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Objectives: The stochastic model of observation information describes the accuracy of observation information and its correlation, and also plays an important role in parameter estimation, quality control and accuracy evaluation. In the process of global navigation satellite system (GNSS) precision positioning, an accurate stochastic model is essential for improving the accuracy of float solution, enhancing the success rate of ambiguity resolution, increasing the accuracy of gross error detection, and obtaining the accurate and reliable positioning results. Methods: An optimization method for stochastic model of BeiDou navigation satellite system (BDS) is proposed by handling the properties of four classic elevation-dependent stochastic models based on the relationship between BDS satellite observation information and elevation. Firstly, the accuracy of BDS four-frequency observation information is evaluated by the simplified Helmert variance estimation method. Then, the model parameters could be fitted based on the estimated precision of observation information. Finally, the statistical characteristics of four stochastic models, including piecewise function, sine function, cosine function and exponential function, are tested by the overall test and ω-test methods. Results: The results show that the accuracy of pseudorange and carrier phase for BDS-3 satellite are related to elevation, and the correlation degree is different by GNSS observation types. The stochastic model of exponential function shows the best performance in the fitting error, the overall test and the ωtest. The maximum fitting errors of pseudorange and carrier phase are 0.029 m and 5.484 mm, respectively. The false alarm rates of the overall test for the float solution and the fixed solution are 5.1 % and 4.9 %, respectively. In addition, the maximum false alarm rates of the ω-test are 5.8 % for the pseudorange and 6.8 % for the carrier phase. Conclusions: The stochastic model of exponential function can get the shortest convergence time and the highest positioning accuracy for BDS-3 quad-frequency precise point positioning. It can also accurately describe the accuracy of BDS observation information and improve the accuracy and reliability of BDS precise positioning results. [ABSTRACT FROM AUTHOR]

Objectives: In precise point positioning (PPP) technology, the correct fixing of ambiguity is al⁃ ways an essential part of achieving high-precision positioning. However, the wrong fixing of ambiguity will lead to serious positioning errors. Therefore, it is necessary to optimize the selection of the ambiguity sub⁃ set to ensure a more reliable fixing of PPP ambiguity. Methods: This paper proposes a PPP partial ambiguity resolution (PAR) method that combines quality control and Gram-Schmidt orthogonalization. By utilizing the multi-GNSS(global navigation satellite system) experiment (MGEX) observations in the un-differenced and un-combined PPP model, the PAR method based on Gram-Schmidt orthogonalization was com⁃ pared and analyzed with the selected reference satellite method with maximum elevation, and the performance of ambiguity resolution and positioning was assessed under the multi-GNSS conditions. Results: Experimental results show that the average epoch fixing rate of each day and each station based on the Gram Schmidt method is improved by 7.74% and 11.46% in the static mode, and 7.90% and 7.78% in the pseudo-kinematic mode, respectively, compared with that of the selected reference satellite method considering the maximum elevation. Meanwhile, time-to-first-fix (TTFF) of each day and each station based on the Gram-Schmidt orthogonalization can be significantly reduced by 22.30% and 25.42% in the static mode, corresponding to an improvement of 20.44% and 19.65% in the pseudo-kinematic mode, respectively, compared with that of the selected reference satellite method considering the maximum elevation. As far as multi-GNSS PPP AR is concerned, multi-GNSS PPP AR has a significant improvement on the convergence time of BDS (BeiDou navigation satellite system) only. The convergence time of horizontal components is shortened by 20.00 min on average at 95% confidence level, and the vertical components are shortened by 19.00 min on average. For the positioning accuracy aspects, the positioning accuracy of horizontal components is improved by 1.50 cm on average, while that of vertical components is improved by 1.12 cm on average. Conclusions: The PPP PAR algorithm based on the Gram-Schmidt method can significantly improve the performance of ambiguity resolution and positioning accuracy. [ABSTRACT FROM AUTHOR]

The uncertainty of distance‐related error of global navigation satellite system is gradually increasing with the increase of distance between the reference stations and the rover station. Therefore, the dual ‐sys‐ tems of global positioning system (GPS) and BeiDou satellite navigation system (BDS) network real ‐ time kinematic (RTK) method was presented to meet the demand of high‐precision long range positioning RTK. Firstly, the wide‐lane ambiguities were fixed by the multi‐frequency observation data of GPS and BDS be‐ tween long‐range reference stations. The satellite clock errors can be eliminated by the double‐difference so‐ lution model, simultaneously the atmospheric error and satellite orbit errors can be weakened. Then the double ‐ difference carrier phase integer ambiguities can be fixed by the resolution model including atmo‐ spheric error and carrier phase ambiguity. The method of classification error corrections between long‐range reference stations network was used. The observation errors were classified, according to the characteris‐ tics of observation errors between long‐range reference station network. The ionosphere errors and non‐dis‐ persive errors of the rover station were calculated by using the reference stations’error correction and regional error interpolation. The atmospheric errors and satellite orbit errors of the rover station can be weakened by the method of interpolation. Then the errors of GPS/BDS carrier phase observation of the rover station were removed by the calculation errors. The carrier phase integer ambiguities of the rover station can be fixed by the method of resolution integer ambiguity with multi ‐frequency carrier phase, and the position of the rover station was obtained by the fixed ambiguities. The algorithm validation was carried out by the data on long ‐ range reference station network. Three long ‐ range reference stations and one rover station were used to test in Central China. The positioning accuracy of centimeter can be obtained by the algorithm of du‐ al ‐ systems of GPS and BDS network RTK. At the same time, single system can also get the centimeter level of position and the GPS is better than BDS. The method of dual ‐systems of GPS and BDS network RTK can guarantee the positioning accuracy of the rover station. The results of experiment indicate that the GPS/BDS long ‐ range network RTK can be realized and the centimeter level positioning accuracy can be achieved by this algorithm. [ABSTRACT FROM AUTHOR]

The experimental satellites of BeiDou global navigation satellite system (BDS‐3) broadcast new B1C / B2a / B2b signals that overlap with GPS L1/L5 signals and European Galileo E1/E5a/E5b signals, which provides the opportunity of tightly combined relative positioning for short baselines with observations from GPS, Galileo, and BDS ‐ 3 experimental satellites. In this contribution， we first evaluate the value and time‐domain stability of differential inter‐system bias (DISB) between overlapping frequencies of GPS, Galileo, and BDS ‐ 3. The results show that the DISB of the same type of receiver is close to 0, and its influence can be ignored in the tightly combined relative positioning. Then we preliminarily evaluated performance of single‐epoch tightly combined relative positioning for short baselines with observations from GPS， Galileo， and BDS‐3 experimental satellites. The results show that, compared with the traditional loosely combined model, the tightly combined model can significantly improve the success rate and reliability of ambiguity resolution. The improvement is especially significant (approximately 25% ‐45%) under environments where the observed satellites for each system are limited and only single‐frequency observations are available. [ABSTRACT FROM AUTHOR]