Evaluating the Bayesian Cramér-Rao Bound for multiple model filtering

We propose a numerical algorithm to evaluate the Bayesian Cramer-Rao bound (BCRB) for multiple model filtering problems. It is assumed that the individual models have additive Gaussian noise and that the measurement model is linear. The algorithm is also given in a recursive form, making it applicable for sequences of arbitrary length. Previous attempts to calculate the BCRB for multiple model filtering problems are based on rough approximations which usually make them simple to calculate. In this paper, we propose an algorithm which is based on Monte Carlo sampling, and which is hence more computationally demanding, but yields accurate approximations of the BCRB. An important observation from the simulations is that the BCRB is more overoptimistic than previously suggested bounds, which we motivate using theoretical results.