In this article, we present an overview of methods for sequential simulation from posterior distributions. These methods are of particular interest in Bayesian filtering for discrete time dynamic models that are typically nonlinear and non-Gaussian. A general importance sampling framework is developed that unifies many of the methods which have been proposed over the last few decades in several different scientific disciplines. Novel extensions to the existing methods are also proposed. We show in particular how to incorporate local linearisation methods similar to those which have previously been employed in the determin-istic filtering literature; these lead to very effective importance distributions. Furthermore we describe a method which uses Rao-Blackwellisation in order to take advantage of the analytic structure present in some important classes of state-space models. In a final section we develop algorithms for prediction, smoothing and evaluation of the likelihood in dynamic models.

. In this report, we present an overview of sequential simulationbased methods for Bayesian filtering of nonlinear and non-Gaussian dynamic models. It includes in a general framework numerous methods proposed independently in various areas of science and proposes some original developments. Keywords: Bayesian estimation, optimal filtering, nonlinear non-Gaussian state space models, hidden Markov models, sequential Monte Carlo methods. 1. Introduction 1 Many problems in statistical signal processing, automatic control, applied statistics or econometrics can be stated as follows. A transition equation describes the prior distribution of the Markovian hidden signal of interest fx k ; k 2 Ng, the so-called hidden state process, and an observation equation describes the likelihood of the observations fy k ; k 2 Ng, k being the discrete time index. The aim is to estimate the hidden state process using the observations. In the Bayesian framework, all relevant information on fx 0 ; x ...

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Robotic and embedded systems have become increasingly pervasive in every-day applications, ranging from space probes and life support systems to autonomous rovers. In order to act robustly in the physical world, robotic systems must handle the uncertainty and partial observability inherent in most real-world situations. A convenient modeling tool for many applications, including fault diagnosis and visual tracking, are probabilistic hybrid models. In probabilistic hybrid models, the hidden state is represented with discrete and continuous state variables that evolve probabilistically. The hidden state is observed indirectly, through noisy observations. A challenge is that real-world systems are non-linear, consist of a large collection of concurrently operating components, and exhibit autonomous mode transitions, that is, discrete state transitions that depend on the continuous dynamics. In this

Robotic and embedded systems have become increasingly pervasive in every-day applications, ranging from space probes and life support systems to autonomous rovers. In order to act robustly in the physical world, robotic systems must handle the uncertainty and partial observability inherent in most real-world situations. A convenient modeling tool for many applications, including fault diagnosis and visual tracking, are probabilistic hybrid models. In probabilistic hybrid models, the hidden state is represented with discrete and continuous state variables that evolve probabilistically. The hidden state is observed indirectly, through noisy observations. A challenge is that real-world systems are non-linear, consist of a large collection of concurrently operating components, and exhibit autonomous mode transitions, that is, discrete state transitions that depend on the continuous dynamics. In this thesis, we introduce an efficient algorithm for hybrid state estimation that combines Rao-Blackwellised particle filtering with a Gaussian representation. Conceptually, our algorithm samples trajectories traced by the discrete variables over time

We investigate the issue of which state functionals can have their uncertainty estimated efficiently in dynamical systems with uncertainty. Because of the high dimensionality and complexity of the problem, sequential Monte Carlo (SMC) methods are used. We prove that the variance of the SMC method is bounded linearly in the number of time steps when the proposal distribution is truncated normal distribution. We also show that for a moderate large number of steps the error produced by approximation of dynamical systems linearly accumulates on the condition that the logarithm of the density function of noise is Lipschitz continuous. This finding is significant because the uncertainty in many dynamical systems, in particular, in chemical engineering systems that can be assumed to have this nature. We demonstrate our findings for a simple test case from chemical engineering. The theoretical findings provide a foundation for the parallel software SISTOS.