Piecewise Monotone Filtering with Small Observation Noise
Wendell H. Fleming, Étienne Pardoux · SIAM Journal on Control and Optimization · 1989
Nonlinear filtering of Markov diffusion processes is considered, in the case in which a piecewise monotone function of the state is observed with additive small observation noise. Under a certain detectability hypothesis, statistical tests are given to discriminate among the intervals of monotonicity during time intervals in which the state does not cross critical points of the observation function. During such time intervals, accurate approximate finite dimensional filters can be used.