scholarly journals An Adaptive Filtering Algorithm for Non-Gaussian Signals in Alpha-Stable Distribution

2020 ◽  
Vol 37 (1) ◽  
pp. 69-75
Author(s):  
Baohai Yang
Keyword(s):  
Adaptive Filtering ◽  
Stable Distribution ◽  
Filtering Algorithm ◽  
Alpha Stable Distribution ◽  
Non Gaussian

Parameterizations and Parameters Relations of Stable Distribution

2014 ◽  
Vol 543-547 ◽  
pp. 1721-1727 ◽  
Author(s):  
Chun Li Liu ◽  
Hai Long Chen ◽  
Lei Shao ◽  
Jun Ting Wang ◽  
Cheng Ji You
Keyword(s):  
Numerical Calculation ◽  
Gaussian Distribution ◽  
Stable Distribution ◽  
Alpha Stable Distribution ◽  
Non Gaussian

For the problem of various non-Gaussian signals and noises have distinct spiky and impulsive characteristics in practice, which cannot be solved by Gaussian distribution, we focus on the Alpha stable distribution. This paper firstly sets forth the representation of standard parameterization, and gives some properties in this parameterization. Secondly, define a representation of the parameterization for the purpose of being suitable for numerical calculation and modeling, clears the meaning of each parameter, finds relations between parameters in these representations. Finally, analyze and prove the properties equally apply in this parameterization.

scholarly journals Frequency domain maximum correntropy criterion spline adaptive filtering

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Wenyan Guo ◽  
Yongfeng Zhi ◽  
Kai Feng
Keyword(s):  
Frequency Domain ◽  
Adaptive Filtering ◽  
Adaptive Filter ◽  
Adaptive Filters ◽  
Operation Time ◽  
Filtering Algorithm ◽  
Impulsive Noises ◽  
Type Frequency ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian

AbstractA filtering algorithm based on frequency domain spline type, frequency domain spline adaptive filters (FDSAF), effectively reducing the computational complexity of the filter. However, the FDSAF algorithm is unable to suppress non-Gaussian impulsive noises. To suppression non-Gaussian impulsive noises along with having comparable operation time, a maximum correntropy criterion (MCC) based frequency domain spline adaptive filter called frequency domain maximum correntropy criterion spline adaptive filter (FDSAF-MCC) is developed in this paper. Further, the bound on learning rate for convergence of the proposed algorithm is also studied. And through experimental simulations verify the effectiveness of the proposed algorithm in suppressing non-Gaussian impulsive noises. Compared with the existing frequency domain spline adaptive filter, the proposed algorithm has better performance.

scholarly journals Robust Signals Detection Algorithm Based on Cyclostationarity in Impulsive Noise

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Order Statistics ◽  
Lower Order ◽  
Stable Distribution ◽  
Impulsive Noise ◽  
Detection Algorithm ◽  
Communication Signals ◽  
Alpha Stable Distribution ◽  
Fractional Lower Order Statistics ◽  
Non Gaussian ◽  
Output Snr

A robust method for detecting the communication signals impinging on an antenna with interference and non-Gaussian impulsive noise is introduced in this paper. Degradation of the conventional cyclic detector which based on max-output-SNR criterion in impulsive noise is shown both theoretically and experimentally. By fusing second-order cyclostationarity and fractional lower-order statistics, a type of cyclic fractional lower-order statistics is developed which is defined for exploiting cyclostationarity property. Then, a new robust type of detection algorithm is developed using the theory of optimal filtering based on max-output-SNR criterion and alpha-stable distribution, including the fractional lower-order cyclic matched filter, which is formulated for detecting the communication signals in the presence of interference and non-Gaussian alpha-stable distribution impulsive noise. It is shown that the new method is robust to Gaussian and non-Gaussian impulsive noises, and is immune to the interfering signals which occupy the same spectral band as that of the received signal. Simulation results show the robustness and effectiveness of the proposed algorithm.

