The Bootstrap Particle Filtering Bias
Jimmy Olsson and Tobias Rydén
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2004
ISSN 14039338

Abstract:

Particle filter methods constitute a class of iterative genetictype algorithms
which provide powerful tools for obtaining approximate solutions to nonlinear
and/or nonGaussian 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.




Key words:

Bootstrap particle filter, interacting particle system, nonlinear filtering,
sequential Monte Carlo methods, state space model
