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Estimation of measurement error of the vector information parameter of the signal along with multiplicative noise

Keywords:

V.M. Artyushenko – Dr. Sc. (Eng.), Professor, Head of Department of Information Technology and Management Systems, Technological University (Korolyov, Moscow region). E-mail: artuschenko@mail.ru V.I. Volovach – Ph. D. (Eng.), Associate Professor, Head of Department of Information and Electronic Service, Volga Region State University of Service (Togliatti). E-mail: volovach.vi@mail.ru


In the article the estimation of error of measurement parameters of the useful signal along with the non-Gaussian multiplicative noise is considered. The problem of the study is defined and it shows that the useful signal is influenced by not only additive noise but also by multiplicative noise. Moreover, additive and multiplicative noise can have both Gaussian and non-Gaussian density of probability distribution. This article estimates the impact of non-Gaussian multiplicative noise on the useful signal. To estimate the information parameters of the signal we use the method of maximum a posteriori probability density and lower bounds of Rao-Cramer inequality. It is shown that in general case the impact of multiplicative noise on the useful signal leads to shift of estimates of measured parameters. The easiest way to determine the shift is when it is not dependent on the estimated parameter, which allows us to get an unbiased estimate of the information parameter. It is shown that with known distribution parameters of the multiplicative noise we can determine the shift value and get to an unbiased estimate. This approach is used in the article. We considered the estimation of measurement accuracy of vector information parameter as a more informative case of estimating the parameters of the useful signal. We considered the change in frequency, derivative of frequency and phase of the useful signal that carry information about the parameters of movement of located object as vector information parameter. Estimation of measurement accuracy of vector information parameter is carried out in multiplicative noise. This noise has both independent and correlated nature. We obtained the calculated ratios for estimating the frequency, the derived frequency and phase of the useful signal for evaluation in different conditions, in particular, during motion of the detected object with a constant velocity, with known initial phase of the useful signal, for motionless detected object. It is shown that to increase the accuracy of measurement of information parameters of the useful signal it is necessary to consider the multiplicative noise that influences the signal. It can be implemented by creating a special channel for estimating multiplicative noise. As a result, it is shown that in general case multiplicative noise leads to a shift of estimated parameters of the information signal, and the bigger is shift value, the worse is measurement accuracy. It is shown that the error of measurement of information parameters of the useful signal can be significantly reduced by accounting for Fisher variance information on modulating noise.
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