Effect of Using Different Types of Threshold Schemes (in Wavelet Space) on Noise Reduction over GPS Times Series

The goal of this study is the role of using different thresholding effects on types of noise reductions based on wavelet schemes. Assumed thresholding techniques are penalized threshold، Birgé-Masssart Strategy، SureShrink threshold، universal threshold، minimax threshold and Stein’s unbiased risk estimate. In order to compare the performance of them in denoising of types of noise components (white noise، flicker noise and random walk noise) we have constructed three kinds of stochastic models: the pure white noise model (I)، the white plus random walk noise model (II) and the white plus flicker noise model (III). The numerical computations are performed through the analyzing 10 years (Jan 2001 to Jan 2011) of raw daily GPS solutions which are selected of 264 stations of SOPAC. According to results of computations، among the thresholding schemes in de-noising of the pure white noise model (I): minimax threshold and Stein’s unbiased risk estimate could reduce the distribution of low amplitude of white noise. However، minimax threshold and SureShrink threshold could reduce the distribution of high amplitude of white noise. Birgé-Masssart Strategy and universal threshold could reduce both low and high amplitudes of white noise. In model II (white noise plus random walk noise) and model III (white noise plus flicker noise)، all of threshold schemes could reduce both high and low amplitudes of white noise in same level. Whereas for power-law noise (flicker noise and random walk noise) penalized threshold and Stein’s unbiased risk estimate led to reduction of low amplitudes and SureShrink threshold and minimax threshold led to reduction of colored noise with high amplitudes. Birgé-Masssart Strategy and universal threshold could reduce both low and high amplitudes of colored noise.