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In this contribution we introduce the dual mixed-integer least-squares problem and study it in relation to its primal counterpart. The dual differs from the primal formulation in the order in which the integer ambiguity vector a ∈ Z n and baseline vector b ∈ R p are estimated. As not the ambiguities, but rather the entries of b are usually the parameters of interest, the attractiveness of the dual formulation stems from its direct computation of b. It is shown that this potential advantage relies on the ease with which an implicit integer least-squares problem of the dual can be solved. For the convoluted cases, we introduce two methods of simplifying approximations. To be able to describe their quality, we provide a complete distributional analysis of their estimators, thus allowing users to judge whether or not the approximations are acceptable for their application. It is shown that this approach implicitly introduces a new class of admissible integer estimators of which we also determine the pull-in regions. As the dual function is shown to lack convexity, special care is required to be able to compute its global minimizer b ˇ . Our proposed method, which has finite termination with a guaranteed ϵ -tolerance, is constructed from combining the branch-and-bound principle, with a special convex-relaxation of the dual, to which the projected-gradient-descent method is applied to obtain the required bounds. Each of the method's three constituents are described, whereby special emphasis is given to the construction of the required continuously differentiable, convex lower bounding function of the dual. [ABSTRACT FROM AUTHOR]

Precise Point Positioning (PPP), coupled with the ambiguity resolution (AR) method, has demonstrated substantial potential in fields like agricultural navigation and airborne mapping. However, there remains a notable deficiency in the comprehensive comparative evaluation of its performance when using rapid and real-time satellite products, especially for mass low-cost receivers. Stations equipped with geodetic and low-cost receivers are analyzed in kinematic and static mode. In the kinematic mode, the GPS+Galileo-combined PPP, employing ambiguity fixing with "WHU" rapid products, achieves the highest positioning accuracy of 0.9 cm, 0.9 cm, and 2.6 cm in the North, East, and Up components, respectively. Real-time PPP using "CNT" products attains accuracies of 2.1 cm, 2.7 cm, and 4.8 cm for these components, utilizing GPS ambiguity-fixed PPP. BDS positioning accuracy is inferior to standalone GPS, but improves when the number of visible BDS satellites exceeds 10. Convergence time analysis shows that approximately 38.2 min are required for single GPS or BDS PPP using the "WHU" products and geodetic receivers, which can be reduced to 18.5 min for dual-system combinations and further to 14.8 min for triple-system combinations. The time can be further reduced by ambiguity fixing. In the static mode, multi-GNSS combination does not significantly impact convergence times, which are more influenced by the precision of the products used. Real-time products require approximately 22 min to achieve horizontal accuracy below 0.1 m, while rapid products reach this accuracy within 10 min. For PPP using low-cost GNSS receivers, more than two hours are necessary to achieve an accuracy better than 0.1 m for kinematic PPP, which is considerably longer than the convergence time observed at MGEX stations. However, the accuracy achieved after convergence, as well as the performance of static PPP, is comparable to that of MGEX stations. [ABSTRACT FROM AUTHOR]

With the rapid progress of Global Navigation Satellite Systems (GNSS), integer ambiguity resolution has gradually become one of the key factors that affecting Precise Point Positioning (PPP) to achieve high-precision positioning results and fast convergence. Fortunately, the proposal of observable-specific code/phase biases (OSB) has greatly alleviated this problem tremendously. Different from obtaining OSB by dual-frequency linear combinations, this research proposed BeiDou Navigation Satellite System (BDS) OSB estimation method from raw observations. This method allows for more flexible estimation in a global network, without the need to compose the complex linear combinations when involving multi-frequency measurements processing. The BDS-3 observation data collected from 112 stations over one month (October 2022), containing B1C/B1I/B2a/B2b/B3I frequencies, were used for five-frequency phase OSBs estimation. Subsequently, static and kinematic PPP were executed utilizing two different ambiguity resolution strategies to corroborate the efficacy of this method. The results revealed that the BDS-3 five-frequency phase OSBs possessed good monthly stability, with standard deviation less than 0.3 cycle. High position accuracy was achieved in the static mode by fixing the ambiguity directly, with root mean square (RMS) of 3.0, 4.8 and 9.9 mm. Meanwhile, the ambiguity fixed rate was maintained at a high level around 96 % in multi-frequency tests. Simultaneously, the kinematic mode also presented the centimeter-level dynamic positioning results and the positioning accuracy improved by 55, 31 and 17 % in the East, North and Up components, respectively. Compared to the float solutions, the adoption of multi-frequency OSBs significantly accelerated the convergence speed by 55 % on average. [ABSTRACT FROM AUTHOR]

