Particle Filters — A Theoretical Perspective

  • Dan Crisan
Part of the Statistics for Engineering and Information Science book series (ISS)


The purpose of this chapter is to present a rigorous mathematical treatment of the convergence of particle filters. In general, we follow the notation and settings suggested by the editors, any extra notation being defined in the next section. Section 2.3.1 contains the main results of the paper: Theorems 2.3.1 and 2.3.2 provide necessary and sufficient conditions for the convergence of the particle filter to the posterior distribution of the signal. As an application of these results, we prove the convergence of a certain class of particle filters. This class includes several known filters (such as those presented in (Carpenter, Clifford and Fearnhead 1999b, Crisan, Del Moral and Lyons 1999, Gordon et al. 1993), but is by no means the most general one. Finally, we discuss some of the issues that are relevant in applications and which arise from the theoretical analysis of these methods.


Probability Measure Theoretical Perspective Particle Filter Conditional Expectation Recurrence Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Dan Crisan

There are no affiliations available

Personalised recommendations