A spatiotemporal deformation modelling method based on geographically and temporally weighted regression

The geographically and temporally weighted regression (GTWR) model is a dynamic model which considers the spatiotemporal correlation and the spatiotemporal nonstationarity. Taking into account these advantages, we proposed a spatiotemporal deformation modelling method based on GTWR. In order to further improve the modelling accuracy and efficiency and considering the application characteristics of deformation modelling, the inverse window transformation method is used to search the optimal fitting window width and furthermore the local linear estimation method is used in the fitting coefficient function. Moreover, a comprehensive model for the statistical tests method is proposed in GTWR. The results of a dam deformation modelling application show that the GTWR model can establish a unified spatiotemporal model which can represent the whole deformation trend of the dam and furthermore can predict the deformation of any point in time and space, with stronger flexibility and applicability. Finally, the GTWR model improves the overall temporal prediction accuracy by 43.6% compared to the single-point time-weighted regression (TWR) model

Dam deformation monitoring data analysis using space-time Kalman filter

Noise filtering, data predicting, and unmonitored data interpolating are important to dam deformation data analysis. However, traditional methods generally process single point monitoring data separately, without considering the spatial correlation between points. In this paper, the Space-Time Kalman Filter (STKF), a dynamic spatio-temporal filtering model, is used as a spatio-temporal data analysis method for dam deformation. There were three main steps in the method applied in this paper. The first step was to determine the Kriging spatial fields based on the characteristics of dam deformation. Next, the observation noise covariance, system noise covariance, the initial mean vector state, and its covariance were estimated using the Expectation Maximization algorithm (EM algorithm) in the second step. In the third step, we filtered the observation noise, interpolated the whole dam unmonitored data in space and time domains, and predicted the deformation for the whole dam using the Kalman filter recursion algorithm. The simulation data and Wuqiangxi dam deformation monitoring data were used to verify the STKF method. The results show that the STKF not only can filter the deformation data noise in both the temporal and spatial domain effectively, but also can interpolate and predict the deformation for the whole da

A centering correction method for GNSS antenna diversity theory and implementation using a software receiver

GPS is performing well in open sky situation. However, severe attenuation or blockage of signals by high buildings may leads to an insufficient number of received satellites. Antenna diversity scheme is viewed as a method to alleviate signal attenuation and enhance the performance of GNSS positioning in the harsh environments. This paper introduces an antenna diversity system, composed of two spatially separated antennas. If relative geometry of two antennas is known, the carrier phase measurement outputs from these two antennas can be combined with Centering Correction Method (CCM). Even each antenna may not able to acquire more than four satellites this antenna diversity system can still precisely estimate each antenna’s location with centimeter-level accuracy, as long as the sum of the captured satellites by two separate antennas is no less than four

Spatiotemporal analysis of GPS time series in vertical direction using independent component analysis

GPS has been widely used in the field of geodesy and geodynamics thanks to its technology development and the improvement of positioning accuracy. A time series observed by GPS in vertical direction usually contains tectonic signals, non-tectonic signals, residual atmospheric delay, measurement noise, etc. Analyzing these information is the basis of crustal deformation research. Furthermore, analyzing the GPS time series and extracting the non-tectonic information are helpful to study the effect of various geophysical events. Principal component analysis (PCA) is an effective tool for spatiotemporal filtering and GPS time series analysis. But as it is unable to extract statistically independent components, PCA is unfavorable for achieving the implicit information in time series. Independent component analysis (ICA) is a statistical method of blind source separation (BSS) and can separate original signals from mixed observations. In this paper, ICA is used as a spatiotemporal filtering method to analyze the spatial and temporal features of vertical GPS coordinate time series in the UK and Sichuan-Yunnan region in China. Meanwhile, the contributions from atmospheric and soil moisture mass loading are evaluated. The analysis of the relevance between the independent components and mass loading with their spatial distribution shows that the signals extracted by ICA have a strong correlation with the non-tectonic deformation, indicating that ICA has a better performance in spatiotemporal analysis

