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...

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...

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...

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...

This paper focuses on sequential Monte Carlo approximations of smoothing distributions in conditionally linear and Gaussian state spaces. To reduce Monte Carlo variance of smoothers, it is typical in these models to use Rao-Blackwellization: particle approximation is used to sample sequences of hidden regimes while the Gaussian states are explicitly integrated conditional on the sequence of reg...

We investigate existence and properties of discrete mixture representations $P_{\theta }=\sum _{i\in E}w_{\theta }(i)\,Q_{i}$ for a given family }$, $\theta \in \Theta $, probability measures. The noncentral chi-squared distributions provide classical example. obtain results about geometric statistical aspects the problem, latter including loss Fisher information, Rao-Blackwellization, asymptot...

The braking rate and train arresting operation is important in the train braking performance. It is difficult to obtain the states of the train on time because of the measurement noise and a long calculation time. A type of Group Stochastic M-algorithm (GSMA) based on Rao-Blackwellization Particle Filter (RBPF) algorithm and Stochastic M-algorithm (SMA) is proposed in this paper. Compared with ...

Multipath is one of the dominant sources of error in highprecision GNSS applications. A tracking algorithm is presented that explicitely accounts for direct signal and multipath replicas in the model, in order to mitigate the contributions of the latter. A Bayesian approach has been taken, to infer some information from the time evolution model of the parameters. Due to the nonlinearity of the ...

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 ...