Approximations to optimal nonlinear filters

Let the signal and noise processes be given as solutions to nonlinear stochastic differential equations. The optimal filter for the problem, derived elsewhere, is usually infinite dimensional. Several methods of obtaining possibly useful finite dimensional approximations are considered here, and some of the special problems of simulation are discussed. The numerical results indicate a number of useful features of the approximating filters and suggest methods of improvement. The paper is concerned with problems where the noise and nonlinear effects are much too large for the use of "linearization" methods, which for the simulated problem, at least, were useless.