Abstract
The problem of identification of non-stationary parameters of a linear object, which can be described by the first-order Markov model, with non-Gaussian interference is considered. The identification algorithm is a gradient minimization procedure of the combined functional. The combined functional, in turn, consists of quadratic and modular functionals, the weights of which are set using the mixing parameter. Such a combination of functionals makes it possible to obtain estimates with robust properties. The identification algorithm does not require knowledge of the degree of non-stationarity of the investigated object. It is the simplest, since information about only one measurement cycle (step) is used in model construction. The use of the Markov model is quite effective, as it allows obtaining analytical estimates of the properties of the algorithm.Conditions of mean and mean-square convergence of the gradient algorithm in the estimation of non-stationary parameters and with non-Gaussian measurement interference are determined.The obtained estimates are quite general and depend both on the degree of object non-stationarity and statistical characteristics of useful signals and interference. In addition, expressions are determined for the asymptotic values of the parameter estimation error and asymptotic accuracy of identification. Since these expressions contain a number of unknown parameters (values of signal and interference dispersion, dispersion characterizing non-stationarity), estimates of these parameters should be used for their practical application. For this purpose, any recurrent procedure for evaluating these unknown parameters should be applied and the resulting estimates should be used to refine the parameters included in the algorithms. In addition, the asymptotic values of the estimation error and identification accuracy depend on the choice of mixing parameter
Highlights
The identification problem is of interest in itself, but is an integral part of the general optimization problem
The identification problem is significantly complicated if the parameters θ change over time, i. e
Identification algorithms in the case of Gaussian interference are based on the least squares (LS) method, and in the case of interference distributed according to Laplace’s law, they are based on the least absolute deviations (LAD) method
Summary
The identification problem is of interest in itself, but is an integral part of the general optimization problem. Identification algorithms in the case of Gaussian interference are based on the least squares (LS) method, and in the case of interference distributed according to Laplace’s law, they are based on the least absolute deviations (LAD) method. Both of these methods are optimal in their conditions and Mathematics and cybernetics – applied aspects the solutions obtained with their help may vary greatly. Since in practice these extreme cases are very rarely implemented, neither the Gauss’s law nor the Laplace’s law are usually fulfilled In this regard, it seems very relevant to develop an approach to robust estimation of non-stationary parameters using some combined functional, which allows combining LS and LAD
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