On the linear-exponential filtering problem for general Gaussian processes

The explicit solution of the filtering problem with exponential criteria for a general Gaussian signal is obtained through an approach which is based on a conditional Cameron-Martin type formula. This key formula is derived for conditional expectations of exponentials of some quadratic functionals of a general continuous Gaussian process. The formula involves conditional expectations and conditional covariances in some auxiliary optimal filtering problem which is used in the proof. Closed form equations of Ito-Volterra and Riccati-Volterra type for these ingredients are provided. Particular cases for which the results can be further elaborated are investigated. Author for correspondence. Fax: [phone] 

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: Marina L. Kleptsyna, Alain Le Breton, Michel Viot
• Keywords: CDC 2009, Conditional Cameron-martin Type, Conditional Expectations, Control Systems, Filtering Problem