Analysis Of GNSS Coordinate Time Series Based On Matrix Low-rank Approximation

With the continuous development and improvement of global navigation satellite systems,GNSS continuous tracking observation sites that distributed around the world have accumulated a large amount of coordinate time series observation data.GNSS coordinate time series can not only be used to obtain various geophysical phenomena,the seasonal variation law of crustal movement and the speed of plate movement,but also provide strong data support for the construction and maintenance of the earth reference frame,which is of great significance to the research of geodesy and geodynamics.Due to seasonal temperature changes,ground mass loads,satellite system errors,and other unknown factors,GNSS coordinate time series usually show certain seasonal oscillations,especially in elevation components.Seasonal signals will not only affect the noise analysis,but also seriously affect the velocity estimation of GNSS station and the accuracy of International Terrestrial Reference Frame(ITRF).Therefore,in the high-precision crustal deformation monitoring,noise analysis,and the construction and maintenance of ITRF,it is necessary to accurately estimate the seasonal periodic signals.This thesis mainly focuses on the detection and extraction of seasonal signals in GNSS coordinate time series.From the perspective of matrix low-rank approximation,the application of matrix low rank approximation method in GNSS coordinate time series analysis is studied in detail.The main research content is divided into the following aspects:(1)The low rank property of Hankel matrix constructed by GNSS coordinate time series is proved.A matrix low-rank approximation method based on nuclear norm minimization is proposed to detect seasonal signals in GNSS coordinate time series.The effectiveness of the proposed method is verified by both the synthetic time series and the coordinate time series of real IGS site.(2)To make use of the prior information of matrix singular values,a weighted nuclear norm minimization is proposed to extract the seasonal signals in GNSS coordinate time series.Same as the nuclear norm minimization method,the weighted nuclear norm minimization can also be solved by the weighted singular value threshold strategy under certain conditions.The introduction of weight vector further improves the ability of the matrix low-rank approximation method in dealing with GNSS coordinate time series.Compared with the nuclear norm minimization method,the weighted nuclear norm minimization improves the accuracy of signal extraction,which is verified in both the synthetic time series and the real IGS time series.(3)In order to better approximate the rank minimization function,the non-convex log-sum function is adopted to replace the previous nuclear norm(or weighted nuclear norm),and a matrix low-rank approximation method based on log-sum regularization is proposed.With the property of super-gradient,this problem can finally be solved by iteratively updating the weighted nuclear norm minimization.Therefore,this method can be regarded as a generalization of the weighted nuclear norm method.That is,the weighted nuclear norm minimization can be regarded as a special case of this approach in some senses.Compared with the convex nuclear norm,the non-convex log-sum function is closer to the rank minimization problem,so it achieves a better performance in the application of synthetic time series and real IGS site data.(4)This thesis proposes an atomic norm minimization method for denoising the GNSS coordinate time series,and applies it to extract the seasonal signals in the real GNSS time series of China's regional IGS sites.Compared with the aforementioned matrix lowrank approximation method,this technology does not need to construct the Hankel matrix of the GNSS time series,and directly reduces the noise of original GNSS coordinate time series so as to extract the seasonal signal.The experimental results indicate that the atomic norm minimization is robust to colored noise,and it achieves reasonable results in the elevation time series of real IGS sites in China.The innovations of this thesis mainly include the following two aspects:(1)It is proved that the Hankel matrix constructed by the GNSS coordinate time series is low-rank,and the matrix low-rank approximation method is adopted to detect and extract the seasonal signals in the GNSS coordinate time series.(2)Atomic norm minimization is proposed to analyse the GNSS coordinate time series.GNSS coordinate time series is denoised by atomic norm minimization,so as to separate the signal and noise in GNSS time series.