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 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.

Maximum Correntropy Criterion Constrained Kalman Filter

2017 ◽  
Author(s):  
Seyed Fakoorian ◽  
Mahmoud Moosavi ◽  
Reza Izanloo ◽  
Vahid Azimi ◽  
Dan Simon
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
State Constraints ◽  
Statistical Information ◽  
Second Order ◽  
System Model ◽  
Error Covariance ◽  
Inequality State ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian

Non-Gaussian noise may degrade the performance of the Kalman filter because the Kalman filter uses only second-order statistical information, so it is not optimal in non-Gaussian noise environments. Also, many systems include equality or inequality state constraints that are not directly included in the system model, and thus are not incorporated in the Kalman filter. To address these combined issues, we propose a robust Kalman-type filter in the presence of non-Gaussian noise that uses information from state constraints. The proposed filter, called the maximum correntropy criterion constrained Kalman filter (MCC-CKF), uses a correntropy metric to quantify not only second-order information but also higher-order moments of the non-Gaussian process and measurement noise, and also enforces constraints on the state estimates. We analytically prove that our newly derived MCC-CKF is an unbiased estimator and has a smaller error covariance than the standard Kalman filter under certain conditions. Simulation results show the superiority of the MCC-CKF compared with other estimators when the system measurement is disturbed by non-Gaussian noise and when the states are constrained.

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 Maximum Correntropy Criterion Kalman Filter for α-Jerk Tracking Model with Non-Gaussian Noise

Entropy ◽  
2017 ◽  
Vol 19 (12) ◽  
pp. 648 ◽  
Author(s):  
Bowen Hou ◽  
Zhangming He ◽  
Xuanying Zhou ◽  
Haiyin Zhou ◽  
Dong Li ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
Tracking Model ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian

scholarly journals First passage dynamics of stochastic motion in heterogeneous media driven by correlated white Gaussian and coloured non-Gaussian noises

2021 ◽  
Author(s):  
Nicholas Mwilu Mutothya ◽  
Yong Xu ◽  
Yongge Li ◽  
Ralf Metzler ◽  
Nicholas Muthama Mutua
Keyword(s):  
Diffusion Coefficient ◽  
Gaussian Noise ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
Stochastic Motion ◽  
First Passage ◽  
The Mean ◽  
Non Gaussian ◽  
Markovian Systems

Abstract We study the first passage dynamics for a diffusing particle experiencing a spatially varying diffusion coefficient while driven by correlated additive Gaussian white noise and multiplicative coloured non-Gaussian noise. We consider three functional forms for position dependence of the diffusion coefficient: power-law, exponential, and logarithmic. The coloured non-Gaussian noise is distributed according to Tsallis' $q$-distribution. Tracks of the non-Markovian systems are numerically simulated by using the fourth-order Runge-Kutta algorithm and the first passage times are recorded. The first passage time density is determined along with the mean first passage time. Effects of the noise intensity and self-correlation of the multiplicative noise, the intensity of the additive noise, the cross-correlation strength, and the non-extensivity parameter on the mean first passage time are discussed.

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