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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unpublished
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in
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
2008-01-14 16:06:59
date last changed
2016-04-16 06:22:32
@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},
}