Optimal Recurrent Nonlinear Filter of a Large Order for Jump Diffusion Markov Signals

In this paper, we consider the problem of the root-mean-square optimal estimation of the current state of a continuous stochastic object of observation exposed to continuous and pulsed random impacts based on the results of discrete measurements of its output at certain clock time points. To obtain real-time estimates using a low-performance computer, a new discrete finite-dimensional filter that provides estimates only at certain clock and possibly inter-cycle time points is proposed. The vector of its state is composed of the last few clock estimates, while the next estimate is sought in the form of its explicit dependence on the last measurement and the previous state of the filter. The number of previous clock estimates to be taken into account can be selected from the condition of a compromise between the required estimation accuracy and the available measurement processing speed. The prediction between measurements is based on the optimal clock and inter-cycle estimates heuristically. The filter synthesis algorithm and methods for constructing its covariance approximations are presented. An example is considered.