Zongze Wu

Kernel recursive maximum correntropy

In this letter, a robust kernel adaptive algorithm, called the kernel recursive maximum correntropy (KRMC), is derived in kernel space and under the maximum correntropy criterion (MCC). The proposed algorithm is particularly useful for nonlinear and non-Gaussian signal processing, especially when data contain large outliers or disturbed by impulsive noises. The superior performance of KRMC is confirmed by simulation results about short-term chaotic time series prediction in alpha-stable noise environments.

Robust Hammerstein Adaptive Filtering under Maximum Correntropy Criterion

The maximum correntropy criterion (MCC) has recently been successfully applied to adaptive filtering. Adaptive algorithms under MCC show strong robustness against large outliers. In this work, we apply the MCC criterion to develop a robust Hammerstein adaptive filter. Compared with the traditional Hammerstein adaptive filters, which are usually derived based on the well-known mean square error (MSE) criterion, the proposed algorithm can achieve better convergence performance especially in the presence of impulsive non-Gaussian (e.g., α-stable) noises. Additionally, some theoretical results concerning the convergence behavior are also obtained. Simulation examples are presented to confirm the superior performance of the new algorithm.

Maximum correntropy unscented filter

ABSTRACT The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilising a derivative-free higher-order approximation by approximating a Gaussian distribution rather than approximating a non-linear function. Applying the UT to a Kalman filter type estimator leads to the well-known unscented Kalman filter (UKF). Although the UKF works very well in Gaussian noises, its performance may deteriorate significantly when the noises are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises. To improve the robustness of the UKF against impulsive noises, a new filter for non-linear systems is proposed in this work, namely the maximum correntropy unscented filter (MCUF). In MCUF, the UT is applied to obtain the prior estimates of the state and covariance matrix, and a robust statistical linearisation regression based on the maximum correntropy criterion is then used to obtain the posterior estimates of the state and covariance matrix. The satisfying performance of the new algorithm is confirmed by two illustrative examples.

Smoothed least mean p-power error criterion for adaptive filtering

In this paper, we propose a novel error criterion for adaptive filtering, namely the smoothed least mean p-power (SLMP) error criterion, which aims to minimize the mean p-power of the error plus an independent and scaled smoothing variable. Some important properties of the SLMP criterion are presented. In particular, we show that if the smoothing variable is symmetric and zero-mean, and p is an even number, then the SLMP error criterion will become a weighted sum of the even-order moments of the error, and as the smoothing factor (i.e. the scale factor) is large enough, this new criterion will be approximately equivalent to the well-known mean square error (MSE) criterion. Based on the proposed error criterion, we develop a new adaptive filtering algorithm and its kernelized version, and derive a theoretical value of the steady-state excess mean square error (EMSE). Simulation results suggest that the new algorithms with proper choice of the smoothing factor may perform quite well.

Minimum Error Entropy Algorithms with Sparsity Penalty Constraints

Recently, sparse adaptive learning algorithms have been developed to exploit system sparsity as well as to mitigate various noise disturbances in many applications. In particular, in sparse channel estimation, the parameter vector with sparsity characteristic can be well estimated from noisy measurements through a sparse adaptive filter. In previous studies, most works use the mean square error (MSE) based cost to develop sparse filters, which is rational under the assumption of Gaussian distributions. However, Gaussian assumption does not always hold in real-world environments. To address this issue, we incorporate in this work an l1-norm or a reweighted l1-norm into the minimum error entropy (MEE) criterion to develop new sparse adaptive filters, which may perform much better than the MSE based methods, especially in heavy-tailed non-Gaussian situations, since the error entropy can capture higher-order statistics of the errors. In addition, a new approximator of l0-norm, based on the correntropy induced metric (CIM), is also used as a sparsity penalty term (SPT). We analyze the mean square convergence of the proposed new sparse adaptive filters. An energy conservation relation is derived and a sufficient condition is obtained, which ensures the mean square convergence. Simulation results confirm the superior performance of the new algorithms.

Convex regularized recursive maximum correntropy algorithm

In this brief, a robust and sparse recursive adaptive filtering algorithm, called convex regularized recursive maximum correntropy (CR-RMC), is derived by adding a general convex regularization penalty term to the maximum correntropy criterion (MCC). An approximate expression for automatically selecting the regularization parameter is also introduced. Simulation results show that the CR-RMC can significantly outperform the original recursive maximum correntropy (RMC) algorithm especially when the underlying system is very sparse. Compared with the convex regularized recursive least squares (CR-RLS) algorithm, the new algorithm also shows strong robustness against impulsive noise. The CR-RMC also performs much better than other LMS-type sparse adaptive filtering algorithms based on MCC. A robust and sparse recursive adaptive filtering algorithm is derived.The regularization parameter in the new algorithm can be automatically selected.Simulation results confirm the excellent performance of the proposed algorithm.

Nonlinear spline adaptive filtering under maximum correntropy criterion

The nonlinear spline adaptive filtering under least mean square (SAF-LMS) uses the mean square error (MSE) based cost function to identify the Wiener-type nonlinear systems, which is rational under the assumption of Gaussian distributions. However, the mere second-order statistics are often not suitable for nonlinear and/or non-Gaussian systems. To address this issue, a new nonlinear adaptive filter, called nonlinear spline adaptive filtering under maximum correntropy criterion (SAF-MCC), is proposed in this work. Compared with the SAF-LMS, the SAF-MCC uses the maximum correntropy criterion (MCC) to replace the MSE criterion to improve the convergence performance especially in heavy-tailed non-Gaussian environments. Simulation results confirm the superior performance of the new algorithm.

An improved proportionate least mean p-power algorithm for adaptive filtering

The least mean p-power error criterion has been successfully used in adaptive filtering due to its strong robustness against large outliers. In this paper, we develop a new adaptive filtering algorithm, named the proportionate least mean p-power (PLMP) algorithm, which uses the mean p-power error as the adaptation cost function. Compared with the standard proportionate normalized least mean square algorithm, the PLMP can achieve much better performance in terms of the mean square deviation, especially in the presence of impulsive non-Gaussian noises. The mean and mean square convergence of the proposed algorithm are analyzed, and some related theoretical results are also obtained. Simulation results are presented to verify the effectiveness of our proposed algorithm.

Kernel least mean square based on conjugate gradient

Kernel least mean square (KLMS) algorithm has been successfully applied in fields of adaptive filtering and online learning due to their ability to solve sequentially nonlinear problems by implicitly mapping the input signal to a high-dimensional reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel adaptive algorithm called KLMS based on conjugate gradient (KLMS-CG), which uses the orthogonal search directions, instead of using the traditional steepest descent approach, to improve the convergence speed. Further, the quantized KLMS based on conjugate gradient (QKLMS-CG) is proposed to curb the growth of network. Simulation results indicate that the new algorithm can converge faster than the original KLMS while maintaining excellent accuracy.

Adaptive convex combination filter under minimum error entropy criterion

Minimum error entropy (MEE) is a robust adaption criterion and has been successfully applied to adaptive filtering, which can outperform the well-known minimum mean square error (MSE) criterion especially in the present of non-Gaussian noise. However, the adaptive algorithms under MEE are still subject to a compromise between convergence speed and steady-state mean square deviation (MSD). To address this issue, we propose in this paper an adaptive convex combination filter under MEE (CMEE), which is derived by using a convex combination of two MEE-based adaptive algorithms of different step-sizes. Monte Carlo simulation results confirm that the new algorithm can achieve fast convergence speed while keeping a desirable performance.