Ambiguity resolution (AR) is essential for quick and accurate Global Navigation Satellite System GNSS location and navigation. In addition to location parameters, there are various additional GNSS characteristics that are relevant for a wide range of applications such as instrumental calibrations, atmospheric sounding, and time transfer. We offer differential code bias and satellite geometry for the GNSS estimable parameters using MANS-PPP software backage. In this research, we used the MANS-PPP software package to execute the processing method and generate the PPP GNSS solution. We demonstrated how differential code bias and satellite geometry can effectively enhance initial time and positioning error for multi-GNSS satellites. PPP Processing observation data in static mode was used by the different DCB files the Chinese Academy of Sciences (CAS), the German Aerospace Centre (DLR), and the Centre for Orbit Determination in Europe (CODE), for the 12 stations from IGS, and we analyzed the impact of errors from the satellite geometry. The results illustration that the correction of DCB significantly improves the PPP ambiguity resolution success rate and quality, which have higher DCB values. The satellite geometry also has a substantial influence on the PPP ambiguity resolution, with a better geometry leading to a higher success rate and quality. Furthermore, the use of multiple GNSS constellations and the optimization of the satellite selection and weighting algorithms can further improve the PPP ambiguity resolution and the resulting positioning accuracy. [ABSTRACT FROM AUTHOR]

With the global service of the BeiDou Navigation Satellite System (BDS), the Galileo Navigation Satellite System (Galileo), and the modernization of the Global Positioning System (GPS), achieving high-precision positioning through triple-frequency-only observations in medium baseline real-time kinematics (RTK) is anticipated. This study investigates the impacts of double-difference (DD) troposphere delay and ionosphere delay on ambiguity resolution (AR) based on six medium baselines at a latitude of 30°. Additionally, it evaluates positioning accuracy, fixing rate, convergence time, and computational time using triple-frequency-only (B1I/B2a/B3I, E1/E5a/E5b, L1/L2/L5) data, comparing these results to those obtained from dual-frequency (B1I/B2a, E1/E5a, L1/L2) and combined dual-frequency and triple-frequency data. The experimental findings suggest that, for geometry-based wide-lane (WL) AR, the DD troposphere delay and ionosphere delay can be disregarded. However, they cannot be overlooked when aiming to resolve the raw ambiguity. Triple-frequency-only RTK exhibits comparable positioning accuracy to dual-frequency RTK, with its primary advantage lying in faster convergence. The probability of achieving convergence within 180 s is approximately 8.0% higher for triple-frequency-only RTK compared to dual-frequency RTK. In terms of computational time, the use of triple-frequency-only data reduces the required time by 8.26 s compared to the approach that simultaneously employs both dual-frequency and triple-frequency data, resulting in a computational time reduction of approximately 20%. Therefore, when conducting medium baseline RTK positioning, it is recommended to adopt the ambiguity resolution method proposed in this paper based on triple-frequency-only observations. [ABSTRACT FROM AUTHOR]

Real-Time (RT) Precise Point Positioning (PPP) uses precise satellite orbits and clock corrections, and employs a separate receiver for positioning. With the growing demand, RT PPP is becoming an increasingly popular research topic. The ambiguity resolution (AR) can significantly improve the positioning accuracy and convergence time of PPP, so it is essential to study PPPAR in RT mode. In this paper, 37 MGEX stations from around the world are chosen, and the RT orbit, clock, and phase biases products broadcast by the Centre National d'Etudes Spatiales (CNES) are applied to PPPAR. Additionally, the residuals of the RT phase biases products, convergence time, and positioning accuracy are investigated. The results indicate that GPS products have the best quality of AR, with wide-lane (WL) and narrow-lane (NL) residuals of 98.9% and 95.3%, respectively, within ±0.25 cycles. Within ±0.25 cycles, the WL and NL residuals of the Galileo are 98.2% and 94.3%, respectively. Within ±0.25 cycles, the (Beidou Navigation Satellite System) BDS has a poor quality of AR, with WL and NL residuals of 97.3% and 73.1%, respectively. Due to the poor quality of the BDS AR, the convergence time of the BDS is not calculated in this paper. The convergence time of other systems is significantly reduced after AR processing, and the convergence time of the GPS/Galileo combination is the fastest, being 17.14 min in kinematic mode and only 11.85 min in static mode. The positioning accuracy of the GPS, Galileo, GPS/Galileo, and GPS/Galileo/BDS in the E and U directions is significantly improved after PPPAR. [ABSTRACT FROM AUTHOR]

