Abstract
Alpha stable noise, determined by four parameters, has been found in the random error of a laser gyroscope. Accurate estimation of the four parameters is the key process for analyzing the properties of alpha stable noise. Three widely used estimation methods—quantile, empirical characteristic function (ECF) and logarithmic moment method—are analyzed in contrast with Monte Carlo simulation in this paper. The estimation accuracy and the application conditions of all methods, as well as the causes of poor estimation accuracy, are illustrated. Finally, the highest precision method, ECF, is applied to 27 groups of experimental data to estimate the parameters of alpha stable noise in a laser gyroscope’s random error. The cumulative probability density curve of the experimental data fitted by an alpha stable distribution is better than that by a Gaussian distribution, which verifies the existence of alpha stable noise in a laser gyroscope’s random error.
Highlights
Despite a strong theoretical background and wide applications, Gaussian noise is inappropriate for modeling noise with an impulsive nature, which could be shown in the form of significant data mutation
There exist many non-Gaussian signals with an impulsive nature and heavy tail in real life, including underwater signals, atmospheric environment signals, telephone line noise and some mobile communication signals [3,4,5,6,7]; secondly, alpha stable distribution has stable properties; thirdly, the Central Limit Theorem is popularized in cases where the second moment does not exist; and there have been many successful applications in various areas [8,9,10,11,12], such as economics, physics, astronomy, biology, electrical engineering and so on
Three widely used estimation methods are analyzed in contrast with Monte Carlo simulation, and the method with highest precision is used to estimate the parameters of alpha stable noise in a laser gyroscope’s random error based on experiment data
Summary
Despite a strong theoretical background and wide applications, Gaussian noise is inappropriate for modeling noise with an impulsive nature, which could be shown in the form of significant data mutation. There are noises with a strong impulsive nature which the Gaussian model fails to describe, such as atmospheric noise caused by lighting, picture noise, radar noise and so on These noises possess a common feature, namely their impulsive nature, which means that both the frequency and the magnitude of their data mutation are higher than what Gaussian noise describes. Three widely used estimation methods are analyzed in contrast with Monte Carlo simulation, and the method with highest precision is used to estimate the parameters of alpha stable noise in a laser gyroscope’s random error based on experiment data. The method with the highest precision is applied to the experiment data to estimate the parameters of the alpha stable noise in the laser gyroscope’s random error.
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