Extract Common-Mode Error in Middle-Scale GPS Network Using Principal Component Analysis

2016 ◽  
pp. 371-379
Author(s):  
Hao Zhang ◽  
Cuilin Kuang ◽  
Chenlong Lu
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Common Mode ◽  
Common Mode Error ◽  
Gps Network

scholarly journals Extracting Common Mode Errors of Regional GNSS Position Time Series in the Presence of Missing Data by Variational Bayesian Principal Component Analysis

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2298 ◽  
Author(s):  
Wudong Li ◽  
Weiping Jiang ◽  
Zhao Li ◽  
Hua Chen ◽  
Qusen Chen ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Time Series ◽  
Missing Data ◽  
Principal Component ◽  
Component Analysis ◽  
Common Mode ◽  
Variational Bayesian ◽  
North East ◽  
Position Time Series ◽  
Gnss Position Time Series

Removal of the common mode error (CME) is very important for the investigation of global navigation satellite systems’ (GNSS) error and the estimation of an accurate GNSS velocity field for geodynamic applications. The commonly used spatiotemporal filtering methods normally process the evenly spaced time series without missing data. In this article, we present the variational Bayesian principal component analysis (VBPCA) to estimate and extract CME from the incomplete GNSS position time series. The VBPCA method can naturally handle missing data in the Bayesian framework and utilizes the variational expectation-maximization iterative algorithm to search each principal subspace. Moreover, it could automatically select the optimal number of principal components for data reconstruction and avoid the overfitting problem. To evaluate the performance of the VBPCA algorithm for extracting CME, 44 continuous GNSS stations located in Southern California were selected. Compared to previous approaches, VBPCA could achieve better performance with lower CME relative errors when more missing data exists. Since the first principal component (PC) extracted by VBPCA is remarkably larger than the other components, and its corresponding spatial response presents nearly uniform distribution, we only use the first PC and its eigenvector to reconstruct the CME for each station. After filtering out CME, the interstation correlation coefficients are significantly reduced from 0.43, 0.46, and 0.38 to 0.11, 0.10, and 0.08, for the north, east, and up (NEU) components, respectively. The root mean square (RMS) values of the residual time series and the colored noise amplitudes for the NEU components are also greatly suppressed, with average reductions of 27.11%, 28.15%, and 23.28% for the former, and 49.90%, 54.56%, and 49.75% for the latter. Moreover, the velocity estimates are more reliable and precise after removing CME, with average uncertainty reductions of 51.95%, 57.31%, and 49.92% for the NEU components, respectively. All these results indicate that the VBPCA method is an alternative and efficient way to extract CME from regional GNSS position time series in the presence of missing data. Further work is still required to consider the effect of formal errors on the CME extraction during the VBPCA implementation.

ICA Spatiotemporal Filtering Method and Its Application in GPS Deformation Monitoring

2012 ◽  
Vol 204-208 ◽  
pp. 2806-2812 ◽  
Author(s):  
Da Wei Huang ◽  
Wu Jiao Dai ◽  
Fei Xue Luo
Keyword(s):  
Simulated Data ◽  
Component Analysis ◽  
Deformation Monitoring ◽  
Common Mode ◽  
Spatiotemporal Filtering ◽  
Filtering Method ◽  
Independent Components ◽  
Common Mode Error ◽  
Gps Network ◽  
Filtering Effect

Principal component analysis (PCA) is a good method to be used in spatiotemporal filtering for regional GPS network. As an extension of PCA, independent component analysis(ICA) is also widely concerded in many fields of sciences and application researches. As a new spatiotemporal filtering method, the application of ICA in spatiotemporal filtering of the regional GPS network and GPS deformation monitoring is explored in this paper. The simulated data test shows the filtering effect of ICA is the same as PCA, both of the PCA and ICA can extract two independent components which implied in simulated common mode error. At the same time, the SCIGN data test shows the filtering effect of ICA is a litter worse than PCA, but ICA extracts not only one independent components as common mode error, it is not unique and independence that can not be provided by the PCA method. It also reflects the essence of common mode error of different station in independence. Therefore, ICA method can be applied to GPS deformation monitoring as a new spatiotemporal filtering method, the feasibility and advantage of ICA is demonstrated in the experiment of simulated data and SCIGN data.

Noise Analysis Method of Radiated EMI based on Non-linear Principal Component Analysis

2020 ◽  
Vol 35 (10) ◽  
pp. 1144-1152
Author(s):  
Zhibo Zhu ◽  
Wei Yan ◽  
Yongan Wang ◽  
Yang Zhao ◽  
Tao Zhang ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Electromagnetic Interference ◽  
Noise Analysis ◽  
Near Field ◽  
Principal Component ◽  
Component Analysis ◽  
Differential Mode ◽  
Noise Sources ◽  
Common Mode ◽  
Non Linear

Aiming at the radiated electromagnetic interference (EMI) noise of electronic equipment, a novel method of radiated EMI noise analysis based on non-linear principal component analysis (NLPCA) algorithm is proposed in this paper. In order to obtain multiple independent common-mode / differential-mode radiated sources, and to find the sources that cause the radiated noises that exceed the limit of standard, NLPCA algorithm is used to process the near-field radiated signals superimposed by multiple radiated sources. The simulation results show that NLPCA can successfully screen out the radiated EMI noises which exceed the limit of standard. Moreover, the experiments are carried out with three models: double-common-mode hybrid sources, double-differential-mode hybrid sources and common-differential-mode hybrid sources. Compared with the traditional independent component algorithm (ICA), the method proposed in this paper can separate the radiated EMI noise sources more accurately and quickly. It can be concluded that the accuracy of NLPCA algorithm is 10% higher than ICA algorithm. This work will contribute to trace the radiated EMI noise sources, and to provide the theoretical basis for the future suppression.

