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

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.

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M. Alcorta-Garcia, S. Rostro and M. Torres, "Optimal Risk-Sensitive Filtering for System Stochastic of Second and Third Degree," Intelligent Control and Automation, Vol. 2 No. 1, 2011, pp. 47-56. doi: 10.4236/ica.2011.21006.

Conflicts of Interest

The authors declare no conflicts of interest.

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