A solution of the Bayesian recursive relations by the particle filter approach is treated. The stress is laid on the sample size setting as the main user design problem. The Cramer-Rao bound was chosen as a tool for setting the sample size for the three basic types of the state estimation, for filtering, prediction and smoothing. The mean square error matrices of particle filter state estimates for different sample sizes and the CR bounds are compared. Quality of the particle filters and their computational load are illustrated in a numerical example.