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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]

Objectives: For global navigation satellite system (GNSS), the ranging performance of observation would influence the system service capability.Methods: Parabolic antenna with large⁃diameter could greatly reduce the impact of the ground equipment and the environment on signal acquisition. Based on data from parabolic antenna, observation characteristics and ranging performance of BeiDou⁃3 global satellite navigation system (BDS⁃3) are analyzed.Results: The results show that, regarding the pseudorange deviation on BeiDou⁃3 satellite, no systematic deviation of the same magnitude, compared with BeiDou⁃2, is found on the signal of B1I, B3I, B1C, B2a, and B2b. There are fluctuations on some signals. However, the correlation with elevation angle is not strong, and the average magnitude of all satellite fluctuations is 0.1 m. This paper analyzes the multipath variation and noise level of carrier observation for BeiDou⁃3 satellite of each signal using triple⁃frequency combinations. The fluctuations of carrier phase triple combination are of the millimeter level, and those fluctuations do not closely correlate with the elevation or time. The root mean square of the triple⁃frequency carrier combination from parabolic antenna is mostly less than 0.6 mm.Conclusions: The results indicate that no systematic bias occurs in code and phase observation of BDS⁃3, and the system has a good ranging performance. [ABSTRACT FROM AUTHOR]

Objectives: With the popularization of smartphones and the evolution of global navigation satellite systems (GNSS), navigation contributes as an indispensable function for smartphones, and the demand of high‑precision positioning for mass‑market smartphones is becoming higher. From 2016, developers can obtain GNSS raw observations through Google Android application programming interface (API). Android 9.0 and above versions, provide the option to turn off the duty cycle, which makes it possible for smartphones to conduct precise point positioning (PPP). Methods: This paper conducts quality analysis of the GNSS observations for several common‑used dual‑frequency smartphones, Huawei Mate 20/30 and Xiaomi 8, and propose a set of quality control schemes that is suitable for smartphone PPP. Gross errors can be removed by data detection according to satellite elevation, signal‑to‑noise ratio, pre‑residuals, etc., while cycle slips can be detected by the accumulated delta range state (ADRS) identifiers as well as the time difference carrier phase (TDCP) observations. A real‑time PPP application based on Android platform was developed. It supports for singe‑ and dual‑frequency, real‑time and post‑processing PPP. To verify the performance of PPP with smartphones, several field experiments were performed with different smartphones in different scenarios. Results: Field results show that: (1) The pseudorange quality of Xiaomi 8 and Huawei Mate 20 are similar, while the carrier phase quality of Huawei Mate 20/30 is significantly worse than Xiaomi 8. (2) The ADRS identifier of Xiaomi 8 can better identify the cycle slip, while it is difficult for Huawei Mate 20/30 to directly determine the cycle slips through the ADRS identifier. By combining the ADRS and TDCP can detect most of cycle slips. (3) The positioning accuracy of single ‑frequency PPP for Xiaomi 8 and Huawei Mate 20/30 reach 0.5‑0.6 m in horizontal, and 1.0‑2.0 m in vertical. The positioning accuracy of dual‑frequency PPP is better than that of single‑frequency PPP after convergence, especially in the vertical direction. (4) For the real‑time and post‑processing PPP, they both have a similar positioning accuracy in the horizontal components, while the positioning accuracy of post‑processing PPP in the vertical direction is higher than that of real‑time PPP by 20% ‑40%. Conclusions: An accuracy of a few decimeters can be achieved for real ‑ time PPP with Android smartphones. Different from geodetic GNSS receivers, the widely‑used smartphones use low‑cost linearly‑polarized antennas. In addition, smartphones are often used in urban complex scenarios, thus the GNSS data they collect have more gross errors, cycle slips and multipath effects. Further study should focus on the multipath mitigation, multi ‑ frequency and multi ‑ GNSS combination, and fusion with other sensors such as gyroscopes, magnetometers, barometers, bluetooth, Wi‑Fi, etc. to realize continuous and seamless positioning both indoor and outdoor. [ABSTRACT FROM AUTHOR]