Optimization of linear stochastic systems based on canonical wavelet expansions. (English. Russian original) Zbl 1457.93075

Sinitsyn, I. N.; Sinitsyn, V. I.; Korepanov, E. R.; Konashenkova, T. D.

Autom. Remote Control 81, No. 11, 2046-2061 (2020); translation from Avtom. Telemekh. 2020, No. 11, 136-154 (2020).

Summary: Design problems for linear mean square (MS) optimal filters are considered on the basis of canonical wavelet expansions (CWEs). To simulate the class of essentially non-stationary stochastic processes, including those describing shock effects, the idea put forward in this paper is to use the CWEs based on the coefficients of its covariance function expanded in terms of an orthogonal two-dimensional wavelet basis. To estimate an observed process represented as a CWE, a linear MS optimal operator in the form of a set of formal rules describing the operator’s response to basic wavelet functions is constructed. Explicit formulas for calculating the MS optimal estimate of the signal and the MS optimal estimate of the quality of the constructed linear MS optimal operator are derived. Sintez-VL, a software tool developed in MATLAB, is described. A test example with the delta function is provided.

MSC:

93E03	Stochastic systems in control theory (general)
93C05	Linear systems in control theory
93-08	Computational methods for problems pertaining to systems and control theory
65T40	Numerical methods for trigonometric approximation and interpolation

Keywords:

canonical wavelet expansion; nonstationary linear mean square optimal filter; orthogonal wavelets with finite support; Haar wavelets

Software:

Sintez-VL; Matlab

References:

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