Particle filtering, also known as sequential importance sampling (SIS), has found widespread use, over the past 15 years or so, as an alternative to Kalman filtering for applications in sequential Bayesian estimation. This filter provides a solution when dealing with nonlinear and/or non-Gaussian estimation. In the past three decades, the following approaches have been used:
– the extended Kalman filter, described in Chapter 5;
– grid-based methods .
However, these two approaches suffer from the drawbacks of limited accuracy.
The particle filter, based on Monte Carlo sampling techniques, benefits from the following three advantages:
– the estimation is no longer based on Gaussian assumption;
– when the estimation problem is nonlinear, the Monte Carlo methods forego the linearization step, unlike the extended Kalman filter;
– as opposed to the grid-based methods, the particle filter is flexible to the dynamics of the process being studied. Furthermore, the computational power is lower for the particle filter.
This chapter introduces the reader to the Monte Carlo estimation techniques, focussing mainly on importance sampling techniques. We present the recursive version of the importance sampling filter and present ways to implement particle filtering.
Monte Carlo methods were first used in the domain of statistical physics during the Second World War, and most notably for the conception of the atomic bomb. In ...