Adaptive Bilinear Filters Research Articles

Diagonal-structure adaptive bilinear filters for multichannel active noise control of nonlinear noise processes

To accommodate multichannel nonlinear active noise control, the second-order Volterra filtered-x LMS (VFXLMS) and filtered-s least mean square (FSLMS) algorithms are usually applied in practical noise control systems. These two algorithms are effective in dealing with polynomial nonlinearity. Recently, a simplified bilinear leaky filtered-x least mean square (SBLFXLMS) algorithm is proposed based on a bilinear model in order to further reduce the computational load but it may have performance degradation. In this paper, we propose a novel nonlinear adaptive algorithm named as the diagonal-structure bilinear filtered-x least mean square (DBFXLMS) algorithm for multichannel nonlinear active noise control. In addition, the developed multichannel DBFXLMS algorithm is equipped with a stability control scheme to maintain a stable condition of the adaptive bilinear filter during the adaptive process. The performance of the proposed algorithm is validated through computer simulations and the computational complexity of the developed algorithm is analyzed. Computer simulations demonstrate that the proposed method has an improvement in terms of control performance in comparison with the conventional first-order FSLMS, second-order VFXLMS, and SBLFXLMS algorithms.

Reweighted adaptive bilinear filters for an active noise control system with a nonlinear secondary path

The nonlinearities of active control systems are the main factors that deteriorate noise-reduction performance. To improve the performance of a control system with a nonlinear secondary path, a filtered-x least mean square algorithm using reweighted bilinear filters is proposed in this paper and a generalized filter to model different nonlinear secondary paths is explored. Within the controller of an adaptive feedforward control system, the proposed algorithm uses trigonometric expansions to achieve high-order nonlinearities and combines the cross terms between the controller output, sine and cosine functions of the input with the reference signal. As a result, satisfactory control performance can be achieved with a shorter memory length of the controller compared to certain control algorithms. It is also found that the introduction of a reweighting factor in the weight-updating process can effectively reduce the interference produced by the small coefficients of the control filter and accelerate the convergence rate. The computational complexity of the proposed algorithm is analyzed and its control performance is verified through simulation experiments with different nonlinear secondary paths and input noises. Simulation results show that the proposed algorithm outperforms four other widely accepted algorithms in terms of convergence rate and residual error.

Comparative Study of CAMSHIFT and RANSAC Methods for Face and Eye Tracking in Real-Time Video

Real-Time Facial and eye tracking is critical in applications like military surveillance, pervasive computing, Human Computer Interaction etc. In this work, face and eye tracking are implemented by using two well-known methods, CAMSHIFT and RANSAC. In our first approach, a frontal face detector is run on each frame of the video and the Viola-Jones face detector is used to detect the faces. CAMSHIFT Algorithm is used in the real- time tracking along with Haar-Like features that are used to localize and track eyes. In our second approach, the face is detected using Viola-Jones, whereas RANSAC is used to match the content of the subsequent frames. Adaptive Bilinear Filter is used to enhance quality of the input video. Then, we run the Viola-Jones face detector on each frame and apply both the algorithms. Finally, we use Kalman filter upon CAMSHIFT and RANSAC and compare with the preceding experiments. The comparisons are made for different real-time videos under heterogeneous environments through proposed performance measures, to identify the best-suited method for a given scenario.

On implementation of adaptive bilinear filters for nonlinear active noise control

In this technical note, the simplified diagonal-structure bilinear filtered-X least mean square (SDBFXLMS) and channel-reduced diagonal-structure bilinear filtered-X least mean square (CRDBFXLMS) algorithms are proposed. Computational complexity for each proposed algorithm is analyzed to show the significant computational reduction in comparison with the diagonal-structure bilinear FXLMS (DBFXLMS) algorithm. For L=15 (memory length of the bilinear filter), P=2 (the corresponding number of the diagonal channels for the SDBFXLMS algorithm is L+2P=19 and the corresponding number of the diagonal channels for the CRDBFXLMS algorithm is 2P=4), and M=64 (memory length of the secondary path estimate), the SDBFXLMS algorithm achieves 45% and 40% reduction of multiplications and additions, respectively, while the CRDBFXLMS algorithm acquires 78% reduction of multiplications and 76% reduction of additions. Computer simulations validate the satisfied control performances of the proposed algorithms.

A novel adaptive bilinear filter based on pipelined architecture

To overcome the computational complexity of the Volterra filter, a novel adaptive joint process filter using pipelined bilinear polynomial architecture (JPBPF) is proposed in this paper. The proposed architecture consists of two subsections: nonlinear subsection performing a nonlinear mapping from the input space to an intermediate space by the bilinear polynomial filter (BPF), and a linear filter performing a linear mapping from the intermediate space to the output space. The corresponding adaptive algorithms are deduced for the nonlinear subsection and linear filter subsection, respectively. To evaluate the performance of the JPBPF, a series of simulations are presented including nonlinear system identification, predicting of speech signals and nonlinear channel equalization. Compared with the conventional second-order Volterra (SOV) filter and BPF, the JPBPF exhibits a slightly better convergence performance in terms of convergence speed and steady-state error. Moreover, since those modules of a JPBPF can be performed simultaneously in a pipelined parallelism fashion, this would lead to a significant improvement in its total computational efficiency.

Nonlinear adaptive bilinear filters for active noise control systems

The reference and error channels of active noise control (ANC) systems may be saturated in real-world applications if the noise level exceeds the dynamic range of the electronic devices. This nonlinear saturation degrades the performance of ANC systems that use linear adaptive filters with the filtered-X least-mean-square (FXLMS) algorithm. This paper derives a bilinear FXLMS algorithm for nonlinear adaptive filters to solve the problems of signal saturation and other nonlinear distortions that occur in ANC systems used for practical applications. The performance of this bilinear adaptive filter is evaluated in terms of convergence speed, residual noise in steady state, and the computational complexity for different filter lengths. Computer simulations verify that the nonlinear adaptive filter with the associated bilinear FXLMS algorithm is more effective in reducing saturation effects in ANC systems than a linear filter and a nonlinear Volterra filter with the FXLMS algorithm.

A stability result for RLS adaptive bilinear filters

The article considers recursive least squares (RLS) adaptive nonlinear filtering using bilinear system models. It is shown that the extended RLS adaptive bilinear filter, as well as the equation-error RLS adaptive bilinear filter, are guaranteed to be stable in the sense that the time average of the squared estimation error is bounded whenever the underlying process that generates the input signals is stable in the same sense.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Adaptive bilinear digital filters

How adaptive algorithms can be applied to low-sensitivity digital filter structures is shown. The considered structure is derived by a bilinear transformation of an analog doubly resistively terminated ladder filter. A fifth-order IIR low-pass filter is used as example. The adaptive algorithm is derived using standard stochastic approximation arguments and both gradient and Newton updating equations are presented. The adaptive bilinear filter is used in system identification simulations and compared to a direct-form IIR filter. It is demonstrated that the adaptive bilinear filter, although not unconditionally stable, has excellent stability properties. It is also shown that the adaptive algorithm can be used as a tool for synthesis of pseudopassive and hence numerically robust fixed filters. The adaptive algorithm is used to minimize a cost function chosen as a weighted difference between the desired transfer function and the adaptive transfer function.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>