Substantiation of selection and dimension reduction of non-centered informative features of signals in information systems of short-range location

In this paper, we consider the issues of selection of informative features, dimension reduction of feature vectors in regression algorithms of detection and recognition of signals and interference, as well as the issues of obtaining informative features using neural network algorithms with ill-conditioned data. The problem is considered in relation to the short-range location, with large dynamic ranges of informative features and small decision intervals, when it is impossible to estimate mathematical expectations, that is, it is impossible to use adaptive algorithms. Regression algorithms for processing non-centered random signals are presented, with a priori unknown mathematical expectations of informative parameters, which consider the specificity of short-range location and use a priori information about the initial regression characteristics of informative features – multiple initial regression coefficients. Unlike it is in traditional regression analysis, the coefficients are determined through the elements of the matrices that are inverse to the matrices of the initial correlation moments. In regression algorithms, it is necessary to calculate the square error of multiple initial regression representations. The residual mean of squares of the initial regression representations are used to justify the methods for selection and dimension reduction of informative features of signals in the problems of detection and recognition of signals and interference. We give examples of application of the proposed methods for the problems of detection and recognition of a helicopter and airplane by acoustic signals when processing histograms of the distributions of the durations of intervals between zeros, samples of envelopes and samples of local extrema of the power spectral density. Good separability of the {airplane} and {helicopter} classes in the space of non-centered parameters of signals (features) is shown. The issue of obtaining regression statistical characteristics with illconditioned data is considered. If the matrices of the correlation moments of the informative features of signals and noise are illconditioned, it becomes impossible to obtain a priori information about the multiple initial regression coefficients. The possibility of using neural network algorithms to obtain estimates of the residual mean squares of regression representations and multiple initial regression coefficients through the weight coefficients on the inputs of neurons with ill-conditioned data is shown. The results can be used in short-range location systems with a large dynamic range of non-centered informative parameters, when it is not possible to estimate the mathematical expectations of the signal parameters due to the limited observation interval.