V.I. Marchuk, V.V. Voronin, V.I. Sherstobitov

In recent years, increasing attention is paid to the use of digital signal processing. The computer processing system uses a variety of methods of mathematics - mathematical statistics, theory of inverse problems. Using new methods of primary processing of measurement results allow us to consider how to build a measurement and information systems and radar systems capable of solving tasks with limited prior information and the limited set of measurements. In this paper present mathematical basis of the method multiply estimations for 1D signal processing by obtaining a multiply of estimates (method multiply estimates). The mathematical formulation of the problem partition of the unique realization 1D signal into segments of random length with a subsequent estimation of average is present. We consider the limiting case when the estimations for each interval is a simple average. Multiply options for partitioning realization of 1D signal provides a set of estimates of its useful component. Presented analytical proof that when using the method of multiply estimations, mean square error of estimating signal asymptotically approaches zero as the increase number of multiply estimates. Using the method of multiply estimates, we can get an approximation of the desired signal in a limited amount of information with accuracy.