Noise Analysis of GPS Time Series with Simulated Data Using EMD, Standard Deviation and Trigonometric Methods

Due to the wide application of GPS time series such as the study of tectonic movements, land crust change and earthquake dynamics, etc., it is important to provide a method to increase the speed in the analysis of variance components. Researchers have shown that nearly 90% of GPS time series have a combination of white+flickr noise and a lower percentage have a combination of white+random-walk noise. Researchers have used a trigonometric relationship inside the maximum likelihood estimation (MLE) method, to reduce the dimensions; instead of calculating 3 unknowns (white, flicker and random-walk noise components) they calculated 2 unknowns, a phase such as phi introducing relationship between white noise and colored noise and a phase such as theta introducing relationship between two colored noise (flicker and random-walk noises). On the other hand, researchers have been able to estimate white noise by empirical mode decomposition (EMD). In this research first we try to estimate the white noise using EMD method and then with the mentioned trigonometric relation, we can estimate the flicker or random-walk noise. It is expected that if this project is successful, the noise components will be estimated immediately. Finally, the results of the proposed method are compared to the results of least square variance estimation (LS-VCE) method. In another new method, since white noise can be extracted and separated by EMD, first white noise is extracted and then GPS time series components including linear trend, periodic movements with annual and semi-annual frequencies are extracted by least squares. The type of colored noise (flicker or random noise) can be determined by the Hurst parameter and assuming that the residual is flicker or random-walk noise, the statistical information of colored noise can be estimated (standard deviation method). The methods were first tested on simulated series and after its success, real GPS time series were used for verification. In this study, extracting white noise by EMD has been fundamentally reviewed; including how to decompose and how to detect white noise through intrinsic mode functions (IMFs) by Hurst parameter. Among Hurst parameter estimation methods, 12 methods were evaluated and boxed-periodogram method had better results. The results of the new methods are very efficient for simulated and GPS time series with white+flicker noise, but challenging for series with white+random-walk noise.