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The bondary spectral functions application for definition of regularization parameter in correction of autoregressive spectral estimates

Keywords:

D.S. Grigoryan


At the decision of signals processing problems in radio engineering systems the signals superresolution necessity on space and adaptation of adaptive antenna arrays forces to search for methods of analysis of the spectral estimates resolution in the set conditions of supervision of a signal depending on indignations of a vector of the weight factors arising owing to presence of noise and processing channels disturbances. For analytical definition of indignations weight vector area border at which the superresolution takes place, it is possible to search for interrelation of indignations weight with spectral function. For definition of indignations border interrelation and spectral function it is offered to use so-called boundary spectral functions. In a case when received by criterion of a minimum least square error vectors of weight factors don\'t provide the superresolution of signals that system of the equations of a linear prediction is possible to correct. One of approaches to the correction of system equations of a linear prediction is use of criterion of minimum of an average square of norm smoothing функционала the errors, defined by a profile vector of weight factors. Thus as a profile vector is possible to choose pseudo-ideal weight vector, defined in the parameters close to the measured. It is necessary to consider such approach as development of a method of regularization of Tikhonov with reference to autoregressive spectral estimation. Regularization application can lead to the superresolution, i.e. to occurrence on spectral function of several peaks. However one of problems of a linear prediction equations system Tikhonov method correction is the selection of the regularization parameter value, providing the most exact estimations of parameters on spectral function. Article purpose – to set an example applications of the device of boundary spectral functions for definition of indignations of a vector of weight factors and calculation with their help of parameter of the regularization providing the superresolution at a building of system equations of a linear prediction method on least smoothing error function.
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