The satellite clocks used in the BeiDou-2 satellite navigation System (BDS) are Chinese self-developed Rb atomic clocks, and their performances and stabilities are worse than GPS and Galileo satellite clocks. Due to special periodic noises and nonlinear system errors existing in the BDS clock offset series, the GPS ultra-rapid clock model, which uses a simple quadratic polynomial plus one periodic is not suitable for BDS. Therefore, an improved prediction model for BDS satellite clocks is proposed in order to enhance the precision of ultra-rapid predicted clock offsets. First, a basic quadratic polynomial model which is fit for the rubidium (Rb) clock is constructed for BDS. Second, the main cyclic terms are detected and identified by the Fast Fourier Transform (FFT) method according to every satellite clock offset series. The detected results show that most BDS clocks have special cyclic terms which are different from the orbit periods. Therefore, two main cyclic terms are added to absorb the periodic effects. Third, after the quadratic polynomial plus two periodic fitting, some evident nonlinear system errors also exist in the model residual, and the Back Propagation (BP) neural network model is chosen to compensate for these nonlinear system errors. The simulation results show that the performance and precision using the improved model are better than that of China iGMAS ultra-rapid prediction (ISU-P) products and the Deutsches GeoForschungsZentrum GFZ BDS ultra-rapid prediction (GBU-P) products. Comparing to ISU-P products, the average improvements using the proposed model in 3 h, 6 h, 12 h and 24 h are 23.1%, 21.3%, 20.2%, and 19.8%, respectively. Meanwhile the accuracy improvements of the proposed model are 9.9%, 13.9%, 17.3%, and 21.2% compared to GBU-P products. In addition, the kinematic Precise Point Positioning (PPP) example using 8 Multi-GNSS Experiment MGEX stations shows that the precision based on the proposed clock model has improved about 16%, 14%, and 38% in the North (N), East (E) and Height (H) components.

The Real-Time Kinematic (RTK) positioning method of the Global Navigation Satellite System (GNSS) has been widely used for landslide monitoring. The stability of its reference station is crucial to obtain accurate and reliable monitoring results. Unstable reference stations due to the geological environment and human activities are difficult to detect and in practical applications often ignored. As a result, it affects the positioning solutions and subsequently the interpretation and detection of landslide motions, which must be addressed in GNSS landslide monitoring. To solve this problem, we propose using the Precise Point Positioning (PPP) technique to analyze the stability of the reference station by verifying its position. The deformations of the monitoring stations are then compensated. First, the reference station coordinates are obtained by the PPP technique and tectonic motion is considered in data processing. The change or breakout of the reference station position is then determined using a cumulative sum control chart method. Finally, each monitoring station’s displacements are compensated according to the displacements of the reference station. According to the results of the Tengqing landslide experiment, the PPP technique can be used in GNSS landslide monitoring to analyze the stability of reference stations. With PPP, millimeter-level accuracy for the coordinates of reference stations is achieved. Compared to the traditional deformation series, the compensated displacement series more reliably reflects the landslide motions. This study will increase the reliability of monitoring results and contribute to implementing GNSS in monitoring landslides.

The determination of slant total electron content (STEC) between satellites and receivers is the first step for establishing an ionospheric model. However, the leveling errors, caused by the smoothed ambiguity solutions in the carrier-to-code leveling (CCL) method, degrade the performance of ionosphere modeling and differential code bias (DCB) estimation. To reduce the leveling errors, an uncombined and undifferenced precise point positioning (PPP) method with ambiguity resolution (AR) was used to directly extract the STEC. Firstly, the ionospheric observables were estimated with CCL, PPP float-ambiguity solutions, and PPP fixed-ambiguity solutions, respectively, to analyze the short-term temporal variation of receiver DCB in zero or short baselines. Then, the global ionospheric map (GIM) was modeled using three types of ionospheric observables based on the single-layer model (SLM) assumption. Compared with the CCL method, the slight variations of receiver DCBs can be obviously distinguished using high precise ionospheric observables, with a 58.4% and 71.2% improvement of the standard deviation (STD) for PPP float-ambiguity and fixed-ambiguity solutions, respectively. For ionosphere modeling, the 24.7% and 27.9% improvements for posteriori residuals were achieved for PPP float-ambiguity and fixed-ambiguity solutions, compared to the CCL method. The corresponding improvement for residuals of the vertical total electron contents (VTECs) compared with the Center for Orbit Determination in Europe (CODE) final GIM products in global accuracy was 9.2% and 13.7% for PPP float-ambiguity and fixed-ambiguity solutions, respectively. The results show that the PPP fixed-ambiguity solution is the best one for the GIM product modeling and satellite DCBs estimation.

Due to the cuboid satellite body of BeiDou-3 satellites, the accuracy of their orbit showed a trend of systematic variation with the sun-satellite-earth angle (ε) using the Extend CODE Orbit Model (ECOM1). Therefore, an a priori cuboid box-wing model (named the cuboid model) is necessary to compensate ECOM1. Considering that the body-dimensions and optical properties of the BeiDou-3 satellites used to construct the box-wing model have not yet been fully released, the adjustable box-wing model (ABW) was used for precise orbit determination (POD). The a priori cuboid box-wing model was directly estimated by the precision radiation accelerations, obtained from ABW POD. When using ECOM1 model, for 14 < β < 40°, a linear systematic variation of D0 related to the elevation of the sun above the orbital plane (β-angle) with a slope of 0.048 nm/s²/°, was found for C30. After adding the cuboid model to assist ECOM1 (named Cuboid + ECOM1), the slope was reduced to 0.005 nm/s²/°, and for C20 satellite, the standard deviation (STD) of D0 was improved, from 1.28 to 0.85 nm/s² (34%). For satellite laser ranging (SLR) validation, when using the ECOM1 model, the systematic variation with the ε angle was about 14 cm for C20 and C30. After using the Cuboid + ECOM1 model, the variation was significantly reduced to about 5 cm. For C20 and C21, compared with the ECOM1 model, the root mean square (RMS) of the ECOM2 and Cuboid + ECOM1 model was improved by about 0.54 (10.3%) and 0.43 cm (8.7%). For C29 and C30, the RMS of ECOM2 and Cuboid + ECOM1 model was improved for about 0.7 (10.9%) and 1.6 cm (25.6%). Finally, the RMS of the SLR residuals of 4.37 to 4.88 cm was achieved for BeiDou-3 POD.