Automatic Calibration of Process Noise Matrix and Measurement Noise Covariance for Multi-GNSS Precise Point Positioning

doi:10.3390/math8040502

	Automatic Calibration of Process Noise Matrix and Measurement Noise Covariance for Multi-GNSS Precise Point Positioning
	Zhang, Xinggang 2,3,4; Li, Pan 2; Tu, Rui 3,4; Lu, Xiaochun 3,4; Ge, Maorong 1,2; Schuh, Harald 1,2
刊名	MATHEMATICS
	2020-04-01
卷号	8 期号:4 页码:20
关键词	EM-algorithm multi-GNSS PPP process noise observation covariance matrix extended Kalman filter machine learning
DOI	10.3390/math8040502
英文摘要	The Expectation-Maximization algorithm is adapted to the extended Kalman filter to multiple GNSS Precise Point Positioning (PPP), named EM-PPP. EM-PPP considers better the compatibility of multiple GNSS data processing and characteristics of receiver motion, targeting to calibrate the process noise matrix Q(t) and observation matrix R-t, having influence on PPP convergence time and precision, with other parameters. It is possibly a feasible way to estimate a large number of parameters to a certain extent for its simplicity and easy implementation. We also compare EM-algorithm with other methods like least-squares (co)variance component estimation (LS-VCE), maximum likelihood estimation (MLE), showing that EM-algorithm from restricted maximum likelihood (REML) will be identical to LS-VCE if certain weight matrix is chosen for LS-VCE. To assess the performance of the approach, daily observations from a network of 14 globally distributed International GNSS Service (IGS) multi-GNSS stations were processed using ionosphere-free combinations. The stations were assumed to be in kinematic motion with initial random walk noise of 1 mm every 30 s. The initial standard deviations for ionosphere-free code and carrier phase measurements are set to 3 m and 0.03 m, respectively, independent of the satellite elevation angle. It is shown that the calibrated R-t agrees well with observation residuals, reflecting effects of the accuracy of different satellite precise product and receiver-satellite geometry variations, and effectively resisting outliers. The calibrated Q(t) converges to its true value after about 50 iterations in our case. A kinematic test was also performed to derive 1 Hz GPS displacements, showing the RMSs and STDs w.r.t. real-time kinematic (RTK) are improved and the proper Q(t) is found out at the same time. According to our analysis despite the criticism that EM-PPP is very time-consuming because a large number of parameters are calculated and the first-order convergence of EM-algorithm, it is a numerically stable and simple approach to consider the temporal nature of state-space model of PPP, in particular when Q(t) and R-t are not known well, its performance without fixing ambiguities can even parallel to traditional PPP-RTK.
资助项目	China Scholarship Council (CSC) ; Chinese Academy of Sciences (CAS) program of "Light of West China"[29Y607YR000103] ; Chinese Academy of Science, Russia ; Chinese Academy of Science, Ukraine ; National Natural Science Foundation of China[41674034] ; National Natural Science Foundation of China[41974032] ; National Natural Science Foundation of China[11903040] ; Chinese Academy of Sciences (CAS) programs of "Pioneer Hundred Talents"[Y923YC1701] ; Chinese Academy of Sciences (CAS) program of "Western Youth Scholar"[Y712YR4701] ; Chinese Academy of Sciences (CAS) program of "Western Youth Scholar"[Y916YRa701] ; Chinese Academy of Sciences (CAS) program of "The Frontier Science Research Project"[QYZDB-SSW-DQC028] ; [2BY711HZ000101]
WOS关键词	GPS ; MODEL ; PPP
WOS研究方向	Mathematics
语种	英语
出版者	MDPI
WOS记录号	WOS:000531824100042
资助机构	China Scholarship Council (CSC) ; China Scholarship Council (CSC) ; Chinese Academy of Sciences (CAS) program of "Light of West China" ; Chinese Academy of Sciences (CAS) program of "Light of West China" ; Chinese Academy of Science, Russia ; Chinese Academy of Science, Russia ; Chinese Academy of Science, Ukraine ; Chinese Academy of Science, Ukraine ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Chinese Academy of Sciences (CAS) programs of "Pioneer Hundred Talents" ; Chinese Academy of Sciences (CAS) programs of "Pioneer Hundred Talents" ; Chinese Academy of Sciences (CAS) program of "Western Youth Scholar" ; Chinese Academy of Sciences (CAS) program of "Western Youth Scholar" ; Chinese Academy of Sciences (CAS) program of "The Frontier Science Research Project" ; Chinese Academy of Sciences (CAS) program of "The Frontier Science Research Project" ; China Scholarship Council (CSC) ; China Scholarship Council (CSC) ; Chinese Academy of Sciences (CAS) program of "Light of West China" ; Chinese Academy of Sciences (CAS) program of "Light of West China" ; Chinese Academy of Science, Russia ; Chinese Academy of Science, Russia ; Chinese Academy of Science, Ukraine ; Chinese Academy of Science, Ukraine ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Chinese Academy of Sciences (CAS) programs of "Pioneer Hundred Talents" ; Chinese Academy of Sciences (CAS) programs of "Pioneer Hundred Talents" ; Chinese Academy of Sciences (CAS) program of "Western Youth Scholar" ; Chinese Academy of Sciences (CAS) program of "Western Youth Scholar" ; Chinese Academy of Sciences (CAS) program of "The Frontier Science Research Project" ; Chinese Academy of Sciences (CAS) program of "The Frontier Science Research Project" ; China Scholarship Council (CSC) ; China Scholarship Council (CSC) ; Chinese Academy of Sciences (CAS) program of "Light of West China" ; Chinese Academy of Sciences (CAS) program of "Light of West China" ; Chinese Academy of Science, Russia ; Chinese Academy of Science, Russia ; Chinese Academy of Science, Ukraine ; Chinese Academy of Science, Ukraine ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Chinese Academy of Sciences (CAS) programs of "Pioneer Hundred Talents" ; Chinese Academy of Sciences (CAS) programs of "Pioneer Hundred Talents" ; Chinese Academy of Sciences (CAS) program of "Western Youth Scholar" ; Chinese Academy of Sciences (CAS) program of "Western Youth Scholar" ; Chinese Academy of Sciences (CAS) program of "The Frontier Science Research Project" ; Chinese Academy of Sciences (CAS) program of "The Frontier Science Research Project" ; China Scholarship Council (CSC) ; China Scholarship Council (CSC) ; Chinese Academy of Sciences (CAS) program of "Light of West China" ; Chinese Academy of Sciences (CAS) program of "Light of West China" ; Chinese Academy of Science, Russia ; Chinese Academy of Science, Russia ; Chinese Academy of Science, Ukraine ; Chinese Academy of Science, Ukraine ; National Natural Science Foundation of China ; National Natural Science Foundation of China ; Chinese Academy of Sciences (CAS) programs of "Pioneer Hundred Talents" ; Chinese Academy of Sciences (CAS) programs of "Pioneer Hundred Talents" ; Chinese Academy of Sciences (CAS) program of "Western Youth Scholar" ; Chinese Academy of Sciences (CAS) program of "Western Youth Scholar" ; Chinese Academy of Sciences (CAS) program of "The Frontier Science Research Project" ; Chinese Academy of Sciences (CAS) program of "The Frontier Science Research Project"
内容类型	期刊论文
源URL	[http://210.72.145.45/handle/361003/9366]
专题	国家授时中心_导航与通信研究室
通讯作者	Li, Pan
作者单位	1.Tech Univ Berlin, Inst Geodesy & Geoinformat Sci, Berlin 10623, Germany 2.German Res Ctr Geosci GFZ, Potsdam 14473, Germany 3.Chinese Acad Sci, Key Lab Precis Nav Positioning & Timing Technol, Xian 710600, Peoples R China 4.Chinese Acad Sci, Natl Time Serv Ctr, Shu Yuan Rd, Xian 710600, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Xinggang,Li, Pan,Tu, Rui,et al. Automatic Calibration of Process Noise Matrix and Measurement Noise Covariance for Multi-GNSS Precise Point Positioning[J]. MATHEMATICS,2020,8(4):20.
APA	Zhang, Xinggang,Li, Pan,Tu, Rui,Lu, Xiaochun,Ge, Maorong,&Schuh, Harald.(2020).Automatic Calibration of Process Noise Matrix and Measurement Noise Covariance for Multi-GNSS Precise Point Positioning.MATHEMATICS,8(4),20.
MLA	Zhang, Xinggang,et al."Automatic Calibration of Process Noise Matrix and Measurement Noise Covariance for Multi-GNSS Precise Point Positioning".MATHEMATICS 8.4(2020):20.