Sequential Monte Carlo methods in filter theory
Department of Statistics,
1, South Parks Road,
Oxford, OX1 3TG.
The need for accurate monitoring and analysis of sequential data arises
in many scientific, industrial and financial problems. Although the Kalman
filter (Kalman and Bucy, 1961)
is effective for linear-Gaussian models, new methods of filtering
are required for the general case.
Nonlinear and non-Gaussian filters are reviewed, with particular
emphasis being placed on the particle filter, a recently developed filter,
which uses sequential Monte Carlo methods. The particle filter is
seen to cover a number of independently proposed, but related, filters,
dating back to the SIR filter of Gordon, Salmond and Smith (1993).
All these particle
filters approach the filtering
problem from a sampling perspective, with the aim
being to generate a random sample from the true posterior distribution.
In this thesis filtering is viewed as a Monte Carlo
integration problem. This perspective is used to suggest a number of
new improvements for the particle filter. Along with these improvements,
guidelines for the efficient implementation of the particle filter are
It is also shown that the application of the particle filter to certain
types of problems naturally leads to a filter similar to, but more
efficient than, the random sampling algorithm of Akashi and Kumamoto (1977).
In order to demonstrate these improvements, the new
particle filters are tested
on various examples. These examples include the much studied
bearings-only tracking problem, and a change-point detection problem
based on oil well data. It is shown that significant
increases in efficiency
can be obtained by using the suggested improvements, and that the
improved particle filters give promising results.
The application of particle filters to problems with
fixed parameters is also considered. These are problems on which sequential
Monte Carlo methods
often struggle. Two simple examples will be studied, on which a number
of different methods are tried. The results obtained will provide guidance
for the construction of efficient methods for analysing more complicated fixed
Importance resampling, Sequential filter, Markov Chain Monte Carlo, Rejection sampling, SIR filter,
MHIR filter, ASIR fitler, Particle filter, Bearings-only tracking, Non-linear,
State-space modelling, Change-point detection.
[Back to Home Page]