Duality Between Point-Mass and Simulation Approaches to State Estimation

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Two significant approaches, point-mass approach and Monte Carlo simulation approach, for an approximation of Bayesian recursive relations representing the general solution of the nonlinear state estimation problem are discussed. The stress is laid on finding their real fundamentals and common features. Both approaches use special types of grids substituting the continuous state space. However, the construction of the grids and the way of storing information about conditional probability density functions of the state are based on different ideas. Although the approaches are seemingly different, it is shown that there is a duality between them. In addition to the duality, an analysis of these nonlinear filter design techniques points out some common aspects and problems to be solved.