Adjoint EKF learning in recurrent neural networks for nonlinear active noise control Riyanto T. Bambang * School of Electrical Engineering and Informatics, Institute Technology of Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia Received 26 January 2007; received in revised form 3 October 2007; accepted 21 October 2007 Available online 6 November 2007 Abstract In this paper, active noise control using recurrent neural networks is addressed. A new learning algorithm for recurrent neural networks based on Adjoint Extended Kalman Filter is developed for active noise control. The overall control structure for active noise control is constructed using two recurrent neural networks: the first neural network is used to model secondary path of active noise control while the second one is employed to generate control signal. Real-time experiment of the proposed algorithm using digital signal processor is carried-out to show the effectiveness of the method. # 2007 Elsevier B.V. All rights reserved. Keywords: Recurrent neural networks; Extended Kalman Filter; Adjoint learning algorithm; Active noise control; Nonlinearity; Real-time experiment; DSP 1. Introduction Due to the effectiveness of adaptive filter algorithm and the advancement of digital signal processors, interest in active noise cancellation (ANC) technology has grown rapidly in recent years. Compared to passive cancellation technique using passive absorber, ANC has the advantage of being able to suppress acoustic noise at low frequency with much smaller size, weight, volume and at much lower cost [1,5,6,8]. The design of ANC is based on the principle of destructive interference between the original primary disturbance sound field measured at the location of (possibly more than one) error sensors, and a secondary sound field that is generated by (possibly more than one) control actuators. Typically, microphones and speakers are used as sensors and control actuators, respectively. In ANC systems, a conventional approach is to use FIR filters as adaptive controllers where the filter coefficients are adjusted according to least mean square (LMS) algorithm to minimize errors between output of the filters and the desired response [1,8]. The adaptive controllers can be configured either in feedback or in feedforward fashion. When IIR filter based on LMS algorithm is employed in ANC, the resulting structure/algorithm is referred to as U-Filtered LMS [1,8,10]. LMS filtering is based on steepest descent algorithm that employs instantaneous estimate of gradient of the mean squared error. To account for secondary path effect, a filtered version of LMS, called filtered-X LMS, is commonly used in ANC systems [1,8]. The application of filtered-X LMS requires modeling the secondary path in terms of FIR filters, and utilizes this model to adapt the control FIR filter coefficients. Filtered-X LMS has been widely used because of its simplicity and its relatively low computational load. There is, however, one potential drawback of FX-LMS because it is limited to linear control/filtering problem [1,5]. In other words, the control input signal, as well as the associated measured error signal utilized in the adaptation process, must be linear functions of reference signal utilized by adaptive filter to generate the control signal. Therefore, FX-LMS structure and algorithm perform worse when significant nonlinear phenomena exist along various paths in ANC systems. In ANC systems, nonlinear phenomena is commonly originated from nonlinearity of the acoustic system under control, or nonlinearity in the secondary actuator, particularly when it operates with an input signal having an amplitude close to (or above) saturation, or when it operates in a frequency range close to (or lower than) the minimum operating frequency of the actuator [2]. To account for nonlinear phenomena, nonlinear structure should be employed in active noise control. One such nonlinear structure that is gradually receiving wider acceptance in the field of control and signal processing is artificial neural networks [7,9]. At first sight it would appear that the active control of such systems would not be appropriate, since active www.elsevier.com/locate/asoc Available online at www.sciencedirect.com Applied Soft Computing 8 (2008) 1498–1504 * Tel.: +62 22 2500960; fax: +62 22 2534217. E-mail address: briyanto@lskk.ee.itb.ac.id. 1568-4946/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2007.10.017