The Sequential Monte Carlo Filter

In this chapter, we consider a sequentialMonte Carlo filter and smoother,

which is also called a particle filter or bootstrap filter. Distinct in charac-

ter from other numerical approximation methods, the sequential Monte

Carlo filter has been developed as a practical method for filtering and

smoothing high-dimensional nonlinear non-Gaussian state-space mod-

els. In the sequential Monte Carlo filter, an arbitrary non-Gaussian distri-

bution is approximated by many particles that can be considered to be in-

dependent realizations of the distribution. Then, a recursive filtering and

smoothing are realized by two simple manipulations of particles, namely,

the time-evolution of each particle and re-sampling, in other words, sam-

pling with replacement (Gordon et al. (1993), Kitagawa (1996), Doucet

et al. (2001)).