On Linear Algebraic System Forming in Parametric Identification Problems

The paper is concerned with parametric identification algorithm for a linear dynamic control object when a priori information about the object is no fully available. In this paper the parametric identification of object is come to estimation of the object mathematical model in the form of n-th order differential equation.Inputs and outputs of object distorted by interference are a priori information for parametric identification problems, while values of these signals derivatives are not available.Estimation of differential equation coefficients is coming to solving the linear algebraic system. In this paper we propose method of forming system of linear algebraic equations using the approach to replace numerical differentiation of the measured signals by differentiating some analytically specified functions. This method is based on integral operators and integration by parts. Functions using in process of forming system of equations satisfy requirements for application in parametric identification problems. It is proposed to use least squares method for solve the system.The article presents simulation results the algorithm study for accuracy and noise immunity depending on the noise frequency properties distorted the output signal.