Reconstruction of observation from distorted data for the optimal dynamic measurement problem

The theory of optimal dynamic measurements is based on the minimization of the difference between the values of virtual observation, i.e. an observation obtained with the help of a computational model, and experimental data, which are usually distorted by some noise. The article describes a mathematical model of optimal dynamic measurement in the presence of various types of interference. In addition, the article proposes an algorithm to reconstruct the values of observation from the values obtained during the experiment, which are assumed to be distorted by some random influences. It is assumed that the experimental data are influenced by "white noise", which is understood as a derivative of Nelson-Gliklich from the Wiener process. In order to reconstruct observation values, we use a priori information about the form of the function describing the observation values. The reconstruction procedure consists of two stages. At the first stage, we formulate the criterion for determining the position of the extreme point of the signal using a special type of statistics. At the second stage, we describe the procedure to reconstruct the signal values on the basis of information about the position of the extreme point and the shape of the signal convexity.