SOLUTION OF THE PROBLEM OF COMPUTATIONAL STABILITY AND CONSISTENCY OF SAMPLE ESTIMATES OF THE CORRELATION MATRIX OF OBSERVATIONS BY THE METHOD OF DYNAMIC REGULARIZATION

Abstract

The problem of forming sample estimates of the correlation matrix of observations that satisfy the criterion "computational stability – consistency" is considered. The variants in which the direct and inverse asymptotic forms of the correlation matrix of observations are approximated by various types of estimates formed from a sample of a fixed volume are investigated. The consistency of computationally stable estimates of the correlation matrix for their static regularization was analyzed. The contradiction inherent in the problem of regularization of the estimates with a fixed parameter is revealed. The dynamic regularization method as an alternative approach is proposed, which is based on the uniqueness theorem for solving the inverse problem with perturbed initial data. An optimal mean-square approximation algorithm has been developed for dynamic regularization of sample estimates of the correlation matrix of observations, using the law of monotonic decrease in the regularizing parameter with increasing sample size. An optimal dynamic regularization function was obtained for sample estimates of the correlation matrix under conditions of a priori uncertainty with respect to their spectral composition. The preference of this approach to the regularization of sample estimates of the correlation matrix under conditions of a priori uncertainty is proved, which allows to exclude the domain of computational instability from solving the inverse problem and obtain its solution in real time without involving prediction data and additional computational cost for finding the optimal value of the regularization parameter. The application of the dynamic regularization method is shown for solving the problem of detecting a signal at the output of an adaptive antenna array in a nondeterministic clutter and jamming environment. The results of a computational experiment that confirm the main conclusions are presented.