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Quasilikelihood estimations the waveform signal appearance and disappearance moments

Keywords:

A.P. Trifonov – Dr. Sc. (Eng.), Honored Scientist of RF, Professor, Head of Department of Radiophysics, Voronezh State University. E-mail: trifonov@phys.vsu.ru Yu.E. Korchagin – Dr. Sc. (Phys.-Math.), Associate Professor, Department of Radiophysics, Voronezh State University. E-mail: korchagin@phys.vsu.ru


In this paper we considered the synthesis and the analysis of the estimation algorithm of the moments of appearance and disappearance of a signal with a priori unknown form. In particular, we studied the quasi-likelihood estimation algorithm where the reference signal of some expected form are used instead of the unknown received signal form, and, in general, the forms of reference and received signals can be different. We also introduced the estimation algorithm of the moment of disappearance when the moment of signal appearance is unknown. Here instead of the unknown moment of signal appearance its some expected value from area of possible values was used. Analyzing the synthesized algorithms by the local Markov approximation method, we found the asymptotically exact (with increasing a signal-to-noise ratio) expressions for estimates statistics, such as probability densities, biases and variances. The obtained expressions allow us to study the influence of prior ignorance of the signal form on accuracy of estimates of the moments of appearance and dis-appearance. As an example, we considered the estimates of the moments of appearance and disappearance of a rectangular pulse with beveled top when a rectangular pulse with flat top is used as a reference signal. We shown that varying the reference signal amplitude we can increase the estimate accuracy of one parameter (for example, the moment of appearance) while deteriorating the estimate accuracy of another parameter (the moment of disappearance). We drawn conclusions by the obtained results.
References:

 

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