Back-Analysis of Slope GNSS Displacements Using Geographically Weighted Regression and Least Squares Algorithms

Numerical simulation is a powerful technique for slope stability assessment and landslide hazard investigation. However, the physicomechanical parameters of the simulation results are susceptible to uncertainty. Displacement back-analysis is considered an effective method for the prediction of the geomechanical parameters of numerical models; therefore, it can be used to deal with the parameter uncertainty problem. In this study, to improve the interpretability of the back-analysis model, an analytical function relationship between slope displacements and physicomechanical parameters was established using geographically weighted regression. By combining the least-squares and linear-algebra algorithms, a displacement back-analysis method based on geographically weighted regression (DBA-GWR) was developed; in particular, the multi-objective displacement back-analysis was represented as an analytical problem. The developed method was subsequently used for a slope of the Guiwu Expressway in Guangxi, China. Simulation experiments and GNSS real-data experiments demonstrated that the GWR could achieve high-precision deformation modelling in the spatial domain with model-fitting precision in the order of mm. Compared with state-of-the-art methods, the precision of the simulated displacement with the proposed method was significantly improved, and equivalent physicomechanical parameters with higher accuracy were obtained. Based on the corrected numerical model, the most severely deformed profiles were forward-analysed, and the simulated deformation and distribution patterns were found to be in good agreement with the field investigation results. This approach is significant for the determination of geomechanical parameters and the accurate assessment of slope safety using monitoring data

BDS/GPS Multi-Baseline Relative Positioning for Deformation Monitoring

The single-baseline solution (SBS) model has been widely adopted by the existing global navigation satellite system (GNSS) deformation monitoring systems due to its theoretical simplicity and ease of implementation. However, the SBS model neglects the mathematical correlation between baselines, and the accuracy and reliability can be degraded for baselines with long length, large height difference or frequent satellite signal occlusion. When monitoring large-area ground settlement or long-spanned linear objects such as bridges and railroads, multiple reference stations are frequently utilized, which can be exploited to improve the monitoring performance. Therefore, this paper evaluates the multi-baseline solution (MBS) model, and constrained-MBS (CMBS) model that has a prior constraint of the spatial-correlated tropospheric delay. The reliability and validity of the MBS model are verified using GPS/BDS datasets from ground settlement deformation monitoring with a baseline length of about 20 km and a height difference of about 200 m. Numerical results show that, compared with the SBS model, the MBS model can reduce the positioning standard deviation (STD) and root-mean-squared (RMS) errors by up to (47.4/51.3/66.2%) and (56.9/60.4/58.4%) in the north/east/up components, respectively. Moreover, the combined GPS/BDS positioning performance for the MBS model outperforms the GPS-only and BDS-only positioning models, with an average accuracy improvement of about 13.8 and 25.8%, with the highest accuracy improvement of about 41.6 and 43.8%, respectively. With the additional tropospheric delay constraint, the CMBS model improves the monitoring precision in the up direction by about 45.0%

Determination of Landslide Displacement Warning Thresholds by Applying DBA-LSTM and Numerical Simulation Algorithms

Numerical simulation has emerged as a powerful technique for landslide failure mechanism analysis and accurate stability assessment. However, due to the bias of simplified numerical models and the uncertainty of geomechanical parameters, simulation results often differ greatly from the actual situation. Therefore, in order to ensure the accuracy and rationality of numerical simulation results, and to improve landslide hazard warning capability, techniques and methods such as displacement back-analysis, machine learning, and numerical simulation are combined to create a novel landslide warning method based on DBA-LSTM (displacement back-analysis based on long short-term memory networks), and a numerical simulation algorithm is proposed, i.e., the DBA-LSTM algorithm is used to invert the equivalent physical and mechanical parameters of the numerical model, and the modified numerical model is used for stability analysis and failure simulation. Taking the Shangtan landslide as an example, the deformation mechanism of the landslide was analyzed based on the field monitoring data, and subsequently, the superiority of the DBA-LSTM algorithm was verified by comparing it with DBA-BPNN (displacement back-analysis based on back-propagation neural network); finally, the stability of the landslide was analyzed and evaluated a posteriori using the warning threshold calculated by the proposed method. The analytical results show that the displacement back-analysis based on the machine learning (DBA-ML) algorithm can achieve more than 95% accuracy, and the deep learning algorithm exemplified by LSTM had higher accuracy compared to the classical BPNN algorithm, meaning that it can be used to further improve the existing intelligent inversion theory and method. The proposed method calculates the landslide’s factor of safety (FOS) before the accelerated deformation to be 1.38 and predicts that the landslide is in a metastable state after accelerated deformation rather than in failure. Compared to traditional empirical warning models, our method can avoid false warnings and can provide a new reference for research on landslide hazard warnings

