Bayesian Estimation and Tracking: A Practical Guide

16.3 The Bootstrap Particle Filter

One of the easiest to implement, and thus one of the most widely used, resampling SIS particle filters is the bootstrap particle filter (BPF) introduced in [12]. In the BPF, the transition density is chosen as the importance density, that is

(16.19)

For this choice of importance density, the weight update equation (16.12) becomes

(16.20)

The BPF has the distinctive feature that the incremental weights do not depend on the past trajectory of the particles but only on the conditional likelihood of the observation . For the BPF, sampling is very straightforward, with the state transition equation (5.1) used to generate new particles by merely transitioning the particle from the previous time step. This is usually followed by the resample and move steps. The complete procedure for the BPF is shown in Table 16.4. Once again, the first and second moments of the distribution can be calculated at the end of each time step.

Table 16.4 Bootstrap SIS Particle Filter with Resampling and Regularization.

A.	Initialize filter
1. Initialize state vector samples
2. Initialize weights
B.	Sequential importance sampling
1. Draw new samples