Optimal Risk-Sensitive Filtering for System Stochastic of Second and Third Degree

Ma Aracelia Alcorta-Garcia, Sonia Gpe Anguiano Rostro, Mauricio Torres Torres

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DOI: 10.4236/ica.2011.21006                

Abstract

The risk-sensitive filtering design problem with respect to the exponential mean-square cost criterion is con-sidered for stochastic Gaussian systems with polynomial of second and third degree drift terms and intensity parameters multiplying diffusion terms in the state and observations equations. The closed-form optimal fil-tering equations are obtained using quadratic value functions as solutions to the corresponding Focker- Plank-Kolmogorov equation. The performance of the obtained risk-sensitive filtering equations for stochastic polynomial systems of second and third degree is verified in a numerical example against the optimal po-lynomial filtering equations (and extended Kalman-Bucy for system polynomial of second degree), through comparing the exponential mean-square cost criterion values. The simulation results reveal strong advan-tages in favor of the designed risk-sensitive equations for some values of the intensity parameters.

Keywords

Optimal Nonlinear Filtering, Risk-Sensitive Filtering, Extended Kalman-Bucy Filtering

Conflicts of Interest

The authors declare no conflicts of interest.

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