GPS Coordinate Time Series Analysis Using Variance-Covariance Components Estimation

In recent decades,more and more GPS regional networks were used in geoscientific applications because of high precision and time resolution.The coordinates of these GPS stations in the regional networks could form the GPS station coordinate time series which could provide the data support for the geoscientific research,such as plate motion field and regional deformation.However,the time series revealed obvious nonlinear trend as well as the white noise and colored noise,which could affect the reliability of the coordinate time series analysis.Accordingly,it's meaningful for the geoscientific research to study the characteristic and origin of the nonlinear trend,correct the noise model(namely stochastic model),and estimate the plate motion model with the uncertainty on the basis of GPS stations velocity using Euler vector method.Consequently,this thesis put main focus on the extraction of nonlinear characteristic using time-frequency transform methods and the estimation of noise model using variance-covariance components estimation method(VCE).Further,this thesis calculated the annual amplitude caused by temperature varying and ground mass loading using the Green's function.In the meantime,we discussed the influence factor of the plate motion field.The main contents could be drawn as(1)This thesis described the data preprocess methods of GPS coordinate time series in details.These methods included IQR criterion and robust least square method for outlier detection,COL-STARTS method for offsets detection,cubic spline method and PCA method for data interpolation,stacking filter and correction stacking filter and PCA for common mode error.Then,we dealt with the GPS station coordinate time series using the above methods,which could provide dataset for the following research on the periodic characteristics and optimized noise model analysis.(2)This thesis described the modeling methods of GPS coordinate time series in details.These methods included four fitting model including regular model,timevarying method,local weighted regression model and ARMA model,four timefrequency transform method including FFT,Lomb-Scargle,Hilbert-Huang and Normal Time-Frequency Transform,the Green function method to calculate the environmental mass loading including the ground mass loading and temperature varying.Additionally,the Euler vector method was introduced to calculate the regional crustal movement speed field.(3)One new VCE method was proposed named Least-Square Variance-Covariance Estimation based on the Equivalent Condition Misclosure(LS-ECM).This thesis researched and pointed out the advantages and disadvantages of the maximum likelihood estimation(MLE)and VCE to estimate the optimized noise model.On the basis,this thesis used the VCE to calculate the noise components in the noise model.Aiming at the low calculation efficiency,we proposed the LS-ECM method and deduced the variance factor estimation formulas and variance estimation formulas.In the meantime,we introduce the w-test method to distinguish the noise species.(4)The thesis researched the characteristic of the 22 stations coordinate time series in Chinese field.The result of period estimation revealed integral long periods vary 3cpy to 6cpy and complicated short period besides annual and semi-annual periods existed in each station.On the basis of the result,we calculated the annual amplitude caused by ground mass loading and temperature varying,the result indicated that ground mass loading and temperature could cause 12 mm and 1mm annual amplitude in the vertical direction,respectively.The environmental loading is one source but not the only source of annual period.(5)This thesis carried out one calculation on the optimized noise amplitude using the w-test and LS-ECM.The results revealed that WN plus FN is the best noise model of the GPS stations in Chinese field,and the power of colored noise was more than the white noise.Based on the results,we analyzed the relation between the noise amplitude and the longitude and latitude,respectively,and then deduced the Chinese crustal motion model.