A class of solvable nonlinear filters

Abstract

The purpose of this paper is to present a new class of nonlinear filters that can be explicitly computed. The systems have drift satisfying a Riccati equation f + f 2 = V where V is Fourier transform of an arbitrary complex even Borel measure on U and we give an explicit formula for the unnormalized conditional density, as a convergent series each term of which depends only on a finite number of statistics.