Článek v odborném periodiku

Šimandl M., Duník J.

Automatica

45

45

2009

7

1749-1757

0005-1098

prof. Ing. Miroslav Šimandl, CSc. (FAV Západočeská univerzita, katedra kybernetiky)

state estimation, estimation theory, filtering techniques

clanek_Automatica09_JD.pdf [file]

The derivative-free nonlinear estimation methods exploiting the Stirling’s interpolation and the unscented transformation for discrete-time nonlinear stochastic systems are treated. The divided dierence and unscented filters, smoothers, and predictors based on the methods are introduced in the unified framework. The new relations among the first order Stirling’s interpolation, the second order Stirling’s interpolation, and the unscented transformation are derived and their impact on the covariance matrices of the state estimates of the corresponding filters is analysed. The theoretical results are illustrated and used for the explanation of the unexpected behaviour of the sigma point Gaussian sum filters given as a mixture of the derivative-free filters.