Characteristics of the BDS Carrier Phase Multipath and Its Mitigation Methods in Relative Positioning

The carrier phase multipath effect is one of the most significant error sources in the precise positioning of BeiDou Navigation Satellite System (BDS). We analyzed the characteristics of BDS multipath, and found the multipath errors of geostationary earth orbit (GEO) satellite signals are systematic, whereas those of inclined geosynchronous orbit (IGSO) or medium earth orbit (MEO) satellites are both systematic and random. The modified multipath mitigation methods, including sidereal filtering algorithm and multipath hemispherical map (MHM) model, were used to improve BDS dynamic deformation monitoring. The results indicate that the sidereal filtering methods can reduce the root mean square (RMS) of positioning errors in the east, north and vertical coordinate directions by 15%, 37%, 25% and 18%, 51%, 27% in the coordinate and observation domains, respectively. By contrast, the MHM method can reduce the RMS by 22%, 52% and 27% on average. In addition, the BDS multipath errors in static baseline solutions are a few centimeters in multipath-rich environments, which is different from that of Global Positioning System (GPS) multipath. Therefore, we add a parameter representing the GEO multipath error in observation equation to the adjustment model to improve the precision of BDS static baseline solutions. And the results show that the modified model can achieve an average precision improvement of 82%, 54% and 68% in the east, north and up coordinate directions, respectively

Scheimpflug Camera-Based Technique for Multi-Point Displacement Monitoring of Bridges

Owing to the limited field of view (FOV) and depth of field (DOF) of a conventional camera, it is quite difficult to employ a single conventional camera to simultaneously measure high-precision displacements at many points on a bridge of dozens or hundreds of meters. Researchers have attempted to obtain a large FOV and wide DOF by a multi-camera system; however, with the growth of the camera number, the cost, complexity and instability of multi-camera systems will increase exponentially. This study proposes a multi-point displacement measurement method for bridges based on a low-cost Scheimpflug camera. The Scheimpflug camera, which meets the Scheimpflug condition, can enlarge the depth of field of the camera without reducing the lens aperture and magnification; thus, when the measurement points are aligned in the depth direction, all points can be clearly observed in a single field of view with a high-power zoom lens. To reduce the impact of camera motions, a motion compensation method applied to the Scheimpflug camera is proposed according to the characteristic that the image plane is not perpendicular to the lens axis in the Scheimpflug camera. Several tests were conducted for performance verification under diverse settings. The results showed that the motion errors in x and y directions were reduced by at least 62% and 92%, respectively, using the proposed method, and the measurements of the camera were highly consistent with LiDAR-based measurements

Reference satellite selection method for GNSS high-precision relative positioning

Selecting the optimal reference satellite is an important component of high-precision relative positioning because the reference satellite directly influences the strength of the normal equation. The reference satellite selection methods based on elevation and positional dilution of precision (PDOP) value were compared. Results show that all the above methods cannot select the optimal reference satellite. We introduce condition number of the design matrix in the reference satellite selection method to improve structure of the normal equation, because condition number can indicate the ill condition of the normal equation. The experimental results show that the new method can improve positioning accuracy and reliability in precise relative positioning