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An adaptive least mean M-estimate algorithm for censored regression (CR-LMM) is presented for the robust parameter estimation of the censored regression system. To correct the bias produced by censored observation, the estimated error derived from the probit regression model is employed to construct an M-estimate cost function. It can expel the adverse impact of the impulsive noise and is solved by the unconstrained optimization method. Furthermore, the robust variable step-size (VSS) strategy, which is also predicted on the robust cost function, is also utilized to improve the convergence performance of the proposed CR-LMM algorithm, i.e., convergence speed and steady-state mean square deviation. The condition which guarantees the CR-LMM algorithm stability is obtained by analyzing the convergence in the mean and mean-square sense, and the theoretical steady-state result is also derived. Computer simulations in system identification scenarios are carried out to demonstrate that the proposed algorithms are superior to the existing algorithms in the impulsive environment with different background noise and the theoretical results are verified. [ABSTRACT FROM AUTHOR]

Due to its low computational burden, the affine-projection-like (APL) adaptive filtering algorithm has been extensively studied for colored signal input. Recently, a robust APL algorithm was designed by adopting the M-estimate cost function in impulsive noise environment; however, its convergence rate is very slow for sparse system identification. This paper proposed a proportionate APL M-estimate (PAPLM) algorithm, which is derived by using the proportionate matrix to heighten the convergence rate. To maintain good steady-state performance of the PAPLM algorithm, a time-varying parameter PAPLM (TV-PAPLM) algorithm is proposed, which uses a modified exponential function to adjust the time-varying parameter according to the ratio of the mean square score function to the system noise variance. Moreover, the steady-state excess mean-square error performance of PAPLM algorithm is analyzed and obtained in detail. Simulation results reveal that the proposed PAPLM and TV-PAPLM algorithms achieve fast convergence rate and good steady-state performance in sparse system identification. [ABSTRACT FROM AUTHOR]

We consider the DOA estimation problem by using adaptive nulling antenna technology and bias-compensated adaptive filtering framework. The adaptive nulling antenna array consists of one reference antenna element and multiple auxiliary antenna elements, which forms nulls in certain directions. By defining the reciprocal of array pattern as the spatial spectrum, the DOA estimation problem is considered as the peak searching for it. In this paper, we present an efficient bias-compensated adaptive filtering algorithm for DOA estimation based on the adaptive nulling array. First of all, a new noise-free mean square error (NF-MSE) cost function associated with the adaptive nulling array is provided. Secondly, the proposed algorithm, called variable step-size bias-compensated least mean square (VSS-BC-LMS) algorithm, can be derived by minimizing the NF-MSE. Due to the bias compensation, the bias of the estimated weight vector caused by noises is canceled. More importantly, in order to resist the unsatisfactory DOA estimation performance when using the fixed step-size, a variable step size scheme is introduced. And then, its mean stability, steady state mean square performance and computational complexity are discussed. Additionally, we also explore a noise variance estimation method for calculating the bias term. Simulation results indicate that the proposed algorithm achieves an improved DOA estimation performance compared with other adaptive methods. [ABSTRACT FROM AUTHOR]

Highlights • Phase error based Widely Linear LMK Algorithm is proposed for Frequency estimation. • It uses best features like widely linear modelling, phase error and robust cost function. • It achieves enhanced frequency estimation performance for several critical cases. • Retains the inherent simplicity of the gradient descent based algorithms. Abstract In this paper, an augmented (widely linear) complex Least Mean Kurtosis (WL-LMK) algorithm that uses the negated kurtosis of the phase angle error instead of the conventional magnitude error is proposed for robust frequency estimation of three-phase power systems. The motivation of the proposed method is based on two underlying facts. First, it is primarily the phase rather than the amplitude that conveys useful information in frequency estimation. Second, the negated kurtosis based cost function is computationally efficient and most celebrated in applications where the noise contamination degrades the performance of the classical adaptive filtering algorithms. To further achieve robust frequency estimation for both balanced and unbalanced conditions, the proposed method makes use of the full second-order information within the complex-valued system voltage through the Clarke's αβ transformation and the concept of augmented complex statistics and widely linear modelling. The estimation performance of the proposed method is evaluated for several critical cases that often arise in power system. Simulation results of both synthetic cases and experimental studies show that the proposed method achieves more accurate frequency estimates than its developed widely linear counterparts in the literature. [ABSTRACT FROM AUTHOR]

