The Alpha stable distribution in ocean ambient noise modelling

Song, Guoli; Guo, Xinglin; Ma, Lingling

doi:10.1051/matecconf/201928308002

Cited by 6 publications

(3 citation statements)

References 14 publications

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“…Among the parameters of the stable distribution, the parameter α is called the characteristic index, which determines the degree of the pulse characteristics of the distribution, the thicker the tail of the corresponding distribution, the larger the α value, the closer the distribution is to the Gaussian distribution, and the maximum α is 2. 26 The parameter β is called the symmetry parameter and is used to determine the slope of the distribution. β =0 corresponds to a symmetric distribution, abbreviated as SaS.…”

Section: Protection Levels Calculation Under Multi-parameter Stable O...mentioning

confidence: 99%

A multi-parameter stable-distribution-based protection levels calculation method for ground-based augmentation systems integrity assessment

Liu

Shi

Sun

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part G:

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The Protection Levels (PL) of Ground-Based Augmentation Systems (GBAS) are bounds of the positioning errors associated with given integrity levels. However, the practical Gaussian Overbounding Method (GOM) cannot describe the non-Gaussian nature of the error model such as “thick tail,” which makes PL tend to be overestimated. To overcome this problem, an error overbounding model based on stable distribution is proposed in this paper. Four stable distribution parameters are involved to accurately describe the GBAS ranging error. The weighted summation feature of the stable distribution is combined with the maximum likelihood estimation when calculating PL. Thus, it is possible to achieve a higher accuracy of PL under similar calculation complexity. In addition, this paper puts forward the Concept of Tightness (CoT) to describe the overbounding effect intuitively and quantitatively. In order to verify the effect of this method, multiple receivers are set to simulate the GBAS system, theyn the Stable Overbounding Method (SOM) is used to calculate the PL in two directions (Vertical and Lateral) under the hypotheses of H0 and H1. The CoT convincingly proves that the SOM has a better overbounding effect and improves the continuity of GBAS. It is evident that the multi-parameter SOM makes the overbounding of the protection level tighter and reduces the probability that the protection level is close to the Alarm Limit (AL), thus improving the accuracy of PL computing and the availability of GBAS systems.

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Section: Protection Levels Calculation Under Multi-parameter Stable O...mentioning

confidence: 99%

A multi-parameter stable-distribution-based protection levels calculation method for ground-based augmentation systems integrity assessment

Liu

Shi

Sun

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part G:

View full text Add to dashboard Cite

show abstract

“…Existing underwater-acoustic-signal-processing methods may be invalidated under such non-Gaussian impulsive noise. To overcome this problem, several studies [16][17][18] have performed statistical analyses and models of non-Gaussian marine ambient noise. It was found that the generation and propagation of underwater impulsive noise are in accordance with the "heavy tail" statistical characteristics of the symmetric α-stable (SαS) distribution [19].…”

Section: Introductionmentioning

confidence: 99%

Joint Detection and Reconstruction of Weak Spectral Lines under Non-Gaussian Impulsive Noise with Deep Learning

Guo

Wang

2023

Remote Sensing

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Non-Gaussian impulsive noise in marine environments strongly influences the detection of weak spectral lines. However, existing detection algorithms based on the Gaussian noise model are futile under non-Gaussian impulsive noise. Therefore, a deep-learning method called AINP+LR-DRNet is proposed for joint detection and the reconstruction of weak spectral lines. First, non-Gaussian impulsive noise suppression was performed by an impulsive noise preprocessor (AINP). Second, a special detection and reconstruction network (DRNet) was proposed. An end-to-end training application learns to detect and reconstruct weak spectral lines by adding into an adaptive weighted loss function based on dual classification. Finally, a spectral line-detection algorithm based on DRNet (LR-DRNet) was proposed to improve the detection performance. The simulation indicated that the proposed AINP+LR-DRNet can detect and reconstruct weak spectral line features under non-Gaussian impulsive noise, even for a mixed signal-to-noise ratio as low as −26 dB. The performance of the proposed method was validated using experimental data. The proposed AINP+LR-DRNet detects and reconstructs spectral lines under strong background noise and interference with better reliability than other algorithms.

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“…erefore, improved bispectrum methods which can be applicable to α-stable distribution environment need to be explored. Recently, α-stable distribution model was used for statistical modeling of the ocean environmental noise [31].…”

Section: Introductionmentioning

confidence: 99%

Fault Characteristic Extraction by Fractional Lower-Order Bispectrum Methods

Wang

Long

Liu

et al. 2020

Mathematical Problems in Engineering

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The generated signals generally contain a large amount of background noise when the mechanical bearing fails, and the fault signals present nonlinear and non-Gaussian feature, which have heavy tail and belong to α -stable distribution ( 1 < α < 2 ); even the background noises are also α -stable distribution process. Then it is difficult to obtain reliable conclusion by using the traditional bispectral analysis method under α -stable distribution environment. Two improved bispectrum methods are proposed based on fractional lower-order covariation in this paper, including fractional low-order direct bispectrum (FLODB) method, fractional low-order indirect bispectrum (FLOIDB) method. In order to decrease the estimate variance and increase the bispectral flatness, the fractional lower-order autoregression (FLOAR) model bispectrum and fractional lower-order autoregressive moving average (FLOARMA) model bispectrum methods are presented, and their calculation steps are summarized. We compare the improved bispectrum methods with the conventional methods employing second-order statistics in Gaussian and S α S distribution environments; the simulation results show that the improved bispectrum methods have performance advantages compared to the traditional methods. Finally, we use the improved methods to estimate the bispectrum of the normal and outer race fault signal; the result indicates that they are feasible and effective for fault diagnosis.

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The Alpha stable distribution in ocean ambient noise modelling

Cited by 6 publications

References 14 publications

A multi-parameter stable-distribution-based protection levels calculation method for ground-based augmentation systems integrity assessment

A multi-parameter stable-distribution-based protection levels calculation method for ground-based augmentation systems integrity assessment

Joint Detection and Reconstruction of Weak Spectral Lines under Non-Gaussian Impulsive Noise with Deep Learning

Fault Characteristic Extraction by Fractional Lower-Order Bispectrum Methods

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