A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking
- ISSN: 1053587X
- DOI: 10.1109/78.978374
Abstract
Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or "particle") representations of probability densities, which can be applied to any state-space model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example
A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking
Nonlinear/Non-Gaussian Bayesian Tracking *
Simon Maskell
Qinetiq Ltd and Cambridge University Engineering Department, UK.
s.maskell@signal.qinetiq.com
Neil Gordon
QinetiQ Ltd, UK.
n.gordon@signal.qinetiq.com
September 2001
1 Introduction
Bayesian methods provide a rigorous general framework for dynamic state estimation problems. The
Bayesian approach is to construct the pdf of the state vector based on all available information. This pdf
summarises the current state of knowledge about the state vector and from it the optimal (with respect
to whatever cost function the user chooses) course of action can be determiued. For the linear/Gaussian
estimation problem, the required pdf remains Gaussian at every iteration of the filter, and the Kalman
filter relations propagate and update the mean and covariance of the distribution. For a nonlinear/ non-
Gaussian problem there is in general no analytic (closed form) expression for the required pdf. However,
for many applications these modelling assumptions are strongly implied by considerations of realiim.
For example, bearings only tracking in a Cartesian cc-ordinate system implies a nonlinear relationship
between the state and the measurement. Similarly, if measurement sensors produce occasional gross
errors (eg radar gliit), a heavy-tailed non-Gaussian error model could be appropriate.
In the following notes we begin with a ddption of the nonlinear/non-Gaush tracking problem and
its optimal Bayesian solution. Since the optimal solution is intractable, several different apprcadmation
strategies are then described. These approaches include the extended Kalman filter and particle filters.
These notes are of a tutorial nature and so, to fadlitate easy implementation, 'pseudmode' for algorithms
has been included at relewt points.
2 Nonlinear Bayesian Tracking
To define the problem of tracking, consider the evolution of the state sequence {xk, k E N) of a target,
given by
where fb : 82"s x 82"- + R"- is a possibly nonlinear function of the state xt-1, tvk-1, k E N) is an i.i.d
process noise sequence, n.,n, are dimensions of the state and process noise vectors, respectively and N
is the set of natural numbers. The objective of tracking is to recursively estimate xk from measurements
XI =fk(Xk-I,Vk-l)r (1)
zk = hs(xk,nr), (2)
*@Copyright QinetiQ Ltd 2001. Published with the permission of QinetiQ Ltd. This paper is a condensed mion of 111.
21 1
Sign up today - FREE
Mendeley saves you time finding and organizing research. Learn more
- All your research in one place
- Add and import papers easily
- Access it anywhere, anytime