Abstract

A multi-platform angle-only tracking system combines the angular measurements from distributed networked sensors in order to estimate the full kinematic target state. This paper investigates the effect of communication bandwidth on track quality in a system which receives angle-only measurements from two networked sensors installed on two airborne moving platforms. The investigation is based on the Cramér–Rao lower bound of the mean-square range error for the case considered. The bound is derived for recursive estimators with prior information and compared with two algorithms: (i) maximum likelihood estimation over a cumulative measurement set and (ii) extended Kalman filter with triangulated range estimates.

Author Keywords: Target tracking; Communication bandwidth; Angle-only measurements; Cramér–Rao bound

T_o

sampling interval

s(k)

state vector (platform 1) at time index k

s₁=x_t

first component of the state vector s

second component of the state vector s

s₃=y_t

third component of the state vector s

forth component of the state vector s

P

covariance matrix

b

delay in the initial measurement transmission

η

parameter which defines the data-link bandwidth

z₁(k)

angle-only measurements from platform 1 at time index k

z₂(k)

angle-only measurements from platform 2 at time index k

J

Fisher information matrix

Article Outline

Nomenclature

1. Introduction

2. Problem description

3. Cramér-Rao bound

3.1. The joint measurement-state density

3.2. Fisher information matrix

3.2.1. Derivation of J₀

3.2.2. Derivation of J₁ and J₂

3.3. CRLB for the target range estimate

4. The influence of bandwidth

4.1. Discussion

4.2. Tracking algorithms against the CRLB

4.2.1. MLE algorithm

4.2.2. EKF with triangulation

4.2.3. Results

5. Summary

References

Corresponding author. Tel.: +61-8-8259-7184; fax: +61-8-8259-6673; email: branko.ristic@dsto.defence.gov.au