Posterior Cramer-Rao bounds for discrete-time nonlinear filtering

Abstract

Abstract-A mean-square error lower bound for the discretetime nonlinear filtering problem is derived based on the Van Trees (posterior) version of the Cramér-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation.

Performance bounds for cooperative RSS emitter tracking using diffusion particle filters

“…We can apply therefore the method introduced in [9] to recursively compute the Fisher matrix J n+1,rn+1 at instant n + 1 given the Fisher matrix J n,rn originated from a node r n and the set of measurements Z n+1,rn+1 available at node r n+1 .…”

“…We extend first the recursive equations derived in [9] to consider multiple observers as in (1) and write…”

“…In this paper, building on previous results in [9], we introduce a methodology for numerical computation of the posterior Cramér-Rao lower bound (PCRLB) for the average network mean-square state estimation error when the proposed random exchange diffusion protocol is used. The computed bound is compared, in a specific application of emitter tracking with received-signal-strength (RSS) sensors, to the empirical performance, assessed via simulations, of the RndEx-PF tracker, and is also compared to the PCRLB for the mean-square state estimation error associated with the optimal centralized filter that assimilates all network measurements at each instant.…”

Distributed inference in wireless sensor networks

“…In particular, it has been shown [126] that the complexity of mutual information-based approaches is exponential in N , whereas the complexity of PCRLB or conditional PCRLB-based approaches is linear in N . A recursive approach to calculate the sequential PCRLB for a general multi-dimensional discrete-time nonlinear filtering problem has been derived [127]. Many researchers have proposed PCRLB-based approaches to solve sensor management problems [128][129][130][131].…”

Estimating the ballistic coefficient of a re-entry vehicle

“…Including a Markovian modelling (e.g. of the ballistic coefficient) leads to consider a Bayesian framework [8] and to replace the 'classical', CRB by the posterior Cramér-Rao bound (PCRB [11]). It is worth mentioning the works of Farina et al for carrying out a systematic comparison between PCRB and the filter performance in this context [6,12].…”