Modified Bayesian Cramé R-rao lower bound for nonlinear tracking

We propose a modified Bayesian Cramér-Rao lower bound (BCRLB) for nonlinear tracking applications where the prediction distribution conditioned on past measurements is used as the prior. The novelty of the proposed modified BCRLB comes from the fact that it utilizes past measurements, therefore it is specific to the current realization of the track which makes it a useful online tool that can be used for real-time sensor management. The computation of our proposed modified BCRLB is not analytically tractable except under very restricted conditions. Therefore, we also develop a particle based numerical computation method for our modified BCRLB so that this new bound can be easily calculated in real-time using the particles already available from the underlying particle filter which is used to track the target. We show by simulations that our developed numerical computation method approaches to its true analytical value as the number of particles in the particle filter increases.