While the filtered-x normalized least mean square (FxNLMS) algorithm is widely applied due to its simple structure and easy implementation for active noise control system, it faces two critical limitations: the fixed step-size causes a trade-off between convergence rate and steady-state residual error, and its performance deteriorates significantly in impulsive noise environments. To address the step-size constraint issue, we propose the switched step-size FxNLMS (SSS-FxNLMS) algorithm. Specifically, we derive the mean-square deviation (MSD) trend of the FxNLMS algorithm, and then by comparing the MSD trends corresponding to different step-sizes, the optimal step-size for each iteration is selected. Furthermore, to enhance the algorithm’s robustness in impulsive noise scenarios, we integrate a robust strategy into the SSS-FxNLMS algorithm, resulting in a robust variant of it. The effectiveness and superiority of the proposed algorithms has been confirmed through computer simulations in different noise scenarios.

In non-Gaussian noise environments, the affine projection generalized maximum correntropy (APGMC) algorithm demonstrates strong robustness. To suppress error accumulation, this paper introduces the linear constraint strategy into APGMC and proposes a novel constrained affine projection generalized maximum correntropy (CAP-GMC) algorithm. Furthermore, to solve the problem of noisy input data, a constrained affine projection generalized maximum total correlation correntropy (CAP-GMTC) algorithm is proposed by combining the total least squares framework with the generalized Gaussian density function. For CAP-GMC and CAP-GMTC, we conduct the convergence analyses from the perspective of mean-square and mean senses to obtain their corresponding step-size bounds. In comparison with existing algorithms, several simulation results verify that the proposed CAP-GMC and CAP-GMTC achieve superior filtering performance in impulsive noise environments.

The time-space (TS) traffic diagram serves as a crucial tool for characterizing the dynamic evolution of traffic flow, with its resolution directly influencing the effectiveness of traffic theory research and engineering applications. However, constrained by monitoring precision and sampling frequency, existing TS traffic diagrams commonly suffer from low resolution. To address this issue, this paper proposes a refinement method for TS traffic diagrams based on neighborhood-adaptive linear regression. Introducing the concept of neighborhood embedding into TS diagram refinement, the method leverages local pattern similarity in TS diagrams, adaptively identifies neighborhoods similar to target cells, and fits the low-to-high resolution mapping within these neighborhoods for refinement. It avoids the over-smoothing tendency of the traditional global linear model, allows the capture of unique traffic wave propagation and congestion evolution characteristics, and outperforms the traditional neighborhood embedding method in terms of local information utilization to achieve target cell refinement. Validation on two real datasets across multiple scales and upscaling factors shows that, compared to benchmark methods, the proposed method achieves improvements of 9.16%, 8.16%, 1.86%, 3.89%, and 5.83% in metrics including Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Congestion Matrix Jaccard Similarity Coefficient (CMJS), Structural Similarity Index Measure (SSIM), and Gradient Magnitude Similarity Deviation (GMSD), respectively. Furthermore, the proposed method exhibits strong generalization and robustness in cross-day and cross-scenario validations. In summary, requiring only a minimal amount of paired high- and low-resolution training data, the proposed method features a concise formulation, providing a foundation for the low-cost, fine-grained refinement of low-sampling-rate traffic data.

Subspace tracking is increasingly important in array signal processing, especially for dynamic direction-of-arrival (DoA) estimation. Among existing methods, gradient descent subspace tracking (GDST) is particularly attractive due to its low computational complexity. However, it is highly sensitive to impulsive noise, and its constant step-size causes a trade-off between convergence speed and steady-state accuracy. To overcome these limitations, the generalized correntropy criterion (GCC) is effectively incorporated into GDST, resulting in the GCC-GDST algorithm. In addition, a step-size regulation (SSR) mechanism is further introduced, leading to the SSR-GCC-GDST algorithm. Simulation results for DoA estimation clearly demonstrate its superiority under $\alpha$-stable impulsive noise.

This paper proposes a robust low-complexity adaptive filtering algorithm for identifying impulse responses in acoustic echo cancellation within practical acoustic environments. Under a low-rank model framework of the filter coefficient vector, a Cauchy estimate function is employed to define a set of robust cost functions, from which the adaptive algorithm is established with a dichotomous coordinate descent scheme. The computational efficiency of the proposed algorithm is significantly improved, and its effectiveness is validated through simulations.

