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The bootstrap particle filtering bias

Olsson, Jimmy LU and Rydén, Tobias LU (2004) In Preprint without journal information
Abstract
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. The aim of this paper is to, using standard tools from probability theory, study the bias of Monte Carlo integration estimates obtained by the bootstrap particle filter. A bound on this bias, which is geometrically growing in time and inversely proportional to the number N of particles of the system, is derived. Under suitable mixing assumptions on the latent Markov model, a bound of the bias which is uniform with respect to the time parameter and inversely proportional to N is obtained. In the last part of the paper we investigate the... (More)
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. The aim of this paper is to, using standard tools from probability theory, study the bias of Monte Carlo integration estimates obtained by the bootstrap particle filter. A bound on this bias, which is geometrically growing in time and inversely proportional to the number N of particles of the system, is derived. Under suitable mixing assumptions on the latent Markov model, a bound of the bias which is uniform with respect to the time parameter and inversely proportional to N is obtained. In the last part of the paper we investigate the behaviour of the bias as N goes to infinity; it will be seen that the bias, for a fixed time point, is indeed asymptotically inversely proportional to N. (Less)
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publication status
unpublished
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Preprint without journal information
issue
2004:24
publisher
Manne Siegbahn Institute
ISSN
0348-7911
language
English
LU publication?
yes
id
a6c5a971-4a6d-4467-b99c-754a51f4fb94 (old id 929081)
date added to LUP
2016-04-04 09:12:40
date last changed
2018-11-21 20:51:31
@article{a6c5a971-4a6d-4467-b99c-754a51f4fb94,
  abstract     = {{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. The aim of this paper is to, using standard tools from probability theory, study the bias of Monte Carlo integration estimates obtained by the bootstrap particle filter. A bound on this bias, which is geometrically growing in time and inversely proportional to the number N of particles of the system, is derived. Under suitable mixing assumptions on the latent Markov model, a bound of the bias which is uniform with respect to the time parameter and inversely proportional to N is obtained. In the last part of the paper we investigate the behaviour of the bias as N goes to infinity; it will be seen that the bias, for a fixed time point, is indeed asymptotically inversely proportional to N.}},
  author       = {{Olsson, Jimmy and Rydén, Tobias}},
  issn         = {{0348-7911}},
  language     = {{eng}},
  number       = {{2004:24}},
  publisher    = {{Manne Siegbahn Institute}},
  series       = {{Preprint without journal information}},
  title        = {{The bootstrap particle filtering bias}},
  year         = {{2004}},
}