We introduce a form of Rao{Blackwellization for Markov chains which uses the transition distribution for conditioning. We show that for reversible Markov chains, this form of Rao{Blackwellization always reduces the asymptotic variance, and derive two explicit forms of the variance reduction obtained through repeated Rao{Blackwellization. The result applies to many Markov chain Monte Carlo metho...

In this letter, numerical algorithms for computing the marginal version of the Bayesian Cramér-Rao bound (M-BCRB) for jump Markov nonlinear systems and jump Markov linear Gaussian systems are proposed. Benchmark examples for both systems illustrate that the M-BCRB is tighter than three other recently proposed BCRBs. Index Terms Jump Markov nonlinear systems, Bayesian Cramér-Rao bound, particle ...

This paper extends the accept reject algorithm to allow the pro posal distribution to change at each iteration We rst establish a necessary and su cient condition for this generalized accept reject al gorithm to be valid and then show how the Rao Blackwellization of Casella and Robert can be extended to this setting An impor tant application of these results is to the perfect sampling technique...

In this article we propose a new Rao-Blackwellized particle filtering based algorithm for tracking an unknown number of targets. The algorithm is based on formulating probabilistic stochastic process models for target states, data associations, and birth and death processes. The tracking of these stochastic processes is implemented using sequential Monte Carlo sampling or particle filtering, an...

We propose a new Rao-Blackwellized sequential Monte Carlo method for tracking multiple targets in presence of clutter and false alarm measurements. The advantage of the new approach is that Rao-Blackwellization allows the estimation algorithm to be partitioned into single target tracking and data association sub-problems, where the single target tracking sub-problem can be solved by Kalman filt...

In an earlier contribution we proposed a particle filter for underwater (UW) navigation, and applied it to an experimental trajectory. Here we focus on performance improvements and analysis. First, the Cramér Rao lower bound (CRLB) along the experimental trajectory is computed, which is only slightly lower than the particle filter estimate after initial transients. Simple rule of thumbs for how...

Recall that the main difficulty with particle filtering is that with a high dimensional state variable xt, an impossibly large number of particles is needed to accurately represent P (xt|z0:t). In some filtering problems, it is possible to exploit conditional independence of components of the state variables x1:t in order to reduce the number of particles needed. In this lecture we will see exa...

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and e...