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

2019 ◽  
Vol 34 (02) ◽  
pp. 2054006
Author(s):  
Shaogang Dai ◽  
Mingming Jin ◽  
Xiaofei Zhang
Keyword(s):  
Adaptive Filtering ◽  
Stable Distribution ◽  
Time Series Prediction ◽  
Gradient Estimation ◽  
Noise Environment ◽  
Affine Projection ◽  
Alpha Stable Distribution ◽  
Input Signals ◽  
Chaotic Time Series Prediction ◽  
Nonlinear Adaptive Filtering

Aiming at improving the performance of the nonlinear adaptive filtering under the alpha-stable distribution noise environment, Kernel Affine Projection P-norm (KAPP) algorithm based on the minimum dispersion coefficient criterion and the affine projection is deduced. The accuracy of the gradient estimation is enhanced by using the input signals and the error signals at multiple times. The simulation results on Mackey–Glass chaotic time series prediction show that the KAPP algorithm has faster convergence speed, better steady-state performance and stronger robustness under the Gaussian noise and stable distributed noise environment.

scholarly journals Application of Stable Distribution Theory-Based in Adaptive Filtering Algorithm

2014 ◽  
Vol 6 (1) ◽  
pp. 1856-1861
Author(s):  
Qiudong Yu ◽  
Kari Olkkonen
Keyword(s):  
Adaptive Filtering ◽  
Stable Distribution ◽  
Distribution Theory ◽  
Filtering Algorithm

Radar Clutter Recognition Using Alpha Stable Distribution

2011 ◽  
Vol 30 (9) ◽  
pp. 2042-2045 ◽  
Author(s):  
Xu-tao Li ◽  
Shou-yong Wang ◽  
Lian-wen Jin
Keyword(s):  
Stable Distribution ◽  
Radar Clutter ◽  
Alpha Stable Distribution

scholarly journals MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLES

2019 ◽  
Vol 35 (6) ◽  
pp. 1234-1270 ◽  
Author(s):  
Sébastien Fries ◽  
Jean-Michel Zakoian
Keyword(s):  
Conditional Distribution ◽  
Stable Distribution ◽  
Financial Time Series ◽  
Domain Of Attraction ◽  
Real Data ◽  
Autoregressive Processes ◽  
Financial Time ◽  
Causal Representation ◽  
Heavy Tailed ◽  
Non Gaussian

Noncausal autoregressive models with heavy-tailed errors generate locally explosive processes and, therefore, provide a convenient framework for modelling bubbles in economic and financial time series. We investigate the probability properties of mixed causal-noncausal autoregressive processes, assuming the errors follow a stable non-Gaussian distribution. Extending the study of the noncausal AR(1) model by Gouriéroux and Zakoian (2017), we show that the conditional distribution in direct time is lighter-tailed than the errors distribution, and we emphasize the presence of ARCH effects in a causal representation of the process. Under the assumption that the errors belong to the domain of attraction of a stable distribution, we show that a causal AR representation with non-i.i.d. errors can be consistently estimated by classical least-squares. We derive a portmanteau test to check the validity of the estimated AR representation and propose a method based on extreme residuals clustering to determine whether the AR generating process is causal, noncausal, or mixed. An empirical study on simulated and real data illustrates the potential usefulness of the results.

scholarly journals Unscented Particle Filter Algorithm Based on Divide-and-Conquer Sampling for Target Tracking

Sensors ◽  
2021 ◽  
Vol 21 (6) ◽  
pp. 2236
Author(s):  
Sichun Du ◽  
Qing Deng
Keyword(s):  
Particle Filter ◽  
State Space ◽  
Adaptive Filtering ◽  
Divide And Conquer ◽  
Particle Swarm Algorithm ◽  
Tracking Accuracy ◽  
Filtering Algorithm ◽  
Maneuvering Target ◽  
Unscented Particle Filter ◽  
Particle Filter Algorithm

Unscented particle filter (UPF) struggles to completely cover the target state space when handling the maneuvering target tracing problem, and the tracking performance can be affected by the low sample diversity and algorithm redundancy. In order to solve this problem, the method of divide-and-conquer sampling is applied to the UPF tracking algorithm. By decomposing the state space, the descending dimension processing of the target maneuver is realized. When dealing with the maneuvering target, particles are sampled separately in each subspace, which directly prevents particles from degeneracy. Experiments and a comparative analysis were carried out to comprehensively analyze the performance of the divide-and-conquer sampling unscented particle filter (DCS-UPF). The simulation result demonstrates that the proposed algorithm can improve the diversity of particles and obtain higher tracking accuracy in less time than the particle swarm algorithm and intelligent adaptive filtering algorithm. This algorithm can be used in complex maneuvering conditions.

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