Kernel Affine Projection P-norm (KAPP) Filtering under Alpha Stable Distribution Noise Environment

Dai, Shaogang; Jin, Mingming; Zhang, Xiaofei

doi:10.1142/s0218001420540063

Cited by 3 publications

(3 citation statements)

References 31 publications

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“…a稳定分布是一种典型的非高斯分布噪声, 具有显著的尖峰脉冲特性, 其概率密度函数的衰减过程比高斯分布慢, 表现为较长的拖尾 [22] , Dai等 [23] 充分考虑了涉及a稳定噪声分布的长尾分布噪声环境, 提出了核仿射投影p范数(kernel affine projection p-norm, KAPP)算法, 该算法代价函数为误差绝对值的p次幂, 当p = 2时算法变为KAP算法, 当p = 1时算法变为核最小平均p功率(kernel least mean square p-power, KLMP)算法 [24] . 文献 [24]提出的KLMP算法, 主要研究在低概率大幅度的非高斯重尾冲激噪声环境中核自适应滤波算法的性能.…”

Section: 引言unclassified

A variable-scale S-type kernel fractional low-power adaptive filtering algorithm

西北师范大学物理与电子工程学院¹,

西北师范大学²

2021

Acta Phys. Sin.

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The adaptive kernel algorithms usually achieve a good convergence performance and a tracking performance due to the universal approximator, offering an excellent solution to many problems with nonlinearities. However, as is well known, the convergence rate and steady-state error of adaptive filtering algorithm are a pair of inherent contradictions, and the kernel method is not exceptional. For this problem, a robust kernel adaptive filtering algorithm, called the variable-scaling factor kernel fractional lower power adaptive filtering algorithm based on the Sigmoid function, is developed by creating a new framework of cost function which combines the kernel fractional low power error criterion with the Sigmoid function for system identification of different noise environments. This new cost framework incorporates a scaling factor into the cost function of the Sigmoid kernel fractional lower power adaptive filtering algorithm (VS-SKFLP) in this paper. One of the main features in the new framework is its scaling factor. This scaling factor is used to control the steepness of the Sigmoid function, and the steepness can affect the convergence speed of filtering algorithm. The scaling factor provides a tradeoff between the convergence rate and the steady-state mean square error (MSE), which improves the convergence rate under the same steady-state mean square error. However, it is also an important problem to choose an appropriate scale factor. Therefore, a variable-scale factor SKFLP algorithm is also proposed to improve the convergence rate and steady-state MSE, simultaneously. The proposed variable-scale factor structure consists of a function of error, featuring the adaptive updates of their parameter estimated by making discerning use of the error. In this paper, the nonlinear saturation characteristic of the Sigmoid function and low order norm criterion are used to overcome the performance degradation of training data destroyed by non-Gaussian impulse noise and colored noise. Through the convergence analysis, the parameter estimation sequence of our proposed algorithm proves convergent. Simulation results show that the proposed algorithm (VS-SKFLP) outperforms other kernel adaptive filtering algorithms in system recognition with different noise environments.

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Section: 引言unclassified

A variable-scale S-type kernel fractional low-power adaptive filtering algorithm

西北师范大学物理与电子工程学院¹,

西北师范大学²

2021

Acta Phys. Sin.

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“…Subsequently, a series of theoretical studies were carried out to prove that. The kernel norm is a good convex proxy for the minimization of rank functions [10]. Yang et al [11] proved that the kernel norm is the most compact convex lower bound of the rank function.…”

Section: Introductionmentioning

confidence: 99%

Quantization and application of low-rank tensor decomposition based on the deep learning model.

