Performance bounds for angle-only filtering with application to sensor network management

In this paper we examine the Posterior Cramir-Rao Lower Bound (PCRLB) for bearings-only tracking. We use a minimum detection range, inside which the target cannot be detected and show that the PCRLB tends to zero as this range tends to Zero. Hence, in the absence of a minimum detection range, the bearings-only PCRLB is uninformative and identifies only that performance of a filter can be no better than perfect. It is also a feature of bearings-only tracking that no closed-form solution exists for the PCRLB, and numerical approximation is necessary via Monte Carlo integration. We show that in the absence of a minimum detection range the bearings-only PCRLB tends to zero as the number of Monte Carlo sample points tends to infinity. However simulation results show the convergence can be slow which may account for this phenomenon previously going unnoticed. In the second half of this paper we introduce an alternative performance measure that resembles the error covariance of the Extended Kalman Filter (EKF) with measurements linearised around the true target state. This adapted performance measure is applied to the problem of managing a sensor network when there is a restriction in the total number of sensors that can be utilised at any one time. This measure is shown to closely match the filter performance and therefore can be used to accurately predict the performance of any combination of sensors. As a result, it is shown to allow more efficient management of the sensor network.