RLS solution for the adaptive recursive filter

The recursive least square (RLS) algorithm is insensitive to the dispersions of the correlation matrix. Consequently, the usage of the RLS algorithm to update the adaptive recursive filter coefficients are attractive for the system modeling and identification fields. In this paper, an error function RLS (EFRLS) algorithm is derived for the adaptive recursive filter. Furthermore, a scaled version of the EFRLS algorithm is proposed where the computation complexity is significantly reduced. The scaled EFRLS algorithm can be realized in real time using the available digital signal processors. The convergence to the optimal solution of both the EFRLS algorithm and its scaled version is ensured while the general RLS algorithm fails to converge to the optimal solution for the multimodal performance criterion.