Features of creation and application of multidimensional adaptive filtering algorithms in time and frequency domains. Part 2. Interpolation
Authors: Butorin E.L. , Vinokurov A.D. , Kupriyanov N.A. , Ulyanov G.N. , Shatalov A.A. , Shatalova V.A. , Chebotar K.I. 
Published: October 2024

Problem statement. In modern technical literature, it is considered that smoothing is an operation of estimating all values of a random process performed inside an observation segment directly based on the results of observations obtained on this segment. At the same time, in order to solve many practical problems of digital spectral analysis and its applications, it becomes necessary to analyze the eigenvalues of the correlation matrix. It is believed that its implementation provides better resolution and frequency estimation characteristics than the autoregressive method and the Proni method, especially with small signal-to-noise ratios, as well as when processing random processes (RP) in adaptive systems. In addition, in digital signal processing (DSP) tasks, it is advisable to use the transformation of input vector random processes with correlated components into RP with uncorrelated components. Such operations are successfully used to obtain at the outputs of a filter with a pulse characteristic (PC) estimates of the signal, interference and noise RP, as well as their combinations. Based on this, it seems relevant to consider the features of the development and use of algorithms for the operation of several multidimensional adaptive filters designed to solve problems of interpolation of multidimensional RP, as well as the possibility of their implementation based on the filtering algorithms described in the first part of the article. Goal. Establishing a connection between PC interpolation (smoothing) filter and PC realizable and unrealizable filters described in the first part of the article. Development of adaptive algorithms for digital spectral analysis of the eigenvalues of the correlation matrix. Research of adaptive bleaching algorithms and algorithms for estimating eigenvalues and eigenvectors. Results. The features of the creation and application of adaptive algorithms for linear RP interpolation, as well as their relationship with adaptive algorithms for realizable and unrealizable filtering, are considered using examples of the development of an adaptive algorithm for the functioning of a Nollen preprocessor and a multidimensional adaptive bleaching filter. Algorithms for adjusting the weight coefficients of filters based on the use of methods of direct calculations of the moments of the laws of distributions of stationary SP, as well as methods of stochastic approximation, are proposed. It is shown that the RP bleaching algorithm has advantages over the Nollen algorithm: a large spread of eigenvalues almost does not affect the convergence rate, but at the same time has relatively low computational costs. Practical significance. As examples of the implementation of adaptive interpolation algorithms, algorithms performed with the help of Nollen and bleaching RP preprocessors are considered, which can be implemented using DSP processors by achieving the maximum possible parallelism of calculations in the positional number system. It is shown that in order to perform DSP in real time with an acceptable identical processing quality, the Nollen preprocessor, in contrast to the bleaching algorithm, needs to provide double the accuracy of calculations.