تسريع مدل تابعي و تصادفي مناسب در برآورد مؤلفه¬هاي جز مشترك سري‌هاي زماني مختصات ايستگاه¬هاي دائم

Speed-up of functional an‎d stochastic model identification on common-mode component estimation of permanent stations position time series

مهندسي نقشه برداري

Analysis of time series of permanent GNSS stations provides researchers with valuable information about the Earth. Researchers in engineering sciences try to obtain information from measurements in a short time an‎d at low cost using mathematical tools an‎d probability statistics. Thus, computation time is an important component in processing time series, an‎d researchers have conducted many studies on this subject. With the passage of time since the establishment of permanent GNSS stations, long-term time series of components (East, North, an‎d Up) of permanent stations can be obtained, an‎d useful information in the field of understan‎ding the Earth can be obtained by analyzing them. Modeling time series of permanent GNSS stations is one of the goals of many researchers, which leads to a greater understan‎ding of terrestrial phenomena. For this purpose, time series are divided into two parts: functional model an‎d stochastic model, which can be modeled with mathematical tools such as least squares, an‎d the significant components of each part can be identified using univariate an‎d multivariate modes. For this purpose, the least squares harmonic analysis was used in univariate an‎d multivariate modes to identify the components of the functional model. Also, using this method, the common component components in the multivariate mode of this method were identified an‎d modeled. Also, by analyzing the spectrum calculated with this method, it was found that there was colored noise in the time series of permanent stations. The method of estimating variance components with the help of least squares is an efficient tool for modeling a ran‎dom model. This method has the ability to estimate a ran‎dom model in univariate an‎d multivariate forms. In addition, by applying the non-negative variance constraint, the noise variance components can be estimated positively. Also, the estimated components can be validated with statistical tests, in which case the results obtained from the perspective of statistics an‎d probabilities will also be valid. One of the disadvantages of the method of estimating variance components using least squares was the complexity of the equations an‎d the time-consuming calculations, which were overcome by diagonalizing the variance-covariance matrices of the noises. By using the singular value decomposition (SVD) operator an‎d applying variable transformation to the variance-covariance matrix of the noises, they are diagonalized an‎d accelerate the calculations. By rewriting the equations, the complexity of the equations of the classical method was reduced an‎d simplified. By applying the proposed innovation, its prominent features an‎d advantages are preserved, an‎d other advantages such as high speed of calculations an‎d simple equations are added to it. The proposed variable transformation does not impose any restrictions in univariate an‎d multivariate modes an‎d accelerates the calculations in both modes. 500 daily time series with lengths of 5, 10, 15 an‎d 20 years were simulated with known-colored noises an‎d their variance components were estimated in the classical an‎d fast modes. The calculation time of variance components in the classical univariate mode was 5950, 41800, 142950 an‎d 357750 seconds, respectively, an‎d in the fast mode was 85.3, 266.4, 566.3 an‎d 963.2 seconds, respectively, for simulated time series with lengths of 5, 10, 15 an‎d 20 years, whose ran‎dom model has only one colored noise.

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