Cramer-Rao bounds for non-linear filtering with measurement origin uncertainty

We are concerned with the problem of tracking a single target using multiple sensors. At each stage the measurement number is uncertain and measurements can either be target generated or false alarms. The Cramer-Rao bound gives a lower bound on the performance of any unbiased estimator of the target state. In this paper we build on earlier research concerned with calculating Posterior Cramer-Rao bounds for the linear filtering problem with measurement origin uncertainty. We derive the Posterior Cramer-Rao bound for the multi-sensor, non-linear filtering problem. We show that under certain assumptions this measurement origin uncertainty again expresses itself as a constant information reduction factor. Moreover we discuss how these assumptions can be relaxed, and the complications that occur when they no longer hold. We present an example concerned with multi-sensor management. We show that by utilizing the Cramer-Rao bound we are able to determine the combination of sensors that will enable us to achieve the most accurate tracking performance. Simulation results, using a probabilistic data association filter confirm our predictions.