A finite dimensional filter with exponential conditional density

Details A finite dimensional filter with exponential conditional density A finite dimensional filter with exponential conditional density

2009-01-14

arxiv.org/abs/0901.1952v1

Mathematics

Probability

Scientific paper

In this paper we consider the continuous--time nonlinear filtering problem, which has an infinite--dimensional solution in general, as proved by Chaleyat--Maurel and Michel. There are few examples of nonlinear systems for which the optimal filter is finite dimensional, in particular Kalman's, Benes', and Daum's filters. In the present paper, we construct new classes of scalar nonlinear filtering problems admitting finite--dimensional filters. We consider a given (nonlinear) diffusion coefficient for the state equation, a given (nonlinear) observation function, and a given finite--dimensional exponential family of probability densities. We construct a drift for the state equation such that the resulting nonlinear filtering problem admits a finite--dimensional filter evolving in the prescribed exponential family augmented by the observaton function and its square.

Affiliated with

Also associated with

No associations

Rating

A finite dimensional filter with exponential conditional density does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A finite dimensional filter with exponential conditional density, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A finite dimensional filter with exponential conditional density will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-375265