Thanks to the international GNSS service (IGS), which has provided multi-GNSS precise products, multi-GNSS precise point positioning (PPP) time and frequency transfer has of great interest in the timing community. Currently, multi-GNSS PPP time transfer is not investigated with different precise products. In addition, the correlation of the receiver clock offsets between adjacent epochs has not been studied in multi-GNSS PPP. In this work, multi-GNSS PPP time and frequency with different precise products is first compared in detail. A receiver clock offset model, considering the correlation of the receiver clock offsets between adjacent epochs using an a priori value, is then employed to improve multi-GNSS PPP time and frequency (scheme2). Our numerical analysis clarify how the approach performs for multi-GNSS PPP time and frequency transfer. Based on two commonly used multi-GNSS products and six GNSS stations, three conclusions are obtained straightforwardly. First, the GPS-only, Galileo-only, and multi-GNSS PPP solutions show similar performances using GBM and COD products, while BDS-only PPP using GBM products is better than that using COD products. Second, multi-GNSS time transfer outperforms single GNSS by increasing the number of available satellites and improving the time dilution of precision. For single-system and multi-GNSS PPP with GBM products, the maximum improvement in root mean square (RMS) values for multi-GNSS solutions are up to 7.4%, 94.0%, and 57.3% compared to GPS-only, BDS-only, and Galileo-only solutions, respectively. For stability, the maximum improvement of multi-GNSS is 20.3%, 84%, and 45.4% compared to GPS-only, BDS-only and Galileo-only solutions. Third, our approach contains less noise compared to the solutions with the white noise model, both for the single-system model and the multi-GNSS model. The RMS values of our approach are improved by 37.8–91.9%, 10.5–65.8%, 2.7–43.1%, and 26.6–86.0% for GPS-only, BDS-only, Galileo-only, and multi-GNSS solutions. For frequency stability, the improvement of scheme2 ranges from 0.2 to 51.6%, from 3 to 80.0%, from 0.2 to 70.8%, and from 0.1 to 51.5% for GPS-only, BDS-only, Galileo-only, and multi-GNSS PPP solutions compared to the solutions with the white noise model in the Eurasia links.

Multi-Global Navigation Satellite System (GNSS) integration can effectively improve the satellite geometry strength, and certain effect on the precise point positioning (PPP) accuracy and convergence speed. Taking the system difference into account, this paper deduces the unified GNSS observation model, which is extended to the multi-GNSS PPP functional model. Meanwhile, the stochastic model used in Kalman filter parameter estimation is presented in the paper. Furthermore, to evaluate the performance of the multi-GNSS PPP in Asia-Pacific region, observed data from the International GNSS Service reference stations are analysed using the self-developed software. In detail, the results from Global Positioning System (GPS)-, GLObal NAvigation Satellite System (GLONASS)- and BeiDou Navigation Satellite System (BDS)-only PPP, double combined PPP and GPS/GLONASS/BDS combined PPP under the different observation duration and cut-off elevation angles are analysed. Results demonstrate: (1) compared with the single system PPP, the convergence speed of the multi-GNSS PPP is improved while the accuracy is not significantly improved after processing the 24-h data set; (2) when the observation duration is short, such as 0.5 h, the mean convergence percentage of the BDS combined with GPS and GLONASS PPP increases by an average of 49.6% compared with the single individual systems except for BDS, respectively, under the cut-off angle of 5° and (3) when PPP positioning with high cut-off elevation angles, and at the point of centimetre-level positioning, the GPS/GLONASS/BDS combined PPP has a better performance on the convergence percentage and convergence speed. For example, the percentages of the position biases within 0–5 cm for GPS/GLONASS/BDS are increased by 7.2 and 4.5% in North and East direction compared with GPS/GLONASS under the cut-off angle of 35°, more than any other. And the mean convergence time is only 14.5 min.

In recent years, more and more expressways pass through the abandoned coal mine, while the surface residual subsidence of the abandoned coal mine threatens the operation safety of the expressway. It is of significance to evaluate the stability of the construction site and take reasonable managements for effectively guaranteeing the traffic safety. How to accurately evaluate the stability of the construction site is the primary problem. This study proposes a stability evaluation model using the overlay and index method and points out that the evaluation scores and weights of evaluation indices are key parameters to determine the reliability of evaluation results. To reasonably determine the evaluation score, the scoring criteria of qualitative indices is obtained by the equidistant method, while the scoring criteria of quantitative indices is obtained by establishing scoring functions. The weights of evaluation indices are got by adopting the FAHP (fuzzy analytic hierarchy process). Then the built model is applied to evaluate the stability of the Wuyun Expressway construction site, and the results show that the Wuyun Expressway construction site is basic stable. Finally, the sensitivity of indices weights on the evaluation result is analyzed with the maximum $C_k(C_m,pc)$ of 5.9% far lower than the weight change of ±30%, and the average residual subsidence velocity of the maximum subsidence point is 0.0456 mm/d using a high-resolution leveling, proving the credibility of the proposed model. Research results provide new ideas and systematic technical references for the stability evaluation of the construction site above an abandoned coal mine.