Výzkumná zpráva

Šimandl M., Duník J., Král L.

Plzeň

2007

73

Ing. Jindřich Duník, Ph.D. (FAV Západočeská univerzita, katedra kybernetiky)

stochastic systems, nonlinear systems, state estimation

report_DFF_JD.pdf [file]

State estimation methods for nonlinear stochastic systems are treated. The Stirling's interpolation and the unscented transformation, used in the design of the derivative-free Kalman filters, are briefly discussed. These approximation techniques are exploited to the design of the derivative-free local smoothers and predictors. Then the numerical properties of different types of the derivative-free local estimators are developed. The derivative-free local estimators are used as the cornerstone of the design of global estimators based on the Gaussian sum approach. Afterwards, a thorough analysis of the derivative-free approximation techniques is given and consequently new relations between the Unscented Kalman Filter and the Divided Difference Filters are derived. The main stress in the analysis is laid on the covariance matrixes which have crucial role for the behaviour explanation of the Derivative-Free Gaussian Sum Filters. The theoretical results are illustrated in numerical examples.