On Nonlinear Filtering of Non-Gaussian Processes Through Volterra Series

Gaussian and obtain conditions under which the optimal filter, which is not necessarily linear, can be represented as a (nonlinear) Volterra functional in a generalized Fock space in the form

We also find the generalized Wiener-Hopf equation that the filter coefficients must satisfy. We will only present some results and the detailed proofs appear elsewhere [1, 2, 3].