Target recognition by maximizing heterogeneity of signal samples collected for discrimination with respect to an observed signal

摘要

This paper deals with the problem of how to identify targets or signals in noise, which represents, mathematically, the problem of classifying an observed target data sample as coming from one of several populations. Some of the information about the alternative distributions of populations has been obtained from signal data samples collected for discrimination. Each sample is declared to be realization of a specific stochastic process. By this step each sample is attached to just one out of a set of possible signals with distinct characteristics. We are dealing with the case when the alternative distributions of populations are multivariate normal with different mean vectors and covariance matrices. It is assumed that all parameters are unknown. Also, the univariate case is considered. It is shown how certain tests of homogeneity or normality of several samples of the data can be used to transform a set of signal data samples into some statistic that measures either distance from homogeneity or distance from normality of these samples, respectively. This statistic is then used to construct sample based discriminant rule which either maximizes distance from homogeneity or minimizes distance from normality, respectively, with respect to an observed signal. The above discriminant rules are applied to obtain new procedures of target recognition which are relatively simple to carry out and can be easily used, say, for bird recognition by radar in order to preclude the possibility of collisions between aircraft and birds, etc. In those situations when we deal with small samples of the data, the procedures proposed herein are recommended. An illustrative numerical example is given.