In recent years, robust linearly constrained adaptive filtering has gained increasing attention, and the constrained generalized maximum correntropy (CGMC) works well in some impulsive noise situations. However, when the input signal contains some noise, the performance of CGMC is greatly affected. To solve this problem, we first propose a fixed-point constrained maximum total generalized correntropy (FP-CMTGC) algorithm based on the errors-in-variables (EIV) model. According to the Banach fixed-point theorem, we have conducted the convergence analysis for FP-CMTGC. To improve its performance in practice, we further apply the gradient and recursive methods to FP-CMTGC, yielding two kinds of online versions, i.e., the CMTGC and recursive CMTGC (RCMTGC) algorithms. Moreover, combining the weighting method and the leading dichotomous coordinate descent (DCD) strategy, we have proposed a low-complexity version of RCTGMC, namely DCD-RCTGMC. In addition, we derive the equivalence analysis between DCD-RCTGMC and the original RCTGMC. Finally, the validity of the convergence and the superiority of the proposed algorithms are verified by several simulations.

While the filtered-x normalized least mean square (FxNLMS) algorithm is widely applied due to its simple structure and easy implementation for active noise control system, it faces two critical limitations: the fixed step-size causes a trade-off between convergence rate and steady-state residual error, and its performance deteriorates significantly in impulsive noise environments. To address the step-size constraint issue, we propose the switched FxNLMS (SSS-FxNLMS) algorithm. Specifically, we derive the deviation (MSD) trend of the FxNLMS algorithm, and then by comparing the MSD trends corresponding to different , the optimal step-size for each iteration is selected. Furthermore, to enhance the algorithm's robustness in impulsive noise scenarios, we integrate a robust strategy into the SSS-FxNLMS algorithm, resulting in a robust variant of it. The effectiveness and superiority of the proposed algorithms has been confirmed through computer simulations in different noise scenarios.

Thanks to the decorrelation capability of the discrete cosine transform (DCT), the DCT-based filtered-x normalized least mean square (DCT-FxNLMS) algorithm has been implemented in feedforward active noise control (ANC) systems. However, its effectiveness is severely degraded in the presence of impulsive noises and constrained by the limitations of the fixed step-size. To address these issues, we first propose a generalized framework of the robust DCT-FxNLMS (R-DCT-FxNLMS) algorithm by introducing the robust correntropy criterion to enhance performance under impulsive noises. We then consider a mean square deviation (MSD) recursion model that characterizes the algorithms behavior and reveals the aforementioned trade-off. Based on the derived MSD recursion, we design a switched step-size (SSS) strategy and propose the SSS-R-DCT-FxNLMS algorithm, which dynamically selects the optimal step-size at each iteration by evaluating the predicted MSD values associated with a predefined set of step-sizes. This SSS-based algorithm enables both fast convergence and low steady-state residual error simultaneously. Simulation results under various noise scenarios validate the superior performance of the proposed algorithms as compared to existing counterparts.

Infrared imaging technology, which detects targets by capturing their infrared radiation, is crucial for applications such as precision guidance and military reconnaissance. However, detecting small infrared targets remains challenging due to their low brightness and lack of texture. Traditional model-driven methods are limited by predefined assumptions, hindering accurate detection. This paper introduces a novel method lever-aging pinwheel-based attribute mining and multi-dimensional attention, specifically designed for targets with a bright centre and darker surroundings. We developed the IRST-TD dataset to facilitate precise identification in complex environments. Our proposed algorithm, comprising a distinctive feature extraction module and a multi-dimensional perception attention module, enhances feature representation and achieves efficient detection. Experimental results on single-frame infrared image datasets demonstrate superior performance with IoU, nIoU, and F1 scores of 0.7852, 0.8209, and 0.8557, respectively.

