Robust Hammerstein Adaptive Filtering under Maximum Correntropy Criterion

Wu, Zongze; Peng, Siyuan; Chen, Badong; Zhao, Haiquan

doi:10.3390/e17107149

Cited by 73 publications

(42 citation statements)

References 43 publications

(43 reference statements)

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“…Based on the ZA techniques [4][5][6][10][11][12][13][22][23][24][25][26][27][28]32] and CIM theory [33][34][35][36][37][38][39][40], we propose a robust sparse LMMN algorithm by exerting a CIM penalty on the channel coefficient vector, and we utilize this constrained term to modify the cost function of the traditional LMMN algorithm. As we know, in the CIM theory, CIM can be used for measuring a similarity in kernel space between two random vectors p = { p 1 , · · · , p N } and q = { q 1 , · · · , q N }, which can be described as [33][34][35][36][37][38][39][40]:…”

Section: Proposed Sparse Cim-lmmn Algorithmmentioning

confidence: 99%

A Robust Sparse Adaptive Filtering Algorithm with a Correntropy Induced Metric Constraint for Broadband Multi-Path Channel Estimation

Jin

Wang

et al. 2016

Entropy

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Abstract:A robust sparse least-mean mixture-norm (LMMN) algorithm is proposed, and its performance is appraised in the context of estimating a broadband multi-path wireless channel. The proposed algorithm is implemented via integrating a correntropy-induced metric (CIM) penalty into the conventional LMMN algorithm to modify the basic cost function, which is denoted as the CIM-based LMMN (CIM-LMMN) algorithm. The proposed CIM-LMMN algorithm is derived in detail within the kernel framework. The updating equation of CIM-LMMN can provide a zero attractor to attract the non-dominant channel coefficients to zeros, and it also gives a tradeoff between the sparsity and the estimation misalignment. Moreover, the channel estimation behavior is investigated over a broadband sparse multi-path wireless channel, and the simulation results are compared with the least mean square/fourth (LMS/F), least mean square (LMS), least mean fourth (LMF) and the recently-developed sparse channel estimation algorithms. The channel estimation performance obtained from the designated sparse channel estimation demonstrates that the CIM-LMMN algorithm outperforms the recently-developed sparse LMMN algorithms and the relevant sparse channel estimation algorithms. From the results, we can see that our CIM-LMMN algorithm is robust and is superior to these mentioned algorithms in terms of both the convergence speed rate and the channel estimation misalignment for estimating a sparse channel.

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Section: Proposed Sparse Cim-lmmn Algorithmmentioning

confidence: 99%

A Robust Sparse Adaptive Filtering Algorithm with a Correntropy Induced Metric Constraint for Broadband Multi-Path Channel Estimation

Jin

Wang

et al. 2016

Entropy

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“…It is noteworthy that well-known second-order statistics, such as the mean square error (MSE) depends heavily on the Gaussian and linear assumptions [17]. However, in presence of non-Gaussian noise and in particular large outliers, i.e., observations greatly deviated from the data bulk, the effectiveness of the MSE-based algorithms will significantly deteriorate [29]. By contrast, the maximization of the correntropy criterion is appropriate for non-Gaussian signal processing, and is robust in particular against large outliers, as shown next.…”

