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  5. The method of mutual correlation evaluating with a small training sample

The method of mutual correlation evaluating with a small training sample

I. Kirillov, A. Dovgal, A. Cygankin, Ya. Snisarenko
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The method of mutual correlation estimation and the algorithm of finding the normalized correlation sequence (NCS) with a small training sample, that takes into account a priori information about the specific of correlation matrix (CM) structure (toeplitz structure), are proposed. A comparative analysis of different methods of estimation the correlation properties of multidimensional random process in a number of statistical parameters is done. It is shown that the proposed method by taking into account a priori information about toeplitz structure of CM and using a special matrix factorization, inverse CM, is not only significantly more accurate than the known one in conditions of limited volume samples, but also allows to estimate the NCS by single multidimensional sample.
Keywords: cross correlation, training sample, nonstationary process, Toeplitz correlation matrix, generalized Levinson factorization, iterative algorithm