Local and global estimation approaches are discussed, above all the Unscented Kalman Filter and the Gaussian Sum Filter. The square root modification of the Unscented Kalman Filter is derived and it is used in the Gau...
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Local and global estimation approaches are discussed, above all the Unscented Kalman Filter and the Gaussian Sum Filter. The square root modification of the Unscented Kalman Filter is derived and it is used in the Gaussian Sum Filter framework. The new Sigma Point Gaussian Sum Filter is designed and some aspects of the filter are presented. Estimation quality and computational demands of the filter are illustrated in a numerical example.
The particle filter for nonlinear state estimation of discrete time dynamic stochastic systems is treated. The functional sampling density of the particle filter strongly affecting estimate quality is studied. The den...
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The particle filter for nonlinear state estimation of discrete time dynamic stochastic systems is treated. The functional sampling density of the particle filter strongly affecting estimate quality is studied. The density is given by weighted mixture of the transition probability density functions. The weights are calculated using distance of two reference variable probability density functions representing prior and measurement information. The aim is to find a suitable distance that does not suffer from problems with its numerical computation and that can be computed for a large set of systems analytically. It seems that the Bhattacharyya distance is feasible for evaluation of such a distance. Quality and computational demands of the functional particle filter with primary weights computed using the Bhattacharyya distance are illustrated in a numerical example.
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