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Parametrical decomposition construction of two-dimensional signals on the basis of Prony’s method modifications

Keywords:

E.V. Verstakov, V.D. Zakharchenko, D.S. Gavrin


In a number of applied tasks for the parametrical experimental data description one-dimensional models are used. However some applications require the researched data description of higher dimension, for example, in tasks of two-dimensional spectrum analysis. Two-dimensional spectral analysis can be used for space-spatial data sets - image processing; spatio-temporal data sets - the processing sonar, seismic and radar signals in the case of the synthesized aperture, time-temporal data sets - the analysis of radar pulse repetition interval, depending on the moment of their arrival. Two-dimensional data processing leads to an increase in comparison with the one-dimensional case the computational difficulties, as well as the problem of the spread of many dimensional methods for two-dimensional case. Modifications of a classical Prony’s method for decomposition parameters searching of the two-dimensional signal provided by the sum of exponents are offered. For potential accuracy determination of decomposition parameters estimation of a two-dimensional signal the Cramer-Rao system of inequalities by criterion of a mean squared error minimum was used. For each parameter the Cramer-Rao bound estimation was received. Statistical modeling showed that the offered algorithms aren't optimum and the received parameters estimates of a two-dimensional signal can be specified.
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