The bootstrap particle filtering bias
(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)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/929081
- author
- Olsson, Jimmy ^{LU} and Rydén, Tobias ^{LU}
- organization
- publishing date
- 2004
- type
- Contribution to journal
- publication status
- unpublished
- subject
- 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}, }