## 3 Methods  
### GPS Data Processing  
Survey-grade GNSS receivers record satellite signals (e.g., time, phase centers, pseudoranges, signal-to-noise ratios), but cannot provide centimeter-accuracy positions directly. GPS observations need to be carefully processed with supplementary information to achieve centimeter-precision positions, in turn, millimeter- or submillimeter-accuracy displacements for SHM purposes. GPS data can be processed in a kinematic mode or a static mode. Numerous algorithms have been developed for both kinematic and static processing for different application purposes. In short, kinematic algorithms solve a position epoch by epoch, while static algorithms solve a position using a period of observations to obtain the best estimate of the position. Kinematic positioning is used for studying dynamic displacements/deformations of civil engineering structures, such as vibrations of long-span bridges and high-rise buildings under wind and earthquakes. Static positioning techniques take advantage of long occupation times (from a few minutes to a day) to achieve high-accuracy positional time series to capture rapid and gradual positional-changes. In general, kinematic GPS processing may result in more outliers compared to static positioning, though kinematic positioning with short baselines can also achieve millimeter accuracy [26; 27]. For the riverbed deformation monitoring, we will target on minor and gradual positional-changes rather than rapid positional-changes. Therefore, static rather than kinematic positioning methods are employed in GPS and BeiDou data processing in this study. The accuracy of GPS-derived displacements does not solely rely on GPS equipment (antenna and receiver), but mostly depends on how the data is collected and processed. Typically, there are two approaches to achieve high-precision GPS positioning solutions: Relative positioning and absolute positioning. Detailed introductions of these two methods are presented in our previous publications [28; 29; 30; 31; 32]. In general, the accuracy and precision of GPS-derived positions have been improved dramatically over the past two decades due to the advances in GPS hardware, software, and reference frames [29; 33]. The relative positioning method is known as carrier-phase double-difference (DD), which uses simultaneous observations from two GPS units to obtain relative positions of one station (rover) with respect to another one (base). The displacements of the rover can be derived from the relative positional time series. The DD method inherits high accuracy from the fact that closely spaced GPS units share significant common errors and biases. Errors introduced by troposphere, ionosphere, satellite orbits, satellite and receiver clocks could be significantly mitigated by the differential processing with short baselines (e.g., <10 km). Because the number of common errors decreases with increasing antenna-to-antenna distance, the performance of the differential method highly depends on the length of the baseline. DD processing is often employed as a core processing engine for network processing that includes multi-base and multi-rover stations. The size of most engineering structures is within a couple of kilometers, such as dams, bridges, and high-rise buildings. One or more reference stations can be installed adjacent to the monitoring object. Short baselines within a few kilometers would result in substantially high repeatability (precision) of the relative positions, in turn, resulting in high-accuracy displacement measurements. Sub-millimeter accuracy, the root-mean-square (RMS) of the residuals of displacements, was achieved in our previous landslide monitoring project using 24-hour continuous GPS observations [22]. The DD method has been frequently applied for detecting instant deformation of ground surface and engineering structures due to its operational simplicity and its ability to achieve millimeter-accuracy displacements.