Due to the good tracking behaviour of the LMS adaptive filter in a noisy environment, the FX-LMS algorithm is proposed in the literature as a method of active noise control, ANC. But each of the LMS and RLS algorithms have their own advantages and disadvantages. In this paper, a new approach based on a mixture of the RLS and LMS algorithms, RLMS, is presented. The optimum weights of the mixture are derived and it is proved that the MMSE of the proposed system is reduced compared to those of the RLS and LMS algorithms. Then, the proposed RLMS algorithm is employed for active noise cancellation to form the FX-RLMS algorithm, in a duct. Experimental results show better performance of the RLMS algorithm compared to both the RLS and LMS algorithms of convergence and tracking behaviour in the system identification problem and noisy chirp tracking. The FX-RLMS algorithm shows better results in active noise cancellation compared to the FX-LMS algorithm.

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