The standard adaptive filtering algorithm with a single error norm exhibits slow convergence rate and poor noise reduction performance under specific environments. To overcome this drawback, a filtered-x generalized mixed norm (FXGMN) algorithm for active noise control (ANC) system is proposed. The FXGMN algorithm is developed by using a convex mixture of l p and l q norms as the cost function that it can be viewed as a generalized version of the most existing adaptive filtering algorithms, and it will reduce to a specific algorithm by choosing certain parameters. Especially, it can be used to solve the ANC under Gaussian and non-Gaussian noise environments (including impulsive noise with symmetric α -stable ( S α S ) distribution). To further enhance the algorithm performance, namely convergence speed and noise reduction performance, a convex combination of the FXGMN algorithm (C-FXGMN) is presented. Moreover, the computational complexity of the proposed algorithms is analyzed, and a stability condition for the proposed algorithms is provided. Simulation results show that the proposed FXGMN and C-FXGMN algorithms can achieve better convergence speed and higher noise reduction as compared to other existing algorithms under various noise input conditions, and the C-FXGMN algorithm outperforms the FXGMN. [ABSTRACT FROM AUTHOR]

This paper presents a new normalized least mean square (NLMS) algorithm for sparse system identification where the input signal is corrupted by white measurement noise. The proposed algorithm, which is called bias-compensated zero attracting NLMS (BC-ZA-NLMS) algorithm, introduces the bias-compensation vector to get rid of the bias resulting from noisy input and introduces an l 1 -norm penalty in the cost function of the NLMS algorithm to make full use of the special property of the sparse system. In addition, to address the time variant sparsity, the bias-compensated reweight ZA-NLMS (BC-RZA-NLMS)) algorithm is also proposed, where the l 1 -norm penalty in the cost function of BC-ZA-NLMS algorithm is replaced by a log-sum function. Owing to the zero attractors in update equation, the proposed algorithms are superior to the conventional NLMS and bias-compensated NLMS (BC-NLMS) algorithms in the application of identifying the sparse system. A transient analysis of the proposed algorithms is also derived, which is able to accurately predict the behaviors of proposed algorithms. In addition, a stability analysis is introduced. Monte Carlo (MC) simulations are conducted to demonstrate the advantage of the proposed algorithms and to validate the theoretical results. [ABSTRACT FROM AUTHOR]

The Unscented Kalman filter (UKF) based on maximum correntropy criterion (MCC) is robust to heavy-tailed non-Gaussian noise. However, the approximate linear measurement equation obtained by statistical linearization technique may be not accurate enough since it only uses prior information. In this paper, a robust stable iterative maximum correntropy criterion UKF (RS-IMCC-UKF) is proposed by using nonlinear measurement function directly and numerical stability methods. Different from the existing UKF algorithms, we only need to perform one-time unscented transformation in each filtering cycle, reducing the execution time of algorithm. Then a nonlinear enhancement model is constructed to handle predictions and observations simultaneously, which will be included in the cost function of robust MCC. In the process of iterative solution, thanks to the latest iteration values which are used to update the measurement information, RS-IMCC-UKF has more accurate results compared with traditional filters. In order to avoid non-positive definite characteristic in covariance matrix and the inverse operation in ill-conditioned matrix, the hyperbolic QR decomposition and Moore–Penrose pseudo-inversion are introduced to improve the numerical stability of the algorithm. Finally, a target tracking is modeled to verify the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

We propose an affine projection M-estimate subband adaptive filter (APM-SAF), which is characterized by its robustness against impulsive noise. Instead of the conventional mean square error (MSE) function, the proposed APM-SAF employs a robust M-estimator-based cost function which is able to suppress the effect of impulsive noise on the filter weight update. Furthermore, to improve the performance of the APM-SAF for sparse impulse response, an improved proportionate APM-SAF (IP-APM-SAF) is proposed by exploiting the sparsity of the impulse response. Simulations in an acoustic echo cancellation (AEC) context show that the APM-SAF performs better than the conventional NSAFs and SSAFs. The improvement in convergence rate is also demonstrated for the IP-APM-SAF. [ABSTRACT FROM AUTHOR]

To ameliorate the performance of the normalized least mean square (NLMS) algorithm applied in identifying block-sparse system, a novel block-sparse proportionate NLMS (BS-PNLMS) algorithm based on the mixed l 2,0 norm is presented in this paper. The cost function of proposed algorithm is obtained by introducing the approximated mixed l 2,0 norm penalty in the cost function of BS-PNLMS algorithm, which is equivalent to attaching the mixed l 2,0 norm zero attraction to the update equation. The proposed algorithm is named as the l 2,0 -BS-PNLMS algorithm. Futhermore, a variable step-size l 2,0 -BS-PNLMS is developed to further improve the performance of the l 2,0 -BS-PNLMS. Simulation results demonstrate the advantages of proposed algorithms. [ABSTRACT FROM AUTHOR]