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With the capability for single-receiver AR (Ambiguity Resolution), real-time GNSS (Global Navigation Satellite System) satellite integer clock has been the research hotspot of GNSS community in the past decade. Robust ambiguity datum is one prerequisite for high-quality integer clock. In this paper, with undifferenced AR model derived, a robust ambiguity datum definition method is proposed to isolate the signal biases from the integer ambiguity. Firstly, based on the ambiguity graph, the ambiguity datum is selected with the minimum spanning tree algorithm. Secondly, the ambiguity datum is transferred to the subsequent epochs through signal bias connection. Moreover, additional datum ambiguities are introduced to accommodate the arising of receiver and satellite in real-time circumstance. With the combination of ambiguity graph and signal bias, the efficient definition and smooth transition of ambiguity datum are assured for the real-time processing. To validate the approach, simulated real-time integer clock estimation for GPS/Galileo/BDS-3 satellites are conducted with one-month (January 2022) data from about 100 global IGS (International GNSS Service) network stations. Experiments show that the proposed robust ambiguity datum can produce accurate real-time integer clock. The average WL (Wide-Lane) and NL (Narrow-Lane) fixed rates exceed 99 % and 95 %, respectively, for most of the GPS/Galileo satellites. While comparable WL fixed rate is achieved for the BDS-3 satellites, the NL fixed rate is about 5 % lower as a result of poor orbit quality and imperfect measurement model. With eclipsing satellites excluded, the standard deviations between real-time integer clock and post-processed reference clock reach 0.018 ns and 0.016 ns for the GPS and Galileo constellations, respectively, which are 28 % and 24 % smaller than those of corresponding float clocks. In contrast, the standard deviations of float and integer clocks are similar for the BDS-3 constellation. Further improvements on the background models, including unconservative force modeling, satellite attitude modeling and antenna calibration are required to achieve ultimate accuracy, especially for the BDS-3 satellites. [ABSTRACT FROM AUTHOR]

[Display omitted] • ZTD retrieval performance of GPS/BDS/Galileo frequency combinations are analyzed. • Optimal frequency combination of GPS/BDS/Galileo ZTD retrieval is L1/L2, B2/B6, and E1/E7. • GNSS-ZTD retrieval performance is related with similarity of the used frequency. • Effect analysis of ambiguity resolution and GNSS system combination on ZTD retrieval. • GNSS-ZTD retrieval performance is affected by La Niña event. The Global Navigation Satellite System (GNSS) is promising technology for zenith tropospheric delay (ZTD) retrieval. With the emergence of new multi-GNSS frequencies and maturity of precise point positioning ambiguity resolution (PPP-AR) technology, opportunities and challenges have arisen in high-precision GNSS-ZTD retrieval. However, certain strategies have usually been adopted, such as the traditional dual-frequency combination of American global positioning system (GPS) technology, for ZTD retrieval, but the influence of AR on ZTD retrieval has been ignored. To address this issue, in this study, the GNSS-ZTD retrieval performance of all existing dual-frequency combinations was first comprehensively evaluated by raw observations. Then, the influences of AR and system combinations were analysed with popular dual-frequency combinations. Finally, La Niña occurred during the GNSS data period considered in this article, and the effect on GNSS-ZTD retrieval was examined. The results of this study could not only provide a reference for GNSS-ZTD retrieval but also provide insight into the relationship between La Niña occurrence and GNSS-ZTD retrieval performance. [ABSTRACT FROM AUTHOR]

The integrated navigation of single-frequency global navigation satellite system (GNSS) and inertial navigation system (INS) has broad application prospects with the development of multi-constellation GNSS. However, GNSS signals are susceptible to interference from a complex environment, which results in low-quality observations. The combination of frequencies cannot be applied for a single-frequency signal, so it is difficult to fix the ambiguity and process cycle slip. Therefore, the method of ambiguity resolution and cycle slip processing with INS aiding is proposed in this paper. When full ambiguities cannot be completely fixed, a subset of ambiguity is determined based on the elevation angle and posteriori residuals. The satellite is firstly eliminated one by one if the absolute value of posteriori residual is over the set threshold. And if the ambiguities still cannot be fixed, the satellite with the minimum elevation angle is eliminated each one. The short-term and high-accuracy position predicted by the INS was used as the constraint equation of the cycle slip detection. The unit weight mean square error of the cycle slip detection equation was used to identify the epoch where the cycle slip occurs, and the residual calculated by robust estimation was used to detect and repair the cycle slip. A set of data collected by a vehicle was used to analyze the proposed method. The experimental results showed that the proposed partial ambiguity resolution can obtain the optimal ambiguity fixing rate and positioning performance compared with the full ambiguity resolution and partial ambiguity resolution based on the elevation angle. The proposed algorithm can effectively detect and accurately repair the cycle slip for the simulated small and large cycle slips, and the cycle slips can still be detected when the global positioning system (GPS), global navigation satellite system of Russia (GLONASS), and BeiDou navigation satellite system (BDS) were outage for 10 s, 5 s, and 10 s without sufficient visible satellites. [ABSTRACT FROM AUTHOR]

• A novel integer ambiguity resolution method for GNSS deformation monitoring. • Utilized baseline prediction construct the mixed integer least-squares criterion. • A validation procedure using real-time dynamic baseline vector predictions. • Achieved substantial performance enhancements in challenging scenarios. Accurate integer ambiguity resolution (IAR) is pivotal for high-precision and high-reliability Global Navigation Satellite Systems (GNSS) positioning. However, traditional IAR methodologies, encompassing integer estimation and validation, often face significant challenges in harsh landslide environments. This paper proposes a new IAR method based on baseline vector predictions. Initially, the real-time baseline vectors predictions are used to substitute the true values of baseline vectors in the mixed integer least-squares (MILS) estimation equation, and the MILS estimation criterion is constructed which contains the quadratic form of baseline vectors. Subsequently, a novel baseline vector validation procedure, built on real-time dynamic predictions, is established. Experiments were carried out at two GNSS landslide monitoring area using GPS + BDS dual-frequency measurement data. These stations underwent both stable deformation stages within complex measurement environments and accelerated deformation stages in open environments. Results indicate that the proposed method overcomes the limitations associated with conventional ambiguity validation methods based on hypothesis testing, addressing the errors of "abandoning trueness" and "accepting mistake" simultaneously. Notably, the ambiguity fixed rate improved by 80.7 % for single-frequency experiments and 39.8 % for dual-frequency experiments at one monitoring station located in a complex environment. This work provides valuable IAR approach for GNSS deformation monitoring applications. [ABSTRACT FROM AUTHOR]

Abstract The performance of Real-Time (RT) Precise Point Positioning (PPP) ambiguity resolution can be further improved by incorporating multiple Global Navigation Satellite System (GNSS) observations. RT PPP with ambiguity resolution based on raw GNSS observations, aided by the satellite clock offsets and GPS un-calibrated phase delays (UPDs), is realized to evaluate the effect of GNSS observations. Compared with previous studies, Galileo observations are integrated in this analysis and the effect of new BeiDou/Galileo systems in RT PPP ambiguity resolution is analyzed for global users. Comparing with the GPS-only and GPS/GLONASS solution, the time to first fix (TTFF) is 18.8% and 7.9% improved for those users in the Asia-Pacific regions, while it is 9.6% and 3.8% improved for other users by adding the BeiDou/Galileo observations. The improvement of the fixing rate and positioning accuracy is similar for users in different regions. The fixing rate is 2.1% and 0.5% improved when adding BeiDou/Galileo observations on top of GPS and GPS/GLONASS respectively. The accuracy of the north, east and up components are 0.4, 0.0 and 0.5 mm improved when adding on top of GPS, while 0.2, 0.1 and 0.4 mm when adding on top of GPS/GLONASS. By utilizing observations of four systems, an accuracy of 9.0, 9.1 and 28.3 mm is achieved for the fixed kinematic PPP solution after a mean initialization time of 797.9 s. [ABSTRACT FROM AUTHOR]

Correct ambiguity resolution (AR) is the key for high-precision positioning. In order to reliably resolve ambiguity, an improved single-epoch segmented ambiguity algorithm is proposed in this paper. First, the double-difference wide-lane ambiguities resolved by the Melbourne-Wubbena (MW) method are divided into two categories based on signal-to-noise ratio (SNR). One is the primary ambiguity group that can be resolved easily, and the other is the secondary ambiguity group that is difficult to resolve. Second, the primary ambiguity group is divided into different levels in a (4,1,1…1) pattern based on SNR, and the different levels’ ambiguities are resolved successively, and the method being that the integer ambiguity is selected from two candidate values built by rounding up and down. Third, the resolved primary ambiguity group is used as a constraint to solve the secondary ambiguity group. Finally, the wide-lane observation equation and the basic observation equation are combined to solve the ambiguity of the L1 carrier phase, and the resolved ambiguity can be obtained by directly rounding. The candidate values of the primary ambiguity group is limited to two cycles through this step, and the (4,1,1…1) pattern can reduce ambiguity search times. Since an appropriate selection enables the correct resolution of primary wide-lane ambiguities, the selection of the threshold for SNR is the key to group wide-lane ambiguity, and we use the data from Novatel receiver as an example to discuss how to confirm the SNR threshold in this paper. Static short baseline data and kinematic short baseline that were less than 20 km were collected to validate the proposed algorithm. These results were compared with the commercial software IE8.60. These experiments show that the successful rate reaches 100%, 99.78% and 99.42%, respectively, for the new single-epoch segmented ambiguity method in the three data sets, and the accuracy is similar to that of IE8.60 for the combined double difference. [ABSTRACT FROM AUTHOR]

• A high-precision temporal relative localization method called Android-odometry is proposed. • Detect and repair temporal ambiguity variation with velocity constraint. • Provide temporal relative positions at centimeter-level with MI8 in a kinematic test. Following extant studies on temporal relative localization (TRL) methods, this study uses a doppler velocity constraint-based temporal ambiguity variation (TAV) detection method and a two-step TAV resolution method to obtain the high-precision temporal relative position variations over time based on raw GNSS observations of Android smartphones, commonly plagued by frequent half-cycle slips and lock-loss. Results show that the proportion of the detectable satellites over 0.65 reaches the 95.57% level and the fix rate of global TAV resolution reaches 82.93%. We then propose the Android-odometry method which is a real-time high-precision TRL method with time-differenced carrier-phase observations of Android smartphones. The experimental results show that the method achieves centimeter-level temporal relative position accuracy during the 13-min dynamic test with Xiaomi MI8, showing a dramatic improvement of over 90% compared to the traditional RTK method. [ABSTRACT FROM AUTHOR]