In this work, to avoid the matrix inverse of the standard AP algorithm, we develop a decorrelation-based AP (DAP) algorithm which has a low computational complexity. For this algorithm, we provide a detailed performance analysis, which reveals that it exists a performance trade-off caused by the constant step-size. To address this trade-off, an optimal DAP algorithm (O-DAP) is derived via minimizing the mean square deviation (MSD) of DAP concerning the gain vectors, which effectively promotes performance improvements in convergence and steady-state stages. Meanwhile, we propose to implement the vectorization update of the autocorrelation matrix of the weight deviation vector and introduce an interval update strategy for it, to reduce complexity of O-DAP. Furthermore, by approximating the autocorrelation matrix as the product of a scalar and an identity matrix, we develop the scalar-based O-DAP (SO-DAP) algorithm with lower complexity. The efficacy of the proposed algorithms is substantiated by simulations in system identification and acoustic/network echo cancellation scenarios, which demonstrate their superiority over the state-of-the-art algorithms.

Numerous adaptive filtering algorithms have been proposed for acoustic echo cancellation. However, whether the performance of the algorithms approaches the optimal performance or if there has been intentionally overstated remains challenging to evaluate. Fortunately, the Cram & eacute;r-Rao Lower Bound (CRLB) provides a theoretical minimum variance for any unbiased estimator under given observational data and statistical models. This paper derives the CRLB of adaptive filtering algorithms for acoustic echo cancellation (AEC), in which the generalized Gaussian distribution (GGD) is utilized to model the Gaussian/non-Gaussian background noises. To accelerate the CRLB calculation process, the recursive resolution of the CRLB is presented by using the matrix inversion lemma, and the computational complexity is also analyzed. The derivation results indicate that CRLB for AEC model depends on the acoustic input (i.e., speaker's voice) and the statistical properties of GGD noise but is unaffected by the channel sparsity. The CRLB derived in this paper can serve as a benchmark to evaluate whether the performance of the adaptive filtering algorithms is optimal and to exclude some adaptive filtering algorithms that deliberately exaggerate their performance.

The discrete cosine transform (DCT) is widely used for its decorrelation capability, which makes the DCT-based least mean square (DCT-LMS) algorithm become attractive. However, the fixed step-size limits its ability to achieve both fast convergence and low steady-state misadjustment. To address this problem, a variable step-size DCT-LMS algorithm is proposed. Unlike conventional variable step-size algorithms, the proposed algorithm assigns an individual time-varying step-size to each filter coefficient through the minimization of the mean-square deviation recursion. The resulting algorithm admits a vectorized implementation with reduced computational complexity, and its convergence behavior is also analyzed. Simulations of system identification and acoustic echo cancellation demonstrate the proposed algorithm's effectiveness.

As a robust adaptive filtering algorithm, the constrained maximum total correntropy (CMTC) algorithm exhibits good filtering performance compared to existing methods, especially when the system has noisy input and output signals. However, CMTC experiences some performance degradation when using a fixed kernel bandwidth. Therefore, we propose the constrained maximum mixture total correntropy (CMMTC) algorithm, which leverages mixture correntropy to enhance flexibility by adjusting the proportion of different kernel bandwidths. In general, increasing kernel bandwidth typically leads to a reduction in the convergence speed of CMTC. Hence, based on a combined strategy, we innovatively introduce two adaptive versions of the CMMTC algorithm by considering a variable mixture coefficient. For the proposed CMMTC algorithm, under some reasonable assumptions, we have derived the mean convergence condition and the theoretical mean-square-deviation expression, which are also verified by simulation results. In comparison with other related algorithms, several experimental results demonstrate that the proposed algorithms can realize superior filtering performance.

The formulation of the exponentially weighted least M-estimate has shown significant promise in addressing acoustic system identification amidst non-Gaussian noise. A common approach to this formulation is the recursive least M-estimate algorithm. However, due to its derivation from nonlinear normal equations, resulting in a slow approximate solution, this algorithm tends to exhibit poor convergence performance. In this paper, we present a Newton-Raphson solution, where the cost function is expanded using the second-order Taylor series to establish the adaptive algorithm. This approach bypasses the nonlinear normal equations, yielding a robust solution that more dynamically reflects changes in the cost function, ultimately leading to improved convergence and tracking performance.

