## 1 Introduction  
Active noise control (ANC) is a method of attenuating unwanted noise. Since the development of digital signal processing (DSP) technology and adaptive filter theory, various ANC technologies have been widely used in the industrial field, and the filtered-x least mean square (FxLMS) is the most representative one [1]. However, this algorithm is based on the minimization theory of the mean square error, which may become unstable when exposed to the impulsive interference. Impulsive interference is usually manifested by power line communication noise, atmospheric noise and mechanical noise [2; 3]. As impulsive noise is non-Gaussian, the signals with outliers that are produced can be described as symmetric \(\alpha\) stable (SaS) distributions [4]. More importantly, the process of burst interference cannot be described by limited second order moments. To solve these problems, many algorithms have been proposed, where the algorithms using off-line \(\alpha\)-estimation are applied earliest [5; 6; 7]. However, the parameter \(\alpha\) is variable in the natural process, which may lead these methods to fail to converge. Therefore, M-estimate functions are developed for active impulsive noise control in [8; 9; 10; 11]. These functions are non-linear transformation methods with different thresholds that are calculated by using prior information. In this circumstance, the methods based on the combination of normalized FxLMS (FxNLMS) algorithm and parameter selection using prior pieces of knowledge have also been proposed [12; 13]. Unfortunately, their constant thresholds and parameters may limit the convergence rate of adaptive filters and degrade the performance of the algorithms. For example, in [8], if the absolute value of the \(n\)-th iteration of the error signal is less than a certain constant, the M-estimate function restrains the updating rate of the FxLogLMS algorithm in the non-impulsive noise environment. Consequently, the FxlogLMS could only works well in strong impulsive noise environment. To enhance the effectiveness of active impulse noise control using M-estimate techniques, some algorithms based on on-line detection without certain thresholds are proposed for the variable-\(\alpha\) impulsive noise environment. In [14], [PERSON] et al. proposed an on-line estimation method for ANC systems to get better attenuation level in variable-\(\alpha\) impulsive noise environments. Nevertheless, the replacement of outliers remains the principle strategy of it for overcoming the interference of impulsive noise, which prevents the tracking process of adaptive filters. A recent method proposed by [PERSON] and [PERSON] using maximum correntropy with adaptive kernel size is demonstrated to perform better than conventional methods on noise attenuation [15]. For this algorithm, the information entropy is used to overcome the influence of impulsive noise. In practical applications, the computational complexity of it is the main barrier to achieve real time noise attenuation. In fact, these mentioned methods are applied in an absolutely impulsive noise environment, which neglects the fact that most ANC systems are working in Gaussian noise with variable-\(\alpha\) impulsive interference environment. To solve these mentioned problems, in this paper, a novel adaptive state detector based post-filtering active control algorithm is proposed. The proposed algorithm uses information entropy method to change the updating of the weight vector, which enhances the tracking abilities compared with conventional method in [13]. By applying the improved version of the optimal detection method of image processing in [16; 17], the proposed method is also able to select parameters to achieve robust or fast-tracking automatically for impulsive interference and Gaussian noise environment. Furthermore, the computational load of the detection method is easy to control because its complexities are determined independently and not related to the length of the weight vector. The rest of this paper is organized as follows.