A new method of real-time cycle-slip detection and repair for BeiDou navigation satellite system (BDS) triple-frequency undifferenced observations is proposed. The method, which is based on code–phase and geometry-free phase combinations, composes linearly independent combination observations to uniquely determine the cycle-slip of original frequency phase observations in two independent steps. First, two extra-wide lane (EWL) code–phase combinations are utilised to determine the EWL combination cycle-slips. The sum of the carrier phase combination coefficients is zero. Second, the geometry-free phase combination with a non-zero sum of combination coefficients composes linearly independent combination observations with two code–phase combinations. Ionospheric delay variance systematic deviation is corrected with several previous carrier-phase observations without cycle-slip, which seriously affect the accuracy of the geometry-free phase combination observations. The BDS triple-frequency carrier-phase and code observations of different satellite types at 30 s sampling interval, which involve increased active ionospheric conditions in 1 day, are utilised to test the method. Results show that the proposed method can efficiently detect and accurately repair any cycle-slip combinations in real-time for different satellite types under active ionospheric conditions. No erroneous and leakage judgments are observed in the test.

The mining area deformation monitoring theory and method using precise point positioning (PPP) ambiguity resolution (AR) were studied, and an ambiguity fixing model with satellite and receiver combination phase delay (CPD) was proposed for zero-differenced PPP ambiguity fixing and its corresponding formula derivation was given. The data processing results for 1 h at six IGS stations in China show that 93% of ambiguities can be fixed within 10 min and all ambiguities can be fixed within 15 min. After ambiguity fixing, the positioning accuracy is improved by more than 85% in the E and N directions, with absolute positioning accuracy reaching millimeter level, and it was improved by 70% in the U direction, reaching centimeter level; the proposed zero-differenced ambiguity fixing model can effectively improve the convergence rate and positioning accuracy in PPP. Data monitoring continuously conducted for half a year at four CORS stations of Shanxi China Coal Pingshuo Group validated the feasibility of using PPP in mining area deformation monitoring.

To achieve fast satellite selection for a multi-Global Navigation Satellite System (GNSS), thereby reducing the burden on a receiver's processing element and the cost of hardware, and improving the utilisation ratio of receiver signal channels, the relationship between the number of satellites and Geometric Dilution Of Precision (GDOP), the number of satellites selected and the computation time is analysed. A fast rotating partition algorithm for satellite selection based on equal distribution of the sky is proposed. The algorithm divides the satellite selection process into two parts: rough selection and detailed selection. Unhealthy satellites, according to a health identifier, and low elevation angle satellites with a large troposphere delay are eliminated during the rough selection process. During the detailed satellite selection process, the satellite sky is divided and rotated to match satellites based on the average angle distance between the satellite and central partition line. Static data from the International GNSS Service (IGS) station and dynamic data collected at China University of Mining and Technology were used to verify the algorithm, and the results demonstrated that an inverse matrix could be avoided to reduce computation complexity. Additionally, the new satellite selection algorithm has the merit that there is little effect on the computation when the selected satellites and number of satellites in the field increased. A single system of the Global Positioning System (GPS) and double system of GPS/Globalnaya Navigazionnaya Sputnikovaya Sistema (GLONASS) both passed the hypothesis test for each epoch. By including BeiDou Navigation Satellite System (BDS) data, data utilisation increased to more than 95% using the rotating partition algorithm. Also, the GDOP and positioning performance of a rotating partition algorithm and an optimal Dilution Of Precision (DOP) algorithm are compared in this paper, and the analysis result shows that both of the algorithms have only a small difference of GDOP and have comparable positioning performance.

A robust Kalman filter improved with IGG (Institute of Geodesy and Geophysics) scheme is proposed and used to resist the harmful effect of gross error from GPS observation in PPP/INS (precise point positioning/inertial navigation system) tightly coupled positioning. A new robust filter factor is constructed as a three-section function to increase the computational efficiency based on the IGG principle. The results of simulation analysis show that the robust Kalman filter with IGG scheme is able to reduce the filter iteration number and increase efficiency. The effectiveness of new robust filter is demonstrated by a real experiment. The results support our conclusion that the improved robust Kalman filter with IGG scheme used in PPP/INS tightly coupled positioning is able to remove the ill effect of gross error in GPS pseudorange observation. It clearly illustrates that the improved robust Kalman filter is very effective, and all simulated gross errors added to GPS pseudorange observation are successfully detected and modified.