Variable Regularized Square Root Recursive Least Square Method

In this paper, we develop the variable regularized square root recursive least square method which is in order to track time-varying parameters extended by an exponential forgetting factor (EF-VR-SRRLS). The proposed approach is arisen from the exact recursification of the original batch mode method solving the restricted quadratic problem. The meanings of the restricted conditions lie in the removal of ambiguity of the cost function and thus to ensure the regularity of the direction matrix. In the examined approach, the regularization terms are the matrix weighting the difference between the next parameter estimate and the initial parameter estimate and the time-varying matrix weighting the distance of the parameter estimate from its currently available estimate. Because the incorporation of the Potter's square root technique requires the actualization of direction matrix using the data dyads only, an effective form of implementation based on the updating quantity of the rank one was performed. The performance of the suggested algorithm combining variable regularization and the square root filtering technique is verified via simulation studies.