Parametric Identification Under Incomplete a Priori Information

The paper considers an algorithm of parametric identification under incomplete a priori information about a linear dynamic object. In article, the parametric identification problem is reduced to the mathematical model determination of the control object in the form of differential equation. In practice, only noisy input and output signals of the control object are available for measurement. Therefore, only the noisy input and output signals of the object as a priori information for solving the problem of parametric identification are used, and there is no information about the derivatives of these signals. An approach to solve the problem of numerical differentiation of noisy signals by using the integration by parts to form a system of linear algebraic equations is proposed. In this approach some analytically given function is differentiated instead of numerical differentiation of noisy signals. This article describes the functions matching the necessary requirements for applying the proposed approach in parametric identification problems. Simulation results presented in the article confirm a good noise immunity of the algorithm using the proposed approach in parametric identification problems.