A New Active Noise Control Algorithm That Requires No Secondary Path Identification Based on the SPR Property

Abstract—Active noise control (ANC) has been widely applied in industry to reduce environmental noise and equipment vibra-tions. Most available control algorithms require the identification of the secondary path, which increases the control system com-plexity, contributes to an increased residual noise power, and can even cause the control system to fail if the identified secondary path is not sufficiently close to the actual path. In this paper, based on the geometric analysis and the strict positive real (SPR) property of the filtered-x LMS algorithm, we introduce a new ANC algorithm suitable for single-tone noises as well as some specific narrowband noises that does not require the identification of the secondary path, though its convergence can be very slow in some special cases. We are able to extend the developed ANC algorithm to the case of ac-tive control of broadband noises through our use of a subband im-plementation of the ANC algorithm. Compared to other available control algorithms that do not require secondary path identifica-tion, our developed method is simple to implement, yields good per-formance, and converges quickly. Simulation results confirm the effectiveness of our proposed algorithm. Index Terms—Active noise control, adaptive filters, filtered-x LMS, strictly positive real. I