Method for synthesizing efficient estimates of signal parameters using functions from complete sufficient statistics

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Abstract

A method for synthesizing efficient estimates of parameters of a random process whose distribution of samples has complete sufficient statistics is proposed. The method is based on the representation of the estimated parameters of the process in the form of a solution to the system of equations for mathematical expectations of functions derived from complete sufficient statistics, selected in such a way that the system of equations was solvable with respect to the estimated parameters. This solution is then replaced by the aforementioned functions in order to obtain the final estimate. The conditions under which the obtained estimates will be efficient are provided. Examples of parameter estimation for sample distributions from a uniform distribution and an additive mixture of Gaussian noise and a sequence of rectangular pulses with unknown amplitudes are presented, and their efficiency is demonstrated.

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А. G. Vostretsov

Novosibirsk State Technical University; Chinakal Institute of Mining of the Siberian Branch of the RAS

Author for correspondence.
Email: vostreczov@corp.nstu.ru
Russian Federation, 20 K. Marx Ave., Novosibirsk, 630073; 54, Krasny Ave., Novosibirsk, 630091

S. G. Filatova

Novosibirsk State Technical University; Federal Institute of Industrial Property

Email: vostreczov@corp.nstu.ru
Russian Federation, 20 K. Marx Ave., Novosibirsk, 630073; 30-1 Berezhkovskaya nab., Moscow, 125993

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