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 paper particle filters for dynamic state space models handling unknown static parameters are discussed. The approach is based on marginalizing the static parameters out of the posterior distribution such that only the state vector needs to be considered. Such a marginalization can always be applied. However, real-time applications are only possible when the distribution of the unknown parameters given both observations and the hidden state vector depends on some low-dimensional sufficient statistics. Such sufficient statistics are present in many of the commonly used state space models. Marginalizing the static parameters avoids the problem of impoverishment which typically occur when static parameters are included as part of the state vector. The filters are tested on several different models, with promising results.

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On-line, spatially localized information about internal network performance can greatly assist dynamic routing algorithms and traffic transmission protocols. However, it is impractical to measure network traffic at all points in the network. A promising alternative is to measure only at the edge of the network and infer internal behavior from these measurements. In this paper we concentrate on the estimation and localization of internal delays based on end-to-end delay measurements from a source to receivers. We propose a sequential Monte Carlo (SMC) procedure capable of tracking nonstationary network behavior and estimating time-varying, internal delay characteristics. Simulation experiments demonstrate the performance of the SMC approach. 1 Introduction In large-scale networks, end-systems cannot rely on the network itself to cooperate in characterizing its own behavior. This has prompted several groups to investigate methods for inferring internal network behavior based on...

In this paper we develop a general simulation-based approach to filtering and sequential parameter learning. We begin with an algorithm for filtering in a general dynamic state space model and then extend this to incorporate sequential parameter learning. The key idea is to express the filtering distribution as a mixture of lag-smoothing distributions and to implement this sequentially. Our approach has a number of advantages over current methodologies. First, it allows for sequential parmeter learning where sequential importance sampling approaches have difficulties. Second

This paper provides a simulation-based approach to filtering and sequential parameter learning for stochastic volatility models. We develop a fast simulation-based approach using the practical filter of Polson, Stroud and Müller (2002). We compute

Abstract — We present an algorithm for pose estimation using fixed-lag smoothing. We show that fixed-lag smoothing enables inclusion of measurements from multiple asynchronous measurement sources in an optimal manner. Since robots usually have a plurality of uncoordinated sensors, our algorithm has an advantage over filtering-based estimation algorithms, which cannot incorporate delayed measurements optimally. We provide an implementation of the general fixed-lag smoothing algorithm using square root smoothing, a technique that has recently become prominent. Square root smoothing uses fast sparse matrix factorization and enables our fixed-lag pose estimation algorithm to run at upwards of 20 Hz. Our algorithm has been extensively tested over hundreds of hours of operation on a robot operating in outdoor environments. We present results based on these tests that verify our claims using wheel encoders, visual odometry, and GPS as sensors.

1.1 Generalized state space model The generalized state space model (GSSM) that we deal with in this study is de ned by a set of two equations system model xt = f(xt;1 � vt) � and (1.1)

This work concerns sequential techniques for the canonical blind deconvolution problem in communications signal processing, relating to the estimation of the transmitted (discrete-valued) data sequence from the observed signal at the receiver input, in the presence of unknown linear channel ltering, without recourse to extended training sequences for start-up. This problem has a significant history within communications signal processing due to its fundamental importance in the design of high-speed modems; common methods include the well-known Viterbi, List Viterbi Algorithms and BCJR algorithms enhanced with suitable blind channel estimators. Of late, the problem has attracted the attention of computational Bayesians such as Liu and Chen Liu and Chen (1995) who introduced Sequential Importance Sampling (SIS). Subsequently, several extensions have been proposed (e.g. Rejuvenation, Rejection Control, Fixed-Lag Smoothing, Metropolis-Hastings Importance Resampling, etc.) as improvements to SIS. Simulations comparing SIS and Rejuvenation to the more traditional methods were inconclusive as to whether Sequential Importance Sampling is always preferable to the traditional methods. Although Sequential Importance Sampling can be helpful in certain circumstances, it shows signs of instability, and therefore, may not be useful in practice. In conclusion, one should be cautious in using Sequential Importance Sampling or Rejuvenation for blind deconvolution problems.

This work concerns sequential techniques for the canonical blind deconvolution problem in communications signal processing, relating to the estimation of the transmitted (discrete-valued) data sequence from the observed signal at the receiver input, in the presence of unknown linear channel filtering, without recourse to extended training sequences for start-up. This problem has a significant history within communications signal processing due to its fundamental importance in the design of high-speed modems; common methods include the well-known Viterbi, List Viterbi Algorithms and BCJR algorithms enhanced with suitable blind channel estimators. Of late, the problem has attracted the attention of computational Bayesians such as Liu and Chen Liu and Chen (1995) who introduced Sequential Importance Sampling (SIS). Subsequently, several extensions have been proposed (e.g. Rejuvenation, Rejection Control, Fixed-Lag Smoothing, Metropolis-Hastings Importance Resampling, etc.) as improvements to SIS. Simulations comparing SIS and Rejuvenation to the more traditional methods were inconclusive as to whether Sequential Importance Sampling is always preferable to the traditional methods. Although Sequential Importance Sampling can be helpful in certain circumstances, it shows signs of instability, and therefore, may not be useful in practice. In conclusion, one should be cautious in using Sequential Importance Sampling or Rejuvenation for blind deconvolution problems.