Real-time Kinematic (RTK) positioning provides centimeter-level positioning accuracy within several seconds, but it has to rely on a nearby base station. Although Precise Point Positioning (PPP) supplies precise positions with one receiver, its convergence time takes several tens of minutes, which makes PPP not well suited for real-time kinematic applications where a rapid convergence is required. PPP-RTK integrates the benefits of PPP and RTK, which actually is PPP augmented by a ground GNSS network. The satellite orbit, clock offsets, signal biases, ionospheric and tropospheric corrections are determined based on this GNSS network, modeled as state space information and transmitted to PPP users. By applying these State Space Representation (SSR) corrections, a real-time kinematic PPP-RTK approach is developed and implemented, which can instantly resolve the ambiguities to integers and realize rapid convergence. In a static scenario, it realized an instant ambiguity resolution and a rapid convergence within 2 s in more than 90% of 120 hourly sessions. The PPP-RTK has been applied and evaluated in a kinematic scenario on the highway. The horizontal positioning errors are almost lower than 0.1 m except for the time of passing through bridges. After passing bridges, the PPP-RTK successfully resolved ambiguities within 2 s in 90.6% of the cases and achieved convergence in horizontal within 5 s in more than 90% of the cases. The PPP-RTK with a precision of 0.1 m and rapid convergence of several seconds benefits the precise navigation of automobile on the highway, which will support the development of autonomous driving in future. [ABSTRACT FROM AUTHOR]

For many years, the navigation team at the French Space Agency (CNES) has been developing its Precise Point Positioning project. The goal was initially to promote a technique called undifferenced ambiguity resolution. One of the main characteristics of this technique is the capability for a user receiver to perform centimeter-level accuracy in real time. To do so, a demonstrator has been built. Its architecture is composed of three main elements: a correction processing software called the server part, a means to transmit the corrections using standardized messages, and a user software capable of handling the corrections to compute an accurate positioning at the user level. In this paper, we present the recent advances in the CNES precise point positioning demonstrator. They are composed of some evolution of the network of stations and server software, the implementation of the new state space representation standard, a new method for instantaneous ambiguity resolution using uncombined four-frequency signals, its implementation in real-time at the server and the user level, and the use of high-rate Doppler measurements to improve the accuracy of the solution in harsh urban environments. On top of that, the computation of high-accuracy post-processed phase biases with the majority of current GNSS signals supported, compatible with the uncombined method and a new online positioning service to demonstrate the capacity of the user software, is demonstrated. [ABSTRACT FROM AUTHOR]

Real-time GNSS PPP is commonly used for high-precision positioning, but its utility is constrained by factors that necessitate extended convergence periods for a dependable accuracy. Multipath, as an unmodeled error, significantly curtails PPP performance in time-constrained scenarios. Approximately 31 consecutive days of multi-GNSS data from the satellite positioning service of the German national survey (SAPOS) network were collected to evaluate the effectiveness of multipath correction for real-time PPP ambiguity resolution (AR). Using principal component analysis (PCA) to extract the common-mode error (CME) from observation residuals prior to multipath modeling, a multipath hemispherical map (MHM) and sidereal filtering (SF) approach were employed to alleviate the effects of multipath and assess the efficacy of multipath correction in real-time PPP-AR. The average RMS reductions of the carrier-phase and pseudorange residual of multi-GNSS were 25.5% and 20.1% with MHM 0.5 , while being 24.4% and 18.3% using SF. With MHM 0.5 correction, the TTFF reductions were approximately 7.0%, 17.7%, 37.5%, and 23.7% for G/GE/GC/GEC kinematic PPP-AR, respectively; and the convergence times for G/GE/GC PPP-AR were reduced to 18.2, 11.7, and 8.6 min, while GEC achieved an average convergence time of 7.1 min; a remarkable improvement compared to the multipath-uncorrected result (18 min). Moreover, 80% of the stations achieved convergence within 10 min, while 40% achieved convergence within 5 min. The kinematic positioning accuracy for the GEC solution improved from 0.97, 0.88, and 2.07 cm, to 0.94, 0.70, and 1.72 cm. In the static results, the TTFF shortened by 30.1%, 19.1%, and 20.1% for G/GE/GC, and the GEC decreased from 10.5 to 9.7 min; the average convergence time for G/GE/GC shortened to 13.0, 10.0, and 11.3 min, and for GEC shortened from 12.5 to 8.3 min. For the GPS-only solution, 78.3% of stations achieved convergence within 15 min. Similarly, for the GE scheme, the convergence time was primarily concentrated within 10 min, and for GC and GEC, with the application of enhanced multipath error correction, some of the stations even achieved convergence of PPP-AR within 5 min. The static positioning accuracy for GEC PPP was 0.50, 0.30, and 0.71 cm for the east, north, and up components. [ABSTRACT FROM AUTHOR]

