scholarly journals Complex Correntropy with Variable Center: Definition, Properties, and Application to Adaptive Filtering

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 70
Author(s):  
Fei Dong ◽  
Guobing Qian ◽  
Shiyuan Wang
Keyword(s):  
Steady State ◽  
Adaptive Filtering ◽  
Gradient Descent ◽  
Gaussian Function ◽  
Complex Domain ◽  
Mean Square ◽  
Kernel Width ◽  
Non Gaussian ◽  
The Cost ◽  
Variable Center

The complex correntropy has been successfully applied to complex domain adaptive filtering, and the corresponding maximum complex correntropy criterion (MCCC) algorithm has been proved to be robust to non-Gaussian noises. However, the kernel function of the complex correntropy is usually limited to a Gaussian function whose center is zero. In order to improve the performance of MCCC in a non-zero mean noise environment, we firstly define a complex correntropy with variable center and provide its probability explanation. Then, we propose a maximum complex correntropy criterion with variable center (MCCC-VC), and apply it to the complex domain adaptive filtering. Next, we use the gradient descent approach to search the minimum of the cost function. We also propose a feasible method to optimize the center and the kernel width of MCCC-VC. It is very important that we further provide the bound for the learning rate and derive the theoretical value of the steady-state excess mean square error (EMSE). Finally, we perform some simulations to show the validity of the theoretical steady-state EMSE and the better performance of MCCC-VC.

scholarly journals Diffusion Generalized MCC with a Variable Center Algorithm for Robust Distributed Estimation

Electronics ◽  
2021 ◽  
Vol 10 (22) ◽  
pp. 2807
Author(s):  
Wentao Ma ◽  
Panfei Cai ◽  
Fengyuan Sun ◽  
Xiao Kou ◽  
Xiaofei Wang ◽  
...  
Keyword(s):  
Adaptive Filtering ◽  
Gaussian Noise ◽  
Distributed Estimation ◽  
Filtering Algorithms ◽  
Combine Strategy ◽  
Stable Performance ◽  
The Mean ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian ◽  
Variable Center

Classical adaptive filtering algorithms with a diffusion strategy under the mean square error (MSE) criterion can face difficulties in distributed estimation (DE) over networks in a complex noise environment, such as non-zero mean non-Gaussian noise, with the object of ensuring a robust performance. In order to overcome such limitations, this paper proposes a novel robust diffusion adaptive filtering algorithm, which is developed by using a variable center generalized maximum Correntropy criterion (GMCC-VC). Generalized Correntropy with a variable center is first defined by introducing a non-zero center to the original generalized Correntropy, which can be used as robust cost function, called GMCC-VC, for adaptive filtering algorithms. In order to improve the robustness of the traditional MSE-based DE algorithms, the GMCC-VC is used in a diffusion adaptive filter to design a novel robust DE method with the adapt-then-combine strategy. This can achieve outstanding steady-state performance under non-Gaussian noise environments because the GMCC-VC can match the distribution of the noise with that of non-zero mean non-Gaussian noise. The simulation results for distributed estimation under non-zero mean non-Gaussian noise cases demonstrate that the proposed diffusion GMCC-VC approach produces a more robustness and stable performance than some other comparable DE methods.

scholarly journals A Kernel Recursive Maximum Versoria-Like Criterion Algorithm for Nonlinear Channel Equalization

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1067 ◽  
Author(s):  
Qishuai Wu ◽  
Yingsong Li ◽  
Wei Xue
Keyword(s):  
Adaptive Filtering ◽  
Impulse Noise ◽  
Channel Equalization ◽  
Mean Square ◽  
Least Mean Square ◽  
Mixed Mean ◽  
Non Gaussian ◽  
Kernel Least Mean Square ◽  
Nonlinear Adaptive Filtering ◽  
Better Than

In this paper, a kernel recursive maximum Versoria-like criterion (KRMVLC) algorithm has been constructed, derived, and analyzed within the framework of nonlinear adaptive filtering (AF), which considers the benefits of logarithmic second-order errors and the symmetry maximum-Versoria criterion (MVC) lying in reproducing the kernel Hilbert space (RKHS). In the devised KRMVLC, the Versoria approach aims to resist the impulse noise. The proposed KRMVLC algorithm was carefully derived for taking the nonlinear channel equalization (NCE) under different non-Gaussian interferences. The achieved results verify that the KRMVLC is robust against non-Gaussian interferences and performs better than those of the popular kernel AF algorithms, like the kernel least-mean-square (KLMS), kernel least-mixed-mean-square (KLMMN), and Kernel maximum Versoria criterion (KMVC).

