The Exponential Projection Filter and the Selection of the Exponential Family
Damiano Brigo, Francois Le Gland, Bernard Hanzon · 1996
: We present the projection filter, an approximate finite--dimensional filter based on the differential geometric approach to statistics. We recall the definition of the projection filter in the case of exponential families, and we give some hints about the selection of the coefficients in the exponential family. 1 INTRODUCTION The filtering problem consists in estimating the state of a stochastic differential system from noisy observations. In the linear Gaussian case the solution consists of the Kalman filter, a finite--dimensional system of equations for the first two conditional moments of the state given the observations. In the general nonlinear case, the filtering problem consists in computing the conditional density of the state given the observations. This density is the solution of a stochastic partial differential equation, the Kushner--Stratonovich equation. The general nonlinear problem is far more complicated because the resulting nonlinear filter is not finite dimensio...