ADAPTIVE GUARANTEED ESTIMATION OF A CONSTANT SIGNAL UNDER UNCERTAINTY OF MEASUREMENT ERRORS

Abstract

ditions, the values of measurement errors , 1, , k v k N  are unknown (uncontrolled). A priori information about measurement errors is formalized by choosing a hypothesis about the properties of errors k v . The following hypotheses are traditional. 1. The measurement errors k v are random and given by probability density function with known parameters. 2. The measurement errors k v are uncertain quantities: k v V  , where V is a given convex set of their possible values. Acceptance of the hypothesis about the probabilistic nature of measurement errors makes it possible to formulate the problem within the framework of the stochastic approach as the problem of finding the optimal estimate in the mean square sense and to use statistical methods [2]. The most common is the use of the least-squares method (LS) [1, 2], i.e. minimizing a function