Swarm Intelligence Techniques Applied to Nonlinear Systems State Estimation - Advances in Heuristic Signal Processing and Applications - page 219

Fig. 10.2 Generic Particle
Filter (GPF) algorithm
10.3 Generic Particle Filter and Limitations
The Particle Filter is a sequential Monte Carlo method for Bayesian state estimation
in nonlinear systems [ 9 ]. The basic idea of PF is to approximate a posterior distri-
bution based on a set of random particles with associated weights. PF has several
variants with different sampling and resampling procedures. All sampling proce-
dures utilized in PF can be derived from the Sequential Importance Sampling (SIS)
algorithm. When the SIS is associated with a resampling procedure, it will be called
Generic PF (GPF) [ 3 ]. Figure 10.2 shows the general iterative structure of GPF.
A high level description of the sequential steps is shown in this figure. A more ex-
tensive introduction to PF can also be found in [ 9 , 18 , 19 ].
PF has a main loop. At first, the position of particles is propagated with their
initial distribution. Then the outputs, estimated using each particle, are made. Later,
each particle is weighted and the weights are normalized. In a resampling procedure,
the particles with small and large weights are eliminated and replicated, respectively.
Finally, the current state is estimated using some statistical properties. Figure 10.3
shows the process of PF. In the following subsections, these steps are discussed in
detail.