Zhao¹

2023

3C TIC

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Watching the presentation of a large-scale network is very important for network state tracking, performance optimization, traffic engineering, anomaly detection, fault analysis, etc. In this paper, we try to develop deep learning technology to solve the defect problem of tensor filling based on inner product interaction. To solve the limitations of the existing tensor-filling algorithms, a new neural tensor-filling (NTC) model is proposed. NTC model can effectively type the third-order communication between data landscapes through outer creation operation. It creates the third-order interaction mapping tensor. On this basis, the interaction between local features of the 3D neural network is studied. In this paper, another fusion neural tensor filling (Fu NTC) model is proposed to solve the problem that the NTC model can only extract the nonlinear complex structural information between potential feature dimensions. In the framework of the neural network, the NTC model and tensor decomposition model share the same potential feature embedding. It can effectively extract nonlinear feature information and linear feature information at the same time. It achieves higher precision data recovery.

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“…关于复杂系统的建模问题, 分数阶微积分模型比整数阶微积分模型更加准确, 同时还能包含系统的遗传和记忆效应 [15] . Gao和En [16] 充分考虑了稳态噪声分布, 提出了一种基于分数低阶统计准则的核最小均方p次幂(kernel least mean p-power, KLMP) 算法. 但上述算法都是基于均方误差准则假设在高斯环境下得出的一般性结论, 而实际在非高斯冲激干扰下均方误差准则会出现严重下降甚至可能失效, 于是研究者们又提出了各种改进算法, 用以解决核自适应滤波算法在非高斯冲激干扰下稳定性不足的问题.…”

unclassified

Kernel adaptive filtering algorithm based on Softplus function under non-Gaussian impulse interference

Huo,

Wang,

Long

et al. 2021

Acta Phys. Sin.

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Kernel adaptive filters are a class of powerful nonlinear filter developed in reproducing kernel Hilbert space (RKHS).The Gaussian kernel is usually the default kernel in KAF algorithm, because the Gaussian kernel has the universal approximation. However, in previous research the kernel adaptive filtering algorithms were mostly based on mean square error criterion and assumed to be in a Gaussian noise environment. When environmental noise is changed, the performance of conventional kernel adaptive filtering algorithm based on mean square error criterion is seriously reduced to failure due to the interference of non-Gaussian noise and the influence of inappropriate non-Gaussian modeling. Therefore, it is important to develop a new method of suppressing the noise of non-Gaussian signals. In this paper, a new kernel fractional lower power adaptive filtering algorithm is proposed by combining the benefits of the kernel method and a new loss function which is robust against non-Gaussian impulsive interferences and has fast convergence under a similar stability condition. The proposed SP-KFLP algorithm generates a new framework of cost function which combines the Softplus function with the KFLP algorithm by updating its weight vector according to the gradient estimation while nonlinear saturation characteristics of output error are used. Compared with the features of sigmoid function the features of the Softplus function guarantee the SP-KFLP an excellent performance for combatting impulsive interference and speeding up the convergence rate. In the kernel fractional low power criterion the reciprocal of the system error is used as the coefficient of the weight vector update formula, and the method of error burst is used to make the weight vector not update to resist the impulse noise. The mean square convergence analysis for SP-KFLP is conducted, and a sufficient condition for guaranteeing convergence is therefore obtained by using the energy conservation relation. The proposed algorithm is very simple computationally. Simulations in a system identification show that the proposed SP-KFLP algorithm outperforms the kernel least-mean-square algorithm, kernel fractional lower power algorithm, and sigmoid kernel fractional lower algorithm in terms of convergence rate and the robustness of against impulsive interference. The proposed algorithm improves not only the capability of resisting impulsive interference, but also the convergence rate. In other words, the contradiction between convergence and tracking performance stability is well taken into account, and the performance under Gaussian noise is also better than the performance of the traditional kernel adaptive algorithm.

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Kernel Affine Projection P-norm (KAPP) Filtering under Alpha Stable Distribution Noise Environment

Cited by 3 publications

References 31 publications

A variable-scale S-type kernel fractional low-power adaptive filtering algorithm

A variable-scale S-type kernel fractional low-power adaptive filtering algorithm

Quantization and application of low-rank tensor decomposition based on the deep learning model.

Kernel adaptive filtering algorithm based on Softplus function under non-Gaussian impulse interference

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