Section: A Correntropymentioning

confidence: 99%

Correntropy Maximization via ADMM: Application to Robust Hyperspectral Unmixing

Zhu

Halimi

Honeiné

et al. 2017

IEEE Trans. Geosci. Remote Sensing

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In hyperspectral images, some spectral bands suffer from low signal-to-noise ratio due to noisy acquisition and atmospheric effects, thus requiring robust techniques for the unmixing problem. This paper presents a robust supervised spectral unmixing approach for hyperspectral images. The robustness is achieved by writing the unmixing problem as the maximization of the correntropy criterion subject to the most commonly used constraints. Two unmixing problems are derived: the first problem considers the fully-constrained unmixing, with both the non-negativity and sum-to-one constraints, while the second one deals with the non-negativity and the sparsity-promoting of the abundances. The corresponding optimization problems are solved efficiently using an alternating direction method of multipliers (ADMM) approach. Experiments on synthetic and real hyperspectral images validate the performance of the proposed algorithms for different scenarios, demonstrating that the correntropy-based unmixing is robust to outlier bands. Index TermsCorrentropy, maximum correntropy estimation, alternating direction method of multipliers, hyperspectral image, unmixing problem. F. Zhu is with the A. Halimi is with the School of Engineering and Physical Sciences, Heriot-Watt University, U.K. (a.halimi@hw.ac.uk) P. Honeine is with the LITIS lab, ) 2 I. INTRODUCTION SPectral unmixing is an essential issue in many disciplines, including signal and image processing, with a wide range of applications, such as classification, segmentation, material identification and target detection. Typically, a hyperspectral image corresponds to a scene taken at many continuous and narrow bands across a certain wavelength range; namely, each pixel is a spectrum. Assuming that each spectrum is a mixture of several pure materials, the unmixing problem consists in two tasks: (i) identifying these pure materials (the so-called endmembers); (ii) estimating their proportions (the so-called abundances) at each pixel [1]. In practice, these two steps can be performed either sequentially or simultaneously [2]. Wellknown endmember extraction algorithms include the pure-pixel-based ones, e.g., the vertex component analysis (VCA) [3] and the N-FINDR [4], as well as the minimum-volume-based ones, e.g., the minimum simplex analysis [5] and the minimum volume constrained nonnegative matrix factorization [6]. While the endmember extraction is relatively easy from geometry, the abundance estimation remains an open problem. Indeed, the abundances can be estimated using least-squares methods, geometric approaches [2], or by tackling recently-raised issues such as nonlinearity [7], [8]. In this paper, we consider the abundance estimation problem. The linear mixture model (LMM) is the most investigated over the past decades [6], [9], [10]. Its underlying premise is that each pixel/spectrum is a linear combination of the endmembers. To be physically interpretable, two constraints are often enforced in the estimation problem: the abundance non-negativity constraint (ANC) and the a...

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“…Nevertheless, conventional identification algorithms, in which least squares or quadratic Lyapunov stability theory are used, are more sensitive to larger errors. To circumvent this difficulty, three possible solutions can be found in literature: (i) outlier modeling; (ii) identification on the basis of constrained LS, which guarantees boundedness of the square norm of the parameters update; and (iii) parameter estimation by minimizing special cost functions that are less sensitive to larger noises such as the p th power of the absolute value of the prediction error piecewise and Gaussian loss functions . In the work of Cui et al, a differentiable function, which approximates the absolute value function, has been proposed to meet the differentiability required by most optimization algorithms.…”

Section: Introductionmentioning

confidence: 99%

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Rahmani

Farrokhi

2019

Intl J Robust & Nonlinear

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Summary This paper introduces a multiple‐input–single‐output (MISO) neuro‐fractional‐order Hammerstein (NFH) model with a Lyapunov‐based identification method, which is robust in the presence of outliers. The proposed model is composed of a multiple‐input–multiple‐output radial basis function neural network in series with a MISO linear fractional‐order system. The state‐space matrices of the NFH are identified in the time domain via the Lyapunov stability theory using input‐output data acquired from the system. In this regard, the need for the system state variables is eliminated by introducing the auxiliary input‐output filtered signals into the identification laws. Moreover, since practical measurement data may contain outliers, which degrade performance of the identification methods (eg, least‐square–based methods), a Gaussian Lyapunov function is proposed, which is rather insensitive to outliers compared with commonly used quadratic Lyapunov function. In addition, stability and convergence analysis of the presented method is provided. Comparative example verifies superior performance of the proposed method as compared with the algorithm based on the quadratic Lyapunov function and a recently developed input‐output regression‐based robust identification algorithm.

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Robust Hammerstein Adaptive Filtering under Maximum Correntropy Criterion

Cited by 73 publications

References 43 publications

A Robust Sparse Adaptive Filtering Algorithm with a Correntropy Induced Metric Constraint for Broadband Multi-Path Channel Estimation

A Robust Sparse Adaptive Filtering Algorithm with a Correntropy Induced Metric Constraint for Broadband Multi-Path Channel Estimation

Correntropy Maximization via ADMM: Application to Robust Hyperspectral Unmixing

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

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