ABSTRACT
This chapter considers a sequential Monte Carlo method of filtering and smoothing for a nonlinear non-Gaussian state-space model, which is usually called a particle filter and smoother. The particle filter and smoother have been developed as a practical and easily implementable method of filtering and smoothing for high-dimensional nonlinear non-Gaussian state-space models. In the particle filter, an arbitrary non-Gaussian distribution is approximated by many particles that can be considered to be independent realizations of the distribution. The chapter considers the problem of state estimation for the nonlinear non-Gaussian state-space model. It presents the particle filter, distinct from the approximations shown above, the true distribution is represented by using many particles. Each particle is considered as a realization from the true distribution.
