Posterior Cramér-rao Bound for Tracking Target Bearing

The posterior Cramér-Rao bound on the mean square error in tracking the bearing, bearing rate, and power level of a narrowband source is developed. The formulation uses a linear process model with additive noise and a general nonlinear measurement model, where the measurements are the sensor array data. The joint Bayesian Cramér-Rao bound on the state variables over the entire observation interval is formulated and a recursive bound on the state variables as a function of time is derived based on the nonlinear filtering bound developed by Tichavsky et al (1998) and analyzed by Ristic et al (2004). The bound is shown to have the same form as when the measurements are bearing and power estimates with variance equal to the deterministic Cramér-Rao bound for a single data snapshot. The bound is compared against simulated performance of the maximum a posteriori penalty function (MAP-PF) tracking algorithm developed in Zarnich et al (2001).