A survey of convergence results on particle filtering methods for practitioners

  title={A survey of convergence results on particle filtering methods for practitioners},
  author={Dan Crisan and A. Doucet},
  journal={IEEE Trans. Signal Process.},
Optimal filtering problems are ubiquitous in signal processing and related fields. Except for a restricted class of models, the optimal filter does not admit a closed-form expression. Particle filtering methods are a set of flexible and powerful sequential Monte Carlo methods designed to. solve the optimal filtering problem numerically. The posterior distribution of the state is approximated by a large set of Dirac-delta masses (samples/particles) that evolve randomly in time according to the… 

The bootstrap particle filtering bias

Particle filter methods constitute a class of iterative genetic-type algorithms which provide powerful tools for obtaining approximate solutions to non-linear and/or non-Gaussian filtering problems.

On Convergence of Particle Filters with General Importance Distributions

This paper is concerned with convergence of particle filter estimates of unbounded functions with general importance distributions. Particle filters are numerical methods for approximating Bayesian

A novel particle filtering approach and its application to target tracking

Particle filters provide asymptotically optimal numerical solutions in problems that can be cast as estimation of unobserved time-varying states of dynamic systems. Such methods rely on knowledge of


In this chapter, we survey some recent results on the particle system approximations to stochastic filtering problems in continuous time. First, a weighted particle system representation of the

A mean-field control-oriented approach to particle filtering

A new formulation of the particle filter for non linear filtering is presented, based on concepts from optimal control, and from the mean-field game theory framework of Huang et. al.. The optimal

Particle filtering with observations in a manifold

  • S. SaidJ. Manton
  • Mathematics
    2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
  • 2015
It is shown that well-chosen connector maps can be used to transform successive samples from a continuous time observation process, evolving on a manifold, into a discrete sequence of random vectors, which are asymptotically independent and normally distributed, in the limit where the sampling interval goes to zero.

Accurate Methods for Approximate Bayesian Computation Filtering

An exact upper bound for the mean squared error is provided, and sufficient conditions on the bandwidth and kernel under which the ABC filter converges to the target distribution as the number of particles goes to infinity are derived.

On the use of particle filtering for maximum likelihood parameter estimation

This contribution investigates maximum likelihood estimation approaches based either on gradient or EM (Expectation-Maximization) techniques and shows that several recently proposed methods share the common feature of requiring the approximation of the expectation of a sum functional of the hidden states, conditionally on all the available observations.

Particle Filtering Convergence Results for Radiation Source Detection

This work designs a Sampling Importance Resampling (SIR) filter to detect and locate a radiation source using a network of sensors and proves the theoretical convergence of the estimate to the state posterior probability density function.

A Tutorial on Particle Filtering and Smoothing: Fifteen years later

A complete, up-to-date survey of particle filtering methods as of 2008, including basic and advanced particle methods for filtering as well as smoothing.



Discrete Filtering Using Branching and Interacting Particle Systems

A particle algorithm designed for solving numerically discrete ltering problems involving a system of n particles which evolve in correlation with each other according to law of the signal process and give birth to a number of oosprings depending on the observation process is described.

Particle Filters - A Theoretical Perspective

  • D. Crisan
  • Mathematics
    Sequential Monte Carlo Methods in Practice
  • 2001
The purpose of this chapter is to present a rigorous mathematical treatment of the convergence of particle filters, and it is proved that a certain class of particle filtering methods is found to convergence.


We study the stability of the optimal filter w.r.t. its initial condition and w.r.t. the model for the hidden state and the observations in a general hidden Markov model, using the Hilbert projective

Measure-valued processes and interacting particle systems. Application to nonlinear filtering problems

In the paper we study interacting particle approximations of discrete time and measure-valued dynamical systems. These systems have arisen in such diverse scientic disciplines as physics and signal

Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models

A new algorithm based on a Monte Carlo method that can be applied to a broad class of nonlinear non-Gaussian higher dimensional state space models on the provision that the dimensions of the system noise and the observation noise are relatively low.

Novel approach to nonlinear/non-Gaussian Bayesian state estimation

An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters, represented as a set of random samples, which are updated and propagated by the algorithm.

Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering

This paper focuses on interacting particle systems methods for solving numerically a class of Feynman-Kac formulae arising in the study of certain parabolic differential equations, physics, biology,

Sequential Monte Carlo Methods for Optimal Filtering

Sequential Monte Carlo methods are powerful tools that allow us to accomplish the state-of-the-art estimation of a nonlinear dynamic model sequentially in time.