Adaptive Estimation of OEMA Model via Variable Regularized Recursive Least Squares Method

Abstract

In this paper, we present a recursive least squares method with variable regularization which is in order to track time varying parameters extended by an exponential forgetting factor (EF-VR-RLS). Regularization of a direction matrix is achieved by adding restricting conditions into the cost function. By definition of the standard recursive least-squares method (RLS) implies that the method removes the ambiguity of the cost function using a constant regularization. The RLS method is therefore an exact formulation of multi-criteria problem. In this case regularization element is the initial value of the direction matrix, which penalizes Euclidean distance between the estimated parameters and their initial values. At the proposed approach the cost function is extended by the penalization of weighted difference between the investigated vector of parameters and its currently available estimate. By introducing the element of variable regularization is possible to better effect the rate of convergence and the actual position of equilibrium than by employing of the standard RLS method. Main emphasis is placed on the efficiency of numerical solution method, in order to implement into the microcontroller.