Posterior Cramér-Rao Bound for Target Tracking in the Presence of Multipath
Marcel L. Hernandez, Alfonso Maria Farina · 2018
This paper considers the general problem of tracking a noncooperative target in the presence of multipath. The multipath effect occurs intermittently, according to a discrete-time Markov chain, and exerts an additional unknown measurement error (i.e, a bias), with biases autocorrelated if they occur across successive sampling times. We calculate the posterior Cramér-Rao bound (PCRB) for this problem by augmenting the target state with the multipath bias. An established, efficient Riccati recursion is then used to determine the PCRB, thereby providing mean squared error performance bounds for both the estimation of the target state and the multipath bias. The approach is demonstrated in a simulated scenario in which an airborne radar tracks a low altitude airborne target that is moving in a horizontal plane with nearly constant velocity, using measurements of azimuth. elevation and range. The measurements are intermittently corrupted by multipath bias resulting from specular reflection at the surface boundary. It is shown that the PCRB increases rapidly when the multipath effect occurs, indicating that optimal target tracking performance is significantly degraded at such times. Future work will compare the PCRB developed herein with alternative PCRB methodologies that do not implicitly condition on the multipath effects, and also compare the bound to the performance of a tracking algorithm that is designed to identify and adjust for the multipath effects.