The normalized multichannel frequency-domain least-mean square (NMCFLMS) algorithm is a prominent method for blind identification of multichannel acoustic systems. However, the NMCFLMS algorithm relies on a constant, determined by a block of microphone signals, to define the regularization parameter. This setup makes the algorithm sensitive to variations in speech segments and noise conditions. In this paper, we propose a variable regularization parameter that incorporates key factors, such as signal-to-noise ratio, output signal power, and filter length, to enhance the robustness of the algorithm against additive noise and the non-stationary nature of speech. Additionally, we introduce a mechanism to update the regularization parameter based on the mean-squared error of the adaptive filter, improving the ability of the algorithm to track time-varying systems. The proposed variable regularization NMCFLMS algorithm is then applied to speech dereverberation using the multichannel input-output inverse theorem method. Simulation results, using room impulse responses measured in real acoustic environments, demonstrate the effectiveness of the approach in both multichannel blind identification and speech dereverberation.

Reverberation caused by sound reflections in enclosed spaces typically degrades the quality and intelligibility of the speech signal of interest, even leading to remarkable performance deterioration of voice communication and speech recognition systems. The adaptive weighted prediction-error (AWPE) algorithm can effectively suppress the late reverberation component of microphone speech, however, the prediction-error filter has to be long enough to accurately estimate the late reverberation component, which results in a high computational complexity, making it challenging to apply in the real-time systems. To address this issue, this paper proposes an improved method based on the third-order tensor decomposition. The long linear prediction-error filter in the AWPE algorithm is decomposed into three groups of short sub-filters through multiple Kronecker product. The high-dimensional correlation matrix is then converted into a set of low-dimensional correlation matrices, thus significantly reducing the computational complexity. Simulation results validate that the proposed approach not only achieves effective dereverberation performance, but greatly improves the computational efficiency.

In order to effectively suppress the phenomenon of whistling in hearing aids, we propose the convex combination scheme of the proportionate adaptive feedback cancellation algorithm with different step sizes through the mixing parameter, with performance in both fast convergence and low steady-state residual error. Importantly, we design a normalized gradient learning rule for updating the mixing parameter, which narrows the range of the learning rate significantly as compared to the non-normalized gradient-based learning rule. Furthermore, to make the transition between convergence and steady-state stages smoother, a novel weight vector transfer strategy is developed. By using the realistic speech input, simulation results have demonstrated the effectiveness of the proposed algorithm in contrast with its counterparts.

This article outlines a collaborative tensor decomposable Volterra filter (CTDVF), featuring a collaborative model that implements tensor decomposition to adjust linear weights and Volterra kernel coefficients, with the capacity to automatically activate or deactivate nonlinearity. Specifically, the tensor product and decomposable Volterra model are incorporated to accelerate the convergence rate. A convergence analysis of the CTDVF is performed to characterize the mean stability. Numerical experiments corroborate the excellent convergence performance of the proposed CTDVF.

Active noise control (ANC) is a technique used to achieve noise cancellation in physical spaces and has a wide range of applications. A key challenge in ANC systems is designing an adaptive filter that balances noise cancellation performance with computational efficiency. This paper presents two sets of robust adaptive filtering algorithms to address this challenge. The first set involves decomposing the adaptive filter’s coefficient vector into a linear combination of two sets of shorter sub-filters using the Kronecker product. This decomposition reduces the size of the matrices and vectors involved in the ANC algorithm. To handle impulsive noise, we employ a class of robust estimators and define several cost functions under the recursive least-squares criterion, resulting in an adaptive control algorithm with two groups of alternately updating equations. We also analyze the low-rank property of the proposed adaptive filter in controlling impulsive noise. To further reduce computational complexity, we integrate the dichotomous coordinate descent scheme into the Kronecker product decomposition-based robust ANC method, forming a second set of algorithms. The effectiveness of the proposed algorithms is demonstrated through simulations.

In this work, to address the fixed step-size problem of the widely linear complex-valued affine projection algorithm (WL-CAPA), we propose a sliding-window step-size (SWSS) selection scheme, which results in the SWSS-WL-CAPA. To devise this scheme, we derive the mean-square deviation (MSD) recursion of WL-CAPA and obtain the optimal step-size at each iteration based on the comparison of MSD trends of the algorithm using two different step-sizes in the sliding-window. Interestingly, the SWSS scheme removes the length limitation of the step-size sequence with iterations, which allows the proposed algorithm to achieve better steady-state behavior. Furthermore, we develop a reset mechanism for enhancing the real-time tracking capability of the algorithm for unknown systems. The efficacy of the proposed algorithm is substantiated through the execution of simulations in scenarios of system identification and stereophonic acoustic echo cancellation.