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Besides accuracy, integrity is another important performance measure of GNSS. The classical least-squares-residual (LSR) method and parity vector (PV) method are often used in the receiver autonomous integrity monitoring (RAIM). The two fault detection methods assume that the observation errors of different satellites are the same, ignoring possible variations of accuracy between observations. In this study, the mathematical models of the weighted least-squares-residual (WLSR) method and the weighted parity vector (WPV) method are derived in detail. The equivalence of the two methods is established with statistical tests. The WPV method is applied to detect those faults based on both GPS and BDS observations collected at Wuhan JiuFeng Station (JFNG). The theoretical results show that this method has lower computational complexity than the WLSR method, hence more suited for cases requiring fast fault detection. The fault detection rate increases as the deviation of the pseudorange observation increases. Thus, using the threshold value T d of the posterior unit weight errorσ 0 , the WPV achieves a higher fault detection rate than using a priori unit weight error σ 0 . The experiments show that these two methods can detect relatively large faults, it is possible to detect them in GPS observations if σ 0 is more than 12×bias (1×bias=8 m) andσ 0 superior to 4×bias, whereas the faults detection in BDS observations requires a deviation bigger than 8×bias and 6×bias, respectively. But these two methods are insensitive when the deviation is smaller.INDEX TERMS Weighted least-squares-residual, weighted parity vectors, receiver autonomous integrity monitoring (RAIM), fault detection.

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The global navigation satellite system (GNSS) has seen tremendous advances in measurement precision and accuracy, and it allows researchers to perform geodynamics and geophysics studies through the analysis of GNSS time series. Moreover, GNSS time series not only contain geophysical signals, but also unmodeled errors and other nuisance parameters, which affect the performance in the estimation of site coordinates and related parameters. As the number of globally distributed GNSS reference stations increases, GNSS time series analysis software should be developed with more flexible format support, better human–machine interaction, and with powerful noise reduction analysis. To meet this requirement, a new software named GNSS time series noise reduction software (GNSS-TS-NRS) was written in MATLAB and was developed. GNSS-TS-NRS allows users to perform noise reduction analysis and spatial filtering on common mode errors and to visualize GNSS position time series. The functions’ related theoretical background of GNSS-TS-NRS were introduced. Firstly, we showed the theoretical background algorithms of the noise reduction analysis (empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD)). We also developed three improved algorithms based on EMD for noise reduction, and the results of the test example showed our proposed methods with better effect. Secondly, the spatial filtering model supported five algorithms on a separate common model error: The stacking filter method, weighted stacking filter method, correlation weighted superposition filtering method, distance weighted filtering method, and principal component analysis, as well as with batch processing. Finally, the developed software also enabled other functions, including outlier detection, correlation coefficient calculation, spectrum analysis, and distribution estimation. The main goal of the manuscript is to share the software with the scientific community to introduce new users to the GNSS time series noise reduction and application.

Extreme loadings, a hostile environment and dangerous operation lead to the unsafe state of bridges under construction, especially large-span bridges. Global Navigation Satellite Systems (GNSS) tend to be the best choice for real-time deformation monitoring due to the significant advantage of automation, continuation, all-weather operation and high precision. Unfortunately, the traditional geodetic GNSS instrument with its high price and large volume is limited in its applications. Hence, we design and develop low-cost GNSS equipment by simplifying the monitoring module. The performance of the proposed solution is evaluated through an experimental dynamic scenario, proving its ability to track abrupt deformation down to 3–5 mm. We take Chongqing Guojiatuo Suspension Bridge in China as a case study. We build a real-time low-cost GNSS monitoring cloud platform. The low-cost bridge GNSS monitoring stations are located at the top of the south and north towers, midspan upstream and downstream respectively and the reference station is located in the stable zone 400 m away from the bridge management buildings. We conducted a detailed experimental assessment of low-cost GNSS on 5 April and a real-time deformation detection experiment of the towers and main cables during the dynamic cable saddle pushing process on 26 February 2022. In the static experiment, the standard deviation of the residual using the multi-GNSS solution is 2 mm in the horizontal direction and 5 mm in the vertical direction. The multi-GNSS solution significantly outperforms the BDS/GPS single system. The dynamic experiment shows that, compared with the movement measured by the robotic total station, the horizontal error of the south tower and north tower measured by low-cost GNSS is below 0.005 m and 0.008 m respectively. This study highlights the potential of low-cost GNSS solutions for Structural Health Monitoring (SHM) applications.