Response Statistics of a Beam-Mass Oscillator Under Combined Harmonic and Random Excitation

1995 ◽  
Vol 1 (2) ◽  
pp. 225-247 ◽  
Author(s):  
Stephen Ekwaro-Osire ◽  
Atila Ertas
Keyword(s):  
Steady State ◽  
Harmonic Component ◽  
Stochastic Averaging ◽  
Random Excitation ◽  
Stochastic Averaging Method ◽  
Time Averaging ◽  
Mean Square ◽  
Mean Square Response ◽  
The Mean ◽  
Non Gaussian

In the present study, the response statistics of a beam-mass oscillator under combined harmonic and random excitation were investigated. The Gaussian and non-Gaussian closure schemes, in conjunction with the stochastic averaging method, were used to solve for the mean square response. The influence of the oscillator parameters on the response statistics was studied. The harmonic component of the excitation was observed to manifest itself, as an oscillation, in the steady-state mean square response. Results obtained showed that the non-Gaussian solution yields higher steady-state mean square responses than those obtained from the Gaussian solution. It was further shown that the harmonic time-varying properties of the oscillator are preserved by omitting the time-averaging in the stochastic averaging procedure.

scholarly journals Research on Robustness of Geometric Algebra Based Adaptive Filtering Algorithms In Non-Gaussian Environment

2021 ◽  
Author(s):  
Rui Wang ◽  
Yi Wang ◽  
Yanping Li ◽  
Wenming Cao
Keyword(s):  
Mean Square Error ◽  
Adaptive Filtering ◽  
Geometric Algebra ◽  
Mean Square ◽  
Robust Algorithms ◽  
Filtering Algorithms ◽  
Minimum Error ◽  
The Mean ◽  
Non Gaussian ◽  
Stable Noise

Abstract In this paper, two new geometric algebra (GA) based adaptive filtering algorithms in non-Gaussian environment are proposed, which are deduced from the robust algorithms based on the minimum error entropy (MEE) criterion and the joint criterion of the MEE and the mean square error (MSE) with the help of GA theory. Some experiments validate the effectiveness and superiority of the GA-MEE and GA-MSEMEE algorithms in α-stable noise environment. At the same time, the GA-MSEMEE algorithm has faster convergence speed compared with the GA-MEE.

scholarly journals Reconstruction of Diffusion Coefficients and Power Exponents from Single Lagrangian Trajectories

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 111
Author(s):  
Leonid M. Ivanov ◽  
Collins A. Collins ◽  
Tetyana Margolina
Keyword(s):  
Black Sea ◽  
Diffusion Coefficients ◽  
Current System ◽  
Mean Square Displacement ◽  
California Current ◽  
The Black Sea ◽  
Mean Square ◽  
California Current System ◽  
The Mean ◽  
Non Gaussian

Using discrete wavelets, a novel technique is developed to estimate turbulent diffusion coefficients and power exponents from single Lagrangian particle trajectories. The technique differs from the classical approach (Davis (1991)’s technique) because averaging over a statistical ensemble of the mean square displacement (<X2>) is replaced by averaging along a single Lagrangian trajectory X(t) = {X(t), Y(t)}. Metzler et al. (2014) have demonstrated that for an ergodic (for example, normal diffusion) flow, the mean square displacement is <X2> = limT→∞τX2(T,s), where τX2 (T, s) = 1/(T − s) ∫0T−s(X(t+Δt) − X(t))2 dt, T and s are observational and lag times but for weak non-ergodic (such as super-diffusion and sub-diffusion) flows <X2> = limT→∞≪τX2(T,s)≫, where ≪…≫ is some additional averaging. Numerical calculations for surface drifters in the Black Sea and isobaric RAFOS floats deployed at mid depths in the California Current system demonstrated that the reconstructed diffusion coefficients were smaller than those calculated by Davis (1991)’s technique. This difference is caused by the choice of the Lagrangian mean. The technique proposed here is applied to the analysis of Lagrangian motions in the Black Sea (horizontal diffusion coefficients varied from 105 to 106 cm2/s) and for the sub-diffusion of two RAFOS floats in the California Current system where power exponents varied from 0.65 to 0.72. RAFOS float motions were found to be strongly non-ergodic and non-Gaussian.

