Development of the theory of optimal dynamic measurement

The paper presents an overview of the results of both an analytical study of optimal dynamic measurement problems and results in the development of algorithms for numerical methods for solving problems of the theory of optimal dynamic measurements. The main position of the theory of optimal dynamic measurements is the modelling of the desired input signal as a solution to the optimal control problem with minimization of the penalty functional, in which the discrepancy between the output simulated and observed signals is estimated. This theory emerged as a new approach for restoring dynamically distorted signals. The mathematical model of a complex measuring device is constructed as a Leontief-type system, the initial state of which reflects the Showalter–Sidorov condition. Initially, the mathematical model took into account only the inertia of the measuring device, later the mathematical model began to take into account the resonances that arise in the measuring device and the degradation of the device over time. The latest results take into account random noise and several approaches were developed here: the first approach is based on the Nelson–Gliklikh derivative, the second one is based on the purification of the observed signal using the Pytiev–Chulichkov method, the third one uses the purification of the observed signal by digital filters, for example, Savitsky–Golay or one-dimensional Kalman filter.