Universal Algorithm of Adaptive Optimal-Invariant Signal Filtering

The algorithm of optimal-invariant adaptive signal filtering for models of interferences of measurement in the form of Markovian processes of k(th) order by the example of a complex system with the filter of a different signal is offered. The demanded level of a priori determinancy concerning the noise of measurement includes knowledge of approximate duration of intervals of a quasi-stationarity noise of measurement, a sort of linear model of measurement, a variance of high-frequency noise, and the presence of a mutual non-correlated signal and noise. The algorithm, in the course of operation, besides optimal filtering of signals, evaluates the quality of the handling of signals and defines adapting time. In the presence of information on correlative functions, the noise of measurement by the algorithm ensures optimally-invariant filtering of Kalman signals without the necessity of a solution of the Rikkati equation.