Optimal solution of finite dimensional filtering problems via solution of linear ODEs

The work of Yau and collaborators on finite dimensional filters is a major advance in the solution of the general nonlinear filtering problem. In this paper, the solution of Yau and Lai for a large class of finite dimensional Yau filters (that includes the linear filter) is further simplified. The complete solution of the finite dimensional filtering problem is given in terms of a system of linear ordinary differential equations, which are easy to implement. A natural and numerically stable numerical techniques, suggested by group theoretical techniques, is also presented.