scholarly journals Adaptive modulation based on steady-state mean square error for underwater acoustic communication

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhiyong Liu ◽  
Zhoumei Tan ◽  
Fan Bai
Keyword(s):  
Steady State ◽  
Mean Square Error ◽  
Adaptive Modulation ◽  
Blind Equalization ◽  
Training Sequence ◽  
Transmission Efficiency ◽  
Underwater Acoustic Communication ◽  
Mean Square ◽  
Modulation Mode ◽  
Simulation Results

AbstractTo improve the transmission efficiency and facilitate the realization of the scheme, an adaptive modulation (AM) scheme based on the steady-state mean square error (SMSE) of blind equalization is proposed. In this scheme, the blind equalization is adopted and no training sequence is required. The adaptive modulation is implemented based on the SMSE of blind equalization. The channel state information doesn’t need to be assumed to know. To better realize the adjustment of modulation mode, the polynomial fitting is used to revise the estimated SNR based on the SMSE. In addition, we also adopted the adjustable tap-length blind equalization detector to obtain the SMSE, which can adaptively adjust the tap-length according to the specific underwater channel profile, and thus achieve better SMSE performance. Simulation results validate the feasibility of the proposed approaches. Simulation results also show the advantages of the proposed scheme against existing counterparts.

scholarly journals A Cost Analysis of School-Based Lifestyle Interventions

2018 ◽  
Vol 19 (6) ◽  
pp. 716-727 ◽  
Author(s):  
Marije Oosterhoff ◽  
Hans Bosma ◽  
Onno C.P. van Schayck ◽  
Manuela A. Joore
Keyword(s):  
Physical Activity ◽  
Steady State ◽  
Primary School ◽  
Relative Effectiveness ◽  
First Year ◽  
Lifestyle Interventions ◽  
Stakeholder Perspectives ◽  
School Based ◽  
The Cost ◽  
Cost Offsets

Abstract A uniform approach for costing school-based lifestyle interventions is currently lacking. The objective of this study was to develop a template for costing primary school-based lifestyle interventions and apply this to the costing of the “Healthy Primary School of the Future” (HPSF) and the “Physical Activity School” (PAS), which aim to improve physical activity and dietary behaviors. Cost-effectiveness studies were reviewed to identify the cost items. Societal costs were reflected by summing up the education, household and leisure, labor and social security, and health perspectives. Cost inputs for HPSF and PAS were obtained for the first year after implementation. In a scenario analysis, the costs were explored for a hypothetical steady state. From a societal perspective, the per child costs were €2.7/$3.3 (HPSF) and €− 0.3/$− 0.4 (PAS) per day during the first year after implementation, and €1.0/$1.2 and €− 1.3/$− 1.6 in a steady state, respectively (2016 prices). The highest costs were incurred by the education perspective (first year: €8.7/$10.6 (HPSF) and €4.0/$4.9 (PAS); steady state: €6.1/$7.4 (HPSF) and €2.1/$2.6 (PAS)), whereas most of the cost offsets were received by the household and leisure perspective (first year: €− 6.0/$− 7.3 (HPSF) and €− 4.4/$− 5.4 (PAS); steady state: €− 5.0/$− 6.1 (HPSF) and €− 3.4/$− 4.1 (PAS)). The template proved helpful for costing HPSF and PAS from various stakeholder perspectives. The costs for the education sector were fully (PAS) and almost fully (HPSF) compensated by the savings within the household sector. Whether the additional costs of HPSF over PAS represent value for money will depend on their relative effectiveness.

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