Optimal Structure of Recurrent Nonlinear Filters of Large Order for Diffusion Signals

We consider the optimal mean-square estimation problem for the state variables of a continuous nonlinear stochastic object by using results of time-discrete measurements. To obtain clock and inter-clock estimates on a computer of limited power in real time, we propose a procedure for the synthesis of a nonlinear structure of a discrete finitedimensional filter, the state vector of which is formed from the desired number of already obtained preceding clock estimates. We describe the synthesis algorithm for the filter and its suboptimal approximations. The advantage of the latter is shown in comparison with the corresponding generalizations of the Kalman filter. Bibliography: 8 titles. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.