Conditional posterior Cramér-Rao lower bounds for nonlinear recursive filtering

Posterior Cramér Rao lower bounds (PCRLBs) [1] for sequential Bayesian estimators pro-vide performance bounds for general nonlinear filtering problems and have been used widely for sensor man-agement in tracking and fusion systems. However, the unconditional PCRLB [1] is an off-line bound that is obtained by taking the expectation of the Fisher infor-mation matrix (FIM) with respect to the measurement and the state to be estimated. In this paper, we in-troduce a new concept of conditional PCRLB, which is dependent on the observation data up to the cur-rent time, and adaptive to a particular realization of the system state. Therefore, it is expected to provide a more accurate and effective performance evaluation than the conventional unconditional PCRLB. However, analytical computation of this new bound is, in gen-eral, intractable except when the system is linear and Gaussian. In this paper, we present a sequential Monte Carlo solution to compute the conditional PCRLB for nonlinear non-Gaussian sequential Bayesian estimation problems.