A tutorial on particle filters for on-line nonlinear/non-Gaussian Bayesian tracking

Bayesian methods provide a rigorous general framework for dynamic state estimation problems. We describe the nonlinear/non-Gaussian tracking problem and its optimal Bayesian solution. Since the optimal solution is intractable, several different approximation strategies are then described. These approaches include the extended Kalman filter and particle filters. For a particular problem, if the assumptions of the Kalman filter hold, then no other algorithm can out-perform it. However, in a variety of real scenarios, the assumptions do not hold and approximate techniques must be employed. The extended Kalman filter approximates the models used for the dynamics and measurement process, in order to be able to approximate the probability density by a Gaussian. Particle filtering approximates the density directly as a finite number of samples. A number of different types of particle filter exist and some have been shown to outperform others when used for particular applications. However, when designing a particle filter for a particular application, it is the choice of importance density that is critical. These notes are of a tutorial nature and so, to facilitate easy implementation, 'pseudo-code' for algorithms are included at relevant points.