Extracting Common Mode Errors of Regional GNSS Position Time Series in the Presence of Missing Data by Expectation-Maximization Principal Component Analysis

2020 ◽  
Author(s):  
wudong li ◽  
weiping jiang
Keyword(s):  
Principal Component Analysis ◽  
Time Series ◽  
Missing Data ◽  
Expectation Maximization ◽  
Principal Component ◽  
Component Analysis ◽  
Computational Time ◽  
Common Mode ◽  
Position Time Series ◽  
Gnss Position Time Series

<p>Removal of the Common Mode Error (CME) is very important for the investigation of Global Navigation Satellite Systems (GNSS) technique error and the estimation of accurate GNSS velocity field for geodynamic applications. The commonly used spatiotemporal filtering methods cannot accommodate missing data, or they have high computational complexity when dealing with incomplete data. This research presents the Expectation-Maximization Principal Component Analysis (EMPCA) to estimate and extract CME from the incomplete GNSS position time series. The EMPCA method utilizes an Expectation-Maximization iterative algorithm to search each principal subspace, which allows extracting a few eigenvectors and eigenvalues without covariance matrix and eigenvalue decomposition computation. Moreover, it could straightforwardly handle the missing data by Maximum Likelihood Estimation (MLE) at each iteration. To evaluate the performance of the EMPCA algorithm for extracting CME, 44 continuous GNSS stations located in Southern California have been selected here. Compared to previous approaches, EMPCA could achieve better performance using less computational time and exhibit slightly lower CME relative errors when more missing data exists. Since the first Principal Component (PC) extracted by EMPCA is remarkably larger than the other components, and its corresponding spatial response presents nearly uniform distribution, we only use the first PC and its eigenvector to reconstruct the CME for each station. After filtering out CME, the interstation correlation coefficients are significantly reduced from 0.46, 0.49, 0.42 to 0.18, 0.17, 0.13 for the North, East, and Up (NEU) components, respectively. The Root Mean Square (RMS) values of the residual time series and the colored noise amplitudes for the NEU components are also greatly suppressed, with an average reduction of 25.9%, 27.4%, 23.3% for the former, and 49.7%, 53.9%, and 48.9% for the latter. Moreover, the velocity estimates are more reliable and precise after removing CME, with an average uncertainty reduction of 52.3%, 57.5%, and 50.8% for the NEU components, respectively. All these results indicate that the EMPCA method is an alternative and more efficient way to extract CME from regional GNSS position time series in the presence of missing data. Further work is still required to consider the effect of formal errors on the CME extraction during the EMPCA implementation.</p>

A German version of the Intermittent Claudication Questionnaire (ICQ): cultural adaptation and validation

VASA ◽  
2012 ◽  
Vol 41 (5) ◽  
pp. 333-342 ◽  
Author(s):  
Kirchberger ◽  
Finger ◽  
Müller-Bühl
Keyword(s):  
Principal Component Analysis ◽  
Intermittent Claudication ◽  
Completion Time ◽  
Short Form ◽  
Principal Component ◽  
Component Analysis ◽  
German Version ◽  
Average Completion Time ◽  
Sf 36 ◽  
Related Quality

Background: The Intermittent Claudication Questionnaire (ICQ) is a short questionnaire for the assessment of health-related quality of life (HRQOL) in patients with intermittent claudication (IC). The objective of this study was to translate the ICQ into German and to investigate the psychometric properties of the German ICQ version in patients with IC. Patients and methods: The original English version was translated using a forward-backward method. The resulting German version was reviewed by the author of the original version and an experienced clinician. Finally, it was tested for clarity with 5 German patients with IC. A sample of 81 patients were administered the German ICQ. The sample consisted of 58.0 % male patients with a median age of 71 years and a median IC duration of 36 months. Test of feasibility included completeness of questionnaires, completion time, and ratings of clarity, length and relevance. Reliability was assessed through a retest in 13 patients at 14 days, and analysis of Cronbach’s alpha for internal consistency. Construct validity was investigated using principal component analysis. Concurrent validity was assessed by correlating the ICQ scores with the Short Form 36 Health Survey (SF-36) as well as clinical measures. Results: The ICQ was completely filled in by 73 subjects (90.1 %) with an average completion time of 6.3 minutes. Cronbach’s alpha coefficient reached 0.75. Intra-class correlation for test-retest reliability was r = 0.88. Principal component analysis resulted in a 3 factor solution. The first factor explained 51.5 of the total variation and all items had loadings of at least 0.65 on it. The ICQ was significantly associated with the SF-36 and treadmill-walking distances whereas no association was found for resting ABPI. Conclusions: The German version of the ICQ demonstrated good feasibility, satisfactory reliability and good validity. Responsiveness should be investigated in further validation studies.

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