Optimal Filtering for Linear Systems: Kalman-Bucy versus Risk-Sensitive

The algorithm for the optimal filter has been obtained for systems with polynomial first degree drift term in the state and observations equations. Two cases are presented: systems with disturbances in L² and systems with Brownian motion and parameter epsiv in the state and observations equations. The algorithms of the optimal risk-sensitive filter are obtained in each case and their performance verified and compared to the algorithms of the optimal Kalman-Bucy filter through an example. The optimal risk-sensitive filter shows better performance than the Kalman-Bucy optimal filter, for large values of the parameter epsiv.