Conditional Posterior Cramér-Rao lower bounds for nonlinear recursive filtering

Posterior Cramér Rao lower bounds (PCRLBs) [1] for sequential Bayesian estimators provide performance bounds for general nonlinear filtering problems and have been used widely for sensor management 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 information matrix (FIM) with respect to the measurement and the state to be estimated. In this paper, we introduce a new concept of conditional PCRLB, which is dependent on the observation data up to the current 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 general, 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.