Efficient computation of the Bayesian Cramer-Rao bound on estimating parameters of Markov models

This paper presents a novel method for calculating the Hybrid Cramer-Rao lower bound (HCRLB) when the statistical model for the data has a Markovian nature. The method applies to both the non-linear/non-Gaussian as well as linear/Gaussian model. The approach solves the required expectation over unknown random parameters by several one-dimensional integrals computed recursively, thus simplifying a computationally-intensive multidimensional integration. The method is applied to the problem of refractivity estimation using radar clutter from the sea surface, where the backscatter cross section is assumed to be a Markov process in range. The HCRLB is evaluated and compared to the performance of the corresponding maximum a-posteriori estimator. Simulation results indicate that the HCRLB provides a tight lower bound in this application.