Piecewise monotone filtering with small observation noise

The authors propose an approximately optimal filter for the filtering problem dx/sub t/=f(x/sub t/) dt+g(x/sub t/) dw/sub t/, dy/sub t/=h(x/sub t/) dt+ epsilon dv/sub t/>or=0, where x/sub t/ is a scalar unobserved process, y/sub t/ is a scalar observed process, epsilon >0 is a small parameter, and w/sub t/, v/sub t/ are mutually independent standard Wiener processes. They treat the case when h(x) is not one-to-one, but has a finite number of maxima and minima.<<ETX>>