Studying the properties of a robust algorithm for identifying linear objects, which minimizes a combined functional

Abstract

This paper addresses the task of identifying the parameters of a linear object in the presence of non-Gaussian interference. The identification algorithm is a gradient procedure for minimizing the combined functional. The combined functional, in turn, consists of the fourth-degree functional and a modular functional, whose weights are set using a mixing parameter. Such a combination of functionals makes it possible to obtain estimates that demonstrate robust properties. We have determined the conditions for the convergence of the applied procedure in the mean and root-mean-square measurements in the presence of non-Gaussian interference. In addition, expressions have been obtained to determine the optimal values of the algorithm's parameters, which ensure its maximum convergence rate. Based on the estimates obtained, the asymptomatic and non-asymptotic values of errors in estimating the parameters and identification errors. Because the resulting expressions contain a series of unknown parameters (the values of signal and interference variances), their practical application requires that the estimates of these parameters should be used. We have investigated the issue of stability of the steady identification process and determined the conditions for this stability. It has been shown that determining these conditions necessitates solving the third-degree equations, whose coefficients depend on the specificity of the problem to be solved. The resulting ratios are rather cumbersome but their simplification allows for a qualitative analysis of stability issues. It should be noted that all the estimates reported in this work depend on the choice of a mixing parameter, the task of determining which remains to be explored. The estimates obtained in this paper allow the researcher to pre-evaluate the capabilities of the identification algorithm and the effectiveness of its use in solving practical problems

Developing a multi-step recurrent algorithm to maximize the criteria of correntropy

“…A combined criterion consisting of a fourth-power and modular criterion was proposed in [27,28]. These works established the asymptotic and non-asymptomatic properties of the identification algorithm and investigated the effect of selecting the mixing parameter value on the properties of estimates.…”

“…Substituting these expressions in (27) and the simple transformations considering the introduced designations (28) produce For the algorithm to converge, one needs to meet the following condition that is, the expression in the right-hand part of (30) should be negative. Because 1, λ ≤ the first term is not positive.…”