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The group radar object resolution method stability

Keywords:

S.A. Klimov


As a rule, the non orthogonal signal resolution methods has been developed over the last 30 years are guided by digital processing. The resolution algorithms are based on pseudo solutions of a system of equations while using a correlation data matrix (the spectral analysis methods) or Gram matrixes of expected signal system (the maximum likelihood methods, the least squares method and their versions). In fact, for such system of equations it is necessary to answer the questions of existence of the solution, its uniqueness and stability. The main problem is the stability of received pseudo solutions. The purpose of this work is to obtain the laws of stability for statistical group radar object resolution methods. The following formula is obtained. In the case of m-signal the signal-to-noise ratio reduces proportionally to a coefficient. The fewer coefficient the more energy is required for m-signal resolution. In this case quality characteristics of resolution even for two signals can’t be better than the corresponding one for alone signal. The formula of article may be considered as synthesis of known in signal detection theory formula for signal-to-noise ratio in the context of resolution theory. If in case of signal detection under static signal-independent noise conditions the signal-to-noise ratio doesn’t depend on transformation operator type but only on energy of received signal and noise power spectral density, in case of signal resolution it depends on transformation operator type and processing method significantly. It is suggested to use the conditioning number of matrix of system as stability characteristic for group radar object resolution methods. The condition number is the universal characteristic connecting among themselves all the major for permission of signals factors. It is shown that linear transformation of the smallest squares given in methods and the maximum credibility leads to square increase in number of conditionality of system of the linear equations. It reduces potential resolution and stability of methods resolution of group radar objects.
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