Nonlinear Filtering Methods: Some Aspects and Performance Evaluation

M. Šimandl and O. Straka (Czech Republic)


Stochastic systems, nonlinear estimation, Cramer-Raobound


Approximate solution of nonlinear filtering problem by Gaussian sums, point-mass and Monte Carlo simulation methods are considered. The stress is laid on real fundamentals, comparison and common features of the methods. The methods use different types of grid substituting the continuous state space, nevertheless the construction of the grid and the way of storing information about conditional probability density functions of the state are based on different ideas. The common problem of the methods is how to specify the efficient number of grid points. It is shown that the Cramer- Rao (CR) bound enables to evaluate nonlinear filter performance. Complementary features of the methods and usability of the CR bound are illustrated in numerical example.

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