The Alpha stable distribution in ocean ambient noise modelling

Key Laboratory of Underwater Acoustic Environment, Institute of Acoustics, CAS, 100190, Beijing, China

^* Corresponding author: guoxinyi@mail.ioa.ac.cn

Abstract

In view of the non-Gaussian of ocean ambient noise, the  stable distribution is applied to the statistical modelling. Firstly, the one-to-one correspondence between the four parameters of stable distribution and the sample mean, variance, skewness and kurtosis are established according to physical meaning. Then, numerical simulations are conducted to analyze the suitability of stable distribution for non-Gaussian ambient noise. In the case of white noise interference, noise is divided into Gaussian state, leptokurtic, and platykurtic separately. The parameters of stable distribution are estimated by the sample quantile and characteristic function method jointly. The simulation results show that, in the Gaussian state,  stable distribution is equivalent to normal distribution. As for leptokurtic distribution, stable distribution is much better than normal distribution, indicating absolute predominance in impulse-like data modeling. But it is not adaptive for low kurtosis state because its characteristic exponent can’t be bigger than two. Finally, the result is verified by ambient noise collected in three environmental conditions, such as quiet ambient noise, airgun interference noise and ship noise. In all three cases,  stable distribution shows good adaptability and accuracy, especially for the airgun dataset it is far superior to normal distribution.