties are captured within lpZ 01:T ,Z

11:T , ...,Z

S1:T |θq,

and, lpR1, ...,RS |θq.

4


Conventional Approaches (1/3)

Cramer-Rao Lower Bounds for lpR1, ...,RS |θq “ś

lpR i |θi q:

High uncertainty because that lpR i |d i “ |θi |q is log-normalresulting with a wide distribution.

5



Target detections based likelihood is given by

l`

Z 01:T ,Z

11:T , ...,Z

S1:T |θ

˘

“

T´1ź

t“0

ppZ 0:St`1|Z

0:S1:t´1, θq

“

T´1ź

t“0

ż

ppZ 0t`1|Xt`1q

Sź

i“1

ppZ it`1|Xt`1, θi q

ˆ ppXt`1|Z01:T ,Z

11:T , ...,Z

S1:T , θq

loooooooooooooooooomoooooooooooooooooon

Prediction distribution of a (centralised) filter.

dpX t`1q

Intractable, in general. Monte Carlo (MC) approx. needed.

Increasing MC variance as the time window length T growslarger „ particle deficiency (Kantas, Doucet, et.al., 2010).

6



Bayesian recursions for an online solution:

pnpθnq 9 lpZ 0:ST pn´1q`1:Tn|θnqpn|n´1pθnq

pn|n´1pθnq “

ż

fnpθn|θn´1qpn´1pθn´1qdθn´1

Scalability of the update with the # of sensors S(equivalently, the dimensionality of θ):

Update is OppSα`1NqpST qMq.N: The number of particles per sensor,M: The number of progressive Importance Sampling (or,stochastic tempering) stages.

With given N,M, and, the sophistication of the samplers,might fail to converge.

7


Proposed Solution (1/2)Divide the problem into simpler subproblems and merge theirsolutions.Use a Junction Tree (equivalently, a triangulated MarkovRandom Field) model for the localisation posterior:

S2

S3

S1 S4

Fusion

centreS0

ppθq9

śS´1k“1 lpZ

0,Z ik ,Z ik`1 |θik , θik`1q

śS´1k“2 lpZ

0,Z ik |θik q

Sź

i“1

p0,i pθi q.

Pairwise MRF models for self-localisation of range-bearing sensors(Uney, Mulgrew, Clark, “Cooperative sensor

localisation for distributed fusion networks”).

8


Proposed Solution (2/2)

Update one marginal of pnpθnq at a time using the JunctionTree message passing algorithm: The Importance Samplingscheme is detailed in the article.

OpNp3T qSβ`1q (as opposed to OppSα`1NqpST qMq) withtypically much smaller N.

Convergence properties are improved by the introduction ofRSS likelihoods lpR i |θi qs to shape priors.

9


Example

0 1000 2000 3000 4000 5000

0

1000

2000

3000

4000

5000

East (m)

No

rth

(m

)

S1

S2

S0

S4

S3 LOS angle standard deviation σi “ 0.5˝.

T “ 10 step window-length , N “ 150particles per sensor.

Final error (averaged over sensors) is45.7m (%2.15 of the nearest peripheraldistance (2121.3m of sensor 2).

Tracking error (Euclideandistance) of the cluster (black)when location estimates are used(in comparison with cluster-headonly (red) tracking).

10


Conclusions and Future Work

We considered sensor localisation in bearing only sensorclusters for target filtering and routing.

Our solution uses target detections and RSS measurements.

Scales well with the number of sensors.

Further empirical study of clutter effects using Bernoulli filters.

Further empirical comparison of the accuracy and complexityof progressive Importance Sampling schemes and the proposedsolution.

This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) and Dstl.

11

Documents

Target aided online sensor ... - SSPD Conference 2020 › sites › sspd.eng.ed.ac.uk › files › publicatio… · Sensor Signal Processing for Defence (SSPD) 2014 Problem De nition