Discrete time piecewise linear filtering with small observation noise

Abstract

The authors describe a procedure that gives an approximate solution to a piecewise linear discrete time filtering problem with small observation noise. They present and compare different tests which make it possible to compute the intervals of linearity of the observation function, under a 'detectability assumption' based on the drift. Over such an interval, one can then approximate the optimal filter by the corresponding Kalman-Bucy filter.<>