(eng): The paper deals with the state estimation of nonlinear stochastic dynamic systems with special attention on a grid-based numerical solution to the Bayesian recursive relations, the point-mass filter (PMF). In the paper, a novel functional decomposition of the transient density describing the system dynamics is proposed. The decomposition is based on a non-negative matrix factorization and separates the density into functions of the future and current states. Such decomposition facilitates a thrifty calculation of the convolution, which is a bottleneck of the PMF performance. The PMF estimate quality and computational costs can be efficiently controlled by choosing an appropriate rank of the decomposition. The performance of the PMF with the transient density decomposition is illustrated in a terrain-aided navigation scenario.