Fast and reliable ambiguity resolution (AR) has been a continuing challenge for real-time precise positioning based on dual-frequency Global Navigation Satellite Systems (GNSS) carrier phase observation. New GNSS systems (i.e., GPS modernization, BDS (BeiDou Navigation Satellite System), GLONASS (Global Navigation Satellite System), and Galileo) will provide multiple-frequency signals. The GNSS multiple-constellation and multiple-frequency signals are expected to bring great benefits to AR. A new GNSS single-epoch AR method for a short-range baseline based on triple-frequency signals is developed in this study. Different from most GNSS multiple-constellation AR methods, this technique takes advantage of the triple-frequency signals and robust estimation as much as possible. In this technique, the double difference (DD) AR of the triple-frequency observations is achieved in the first step. Second, the triple-frequency carrier phase observations with fixed ambiguities are used with the dual-frequency carrier phase observations to estimate their ambiguity. Finally, to realize reliable GNSS single-epoch AR, robust estimation is involved. The performance of the new technique is examined using 24 hours of GPS/GLONASS/BDS observation collected from a short-range baseline. The results show that single-epoch AR of the GNSS signals can be realized using this new technique. Moreover, the AR of BDS Geostationary Earth Orbit (GEO) satellites’ observations is easier than are those of the Medium Earth Orbit (MEO) and Inclined Geosynchronous Satellite Orbit (IGSO) satellites’ observations.

The correct ambiguity resolution between reference stations is the core issue of the whole Network Real-Time Kinematic (RTK) technology. Aimed at long fixed time and low reliability of the low elevation angle satellite ambiguity resolution during the initialisation of the Network RTK system, a three-step algorithm is proposed in this paper. Firstly, the double difference wide-lane ambiguities are fixed on the basis of the Melbourne-Wubbena (MW) method. Secondly, the double difference L1 carrier phase ambiguities of the high elevation angle satellites are fixed rapidly based on the ionosphere-free combination model. Thirdly, the corresponding ambiguities of the satellites with low elevation angles are solved with restrictions from the double difference tropospheric information, which is obtained from observations of the high elevation angle satellites. Based on this algorithm, an overall scheme of the ambiguity resolution during the initialisation process of the Network RTK system is designed. Results from Global Positioning System (GPS)/Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS) data demonstrate that the three-step algorithm can reduce the ill-posed problems of the observation model effectively. Moreover, the speed and accuracy performances of the ambiguity resolution for the low elevation angle satellites using the proposed algorithm are better than those of the conventional method.

The use of global navigation satellite system (GNSS) is entering a new era of joint positioning based on the use of multifrequencies and multimodes. Ensuring the correct weighting of observations from each system and satellite has become a key problem during real-time positioning. This paper addresses the issue of weights of observations as well as the quality control of GPS/BDS pseudoranges in the context of real-time relative positioning. Thus, in the first place, the Helmert variance component estimation (VCE) is used to determine the relative weighting of observations from the two systems, and then, we introduce robustness estimation theory and construct a new method. The method is resistant to the influence of outliers in the observations by selecting weight iterations. To do this, we selected GPS/BDS observation data at baseline lengths of 40 km, 46 km, and 64 km for verification and analysis. Experimental results show that, in terms of the relative positioning of medium-to-long baseline based on GPS/BDS pseudorange observations, when observed values incorporate large gross errors, our method can reduce the weighting of suspicious or abnormal values and weaken their impact on positioning solutions, so that the positioning results will not appear to have large deviation.

In order to overcome the limitations of traditional stochastic models for smartphones, we introduce a double-difference code pseudorange residual (DDPR)-dependent stochastic model based on an optimal satellite subset, with the goal of mitigating the constraints imposed by the quality of GNSS observations in smartphones on the accuracy and reliability of phone-based GNSS positioning. In our methodology, the satellite selection process involved considering the integrated carrier-to-noise density ratio (C/N0) index of both the reference station and the smartphone, enabling us to construct a satellite subset characterized by superior observation quality. Furthermore, by leveraging the optimal subset of satellites and incorporating the C/N0-dependent stochastic model, we could determine the approximate location of the terminal through pseudorange differential positioning. Subsequently, we estimated the DDPRs for all satellites and utilized these values as prior information to build a stochastic model of the observations. Our findings indicate that in occluded environments, the DDPR-dependent stochastic model significantly enhances positioning accuracy for both the Huawei Mate40 and P40 terminals compared to the C/N0-dependent model. Numerically, the improvements in the north (N), east (E), and up (U) directions were approximately 30%, 32%, and 34% for the Mate40, and 26%, 33%, and 24% for the P40 terminal. This suggests that the proposed DDPR-dependent stochastic model effectively identifies and mitigates large gross error signals caused by multipath and non-line-of-sight (NLOS) signals, thereby assigning lower weights to these problematic observations and ultimately enhancing positioning accuracy. Moreover, the weighting method involves minimal computations and is straightforward to implement, making it particularly suitable for GNSS positioning applications on smartphones in complex urban environments.