State estimation of discrete-time nonlinear non-Gaussian stochastic systems by point-mass approach, which is based on discretization of state space by a regular grid and numerical solution of Bayesian recursive relations, is treated. The stress is laid to grid design which is crucial for estimator quality and significantly affects the computational demands of the estimator. Boundary-based grid design, thrifty convolution, and multigrid design with grid splitting and merging are proposed. The main advantages of these techniques are nonnegligible support delimitation, time-saving computation of convolution, and effective processing of multimodal probability density functions, respectively. The techniques are involved into the basic point-mass approach and a new general-purpose, more sophisticated point-mass algorithm is designed. Computational demands and estimation quality of the designed algorithm are presented and compared with the particle filter in a numerical example. (c) 2006 Elsevier Ltd. All rights reserved.