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

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.

Analysis of BDS Fractional Cycle Biases and PPP Ambiguity Resolution.

It is difficult to enable traditional precise point positioning (PPP) with ambiguity resolution (AR) due to fractional cycle biases (FCBs), which limit the accuracy and reliability of positioning results. The BeiDou Navigation Satellite System (BDS) has been providing continuous positioning, navigation, and timing (PNT) services in the global region since the end of 2018. The BDS constellation includes geostationary earth orbit (GEO), inclined geostationary orbit (IGSO), and medium earth orbit (MEO) satellites. However, its hybrid constellation structure and the satellite-side multipath effect have hindered the BDS PPP AR for two main reasons: (1) some receivers have half-cycle biases between GEO and non-GEO satellites, which result in the inconsistency of hardware delays for each satellite type; (2) the correction model for elevation-dependent satellite-side multipath effect is only applicable to IGSO and MEO, while in the case of GEO the effect cannot be effectively weakened or eliminated. To rectify these problems, a suitable strategy is proposed for estimating BDS FCBs, whereby the GEO FCBs and non-GEO FCBs are estimated independently. Results show that the FCBs estimated by the new strategy for GEO and non-GEO are more stable compared to the traditional strategy. The GEO wide-lane (WL) FCBs fluctuate less than 0.3 cycle in one month, except for C05, while the variation of non-GEO WL FCBs is about 0.1 cycle. In addition, compared to the traditional strategy, the fractions of GEO WL ambiguities after the removal of FCBs estimated by the new strategy can be improved noticeably from 53.5% to 78.5%, and from 71.8% to 92.3% for <0.15 cycle and <0.25 cycle respectively, which could be comparable with non-GEO. Simultaneously, the improvement of GEO narrow-lane (NL) ambiguities is from 28.9% to 40.2%, and from 40.4% to 53.3% for <0.10 cycle and <0.15 cycle respectively, are less noticeable. This is mainly due to the low precision IGS products for GEO. After PPP AR, the mean convergence time is shorted from 56.0 min to 43.6 min, and from 71.6 min to 62.7 min for static PPP and kinematic PPP, respectively.

Effective Cycle Slip Detection and Repair for PPP/INS Integrated Systems.

Cycle slip (CS) is a primary error source in Precise Point Positioning/Inertial Navigation System (PPP/INS) integrated systems. In this study, an INS-aided CS detection and repair method is presented. It utilizes high-precision INS information instead of a pseudorange to remove the satellite⁻receiver geometric range in the wide-lane (WL) and ionospheric-free (IF) phase combinations and creates an INS-aided WL (WL-INS) model and an INS-aided IF (IF-INS) model. Since INS information is superior to pseudorange, the INS-aided models have high detection accuracy. However, the effectiveness of INS-aided models cannot persist for a long time because of INS accumulation error. To overcome the disturbance of INS error, improved INS-aided models are proposed. This idea takes advantage of the long wavelength of WL combination and tries to fix WL CS. Once it succeeds, the INS error can be evaluated and removed. The proposed method was tested using land vehicle data, in which simulated cycle slips and signal interruption were introduced. The results show that this method can accurately detect and repair different cycle slips between the continuous Global Positioning System (GPS) epoch. When it comes to the cycle slip after a GPS interruption, the method can also accelerate PPP re-convergence, as it is not affected by the inertial accumulation error.

Design and Implementation of a New System for Large Bridge Monitoring-GeoSHM.

Structural Health Monitoring (SHM) is a relatively new branch of civil engineering that focuses on assessing the health status of infrastructure, such as long-span bridges. Using a broad range of in-situ monitoring instruments, the purpose of the SHM is to help engineers understand the behaviour of structures, ensuring their structural integrity and the safety of the public. Under the Integrated Applications Promotion (IAP) scheme of the European Space Agency (ESA), a feasibility study (FS) project that used the Global Navigation Satellite Systems (GNSS) and Earth Observation (EO) for Structural Health Monitoring of Long-span Bridges (GeoSHM) was initiated in 2013. The GeoSHM FS Project was led by University of Nottingham and the Forth Road Bridge (Scotland, UK), which is a 2.5 km long suspension bridge across the Firth of Forth connecting Edinburgh and the Northern part of Scotland, was selected as the test structure for the GeoSHM FS project. Initial results have shown the significant potential of the GNSS and EO technologies. With these successes, the FS project was further extended to the demonstration stage, which is called the GeoSHM Demo project where two other long-span bridges in China were included as test structures. Led by UbiPOS UK Ltd. (Nottingham, UK), a Nottingham Hi-tech company, this stage focuses on addressing limitations identified during the feasibility study and developing an innovative data strategy to process, store, and interpret monitoring data. This paper will present an overview of the motivation and challenges of the GeoSHM Demo Project, a description of the software and hardware architecture and a discussion of some primary results that were obtained in the last three years.