Recently, an affine projection tanh (APT) algorithm has been designed based on optimization criteria with hyperbolic tangent function constraints. However, there is a significant steady-state error in the APT algorithm. To address this drawback, this article presents an improved APT (IAPT) algorithm based on the optimization framework with hyperbolic tangent function square constraints. It is shown that the proposed IAPT algorithm displays strong robustness, higher convergence speed, and smaller estimation error compared to affine projection (AP) algorithm, AP sign algorithm (APSA) and APT algorithms under the impulsive noise disturbance in the system identification application scenario.
In adaptive filtering, the maximum correntropy criterion (MCC) is a strategy that can effectively deal with impulse noise interference. The least mean square (LMS) algorithm of the graph signal processing (GSP) based on the MCC (GSP LMSMCC) shows good performance against impulse noise and Gaussian noise. Nevertheless, the GSP LMSMCC algorithm has two parameters that need to be analyzed, namely the step factor and kernel parameter, and a fixed step size cannot achieve better coordination between steady-state error and convergence rate. Therefore, based on the advantages of deep learning such as the ability to train on parameters, we extend the iterative formulation of the GSP LMSMCC algorithm to a multilayer network with the step size and kernel parameter trainable at each layer, where the input of each layer is the noisy graph signal and estimation of the graph signal, and the output is the next estimation of the graph signal after iteration. We train the network with the signal dataset and back propagation. Simulation results show that the method proposed not only avoids the discussion of the two related parameters, but also achieves a better compromise between steady-state error and convergence speed.
Unscented Kalman filter (UKF) based on correntropy criterion shows robustness when power system measurement suffers from non-Gaussian noise. To improve the performance of traditional algorithms, this paper proposed a generalized mixture correntropy unscented Kalman filter (GMC-UKF) for power system dynamic state estimation. Specifically, we construct the mixture correntropy by two generalized Gaussian kernels. After introducing the weighted state error and measurement error into the mixture correntropy cost function, we adopt fixed-point iteration to obtain optimal estimation. Finally, the robustness and accuracy of the proposed algorithm for power system state estimation are verified on IEEE-30bus.
In the linear systems, the conventional least mean fourth (LMF) algorithm has faster convergence and lower steady-state error than LMS algorithm, However, in many applications, the censored observations occur frequently. In this paper, a least mean fourth (LMF) algorithm with censored regression is proposed for adaptive filtering. When the identified system possesses a certain extent of sparsity, the least mean fourth algorithm for Censored Regression (CRLMF) algorithm may encounter performance degradation. Therefore, a reweighted zero-attracting LMF algorithm based on the censored regression model (RZA-CRLMF) is proposed further. Simulations are carried out in system identification and echo cancellation scenarios. The results verify the effectiveness of the proposed CRLMF and RZA-CRLMF algorithms. Moreover, in sparse system, the RZA-CRLMF algorithm improves further the filter performance in terms of the convergence speed and the mean squared deviation for the presence of sub-Gaussian noise.
In this paper, a novel robust algorithm called geometric algebra least mean M-estimate (GA-LMM) is proposed, which is the extension of the conventional LMM algorithm in GA space. To further improve the convergence performance, variable step-size GA-LMM (VSS-GA-LMM) algorithm is also proposed, which effectively balances the trade-off between convergence rate and steady-state misalignment. Finally, a multidimensional system identification problem is considered to verify the performance of the proposed GA-LMM and VSS-GA-LMM algorithms. Simulation results show that the proposed algorithms are superior to other GA-based algorithms in terms of convergence rate and steady-state misalignment in impulsive noise environments.
In order to deal with impulsive noise, the traditional filtered-s normalized maximum correntropy criterion (FsNMCC) adaptive algorithm has good robustness in nonlinear active noise control (ANC) systems. However, the FsNMCC algorithm has a single Gaussian kernel, of which the noise reduction performance is susceptible to the value of the kernel width. To surmount this shortcoming, the filtered-s normalized maximum mixture correntropy criterion (FsNMMCC) algorithm is designed for a functional link artificial neural network (FLANN) based on ANC systems. Simulation results show that the proposed FsNMMCC algorithm in this paper has better noise reduction performance than the FsNMCC algorithm in active noise control of impulsive noise with standard symmetric α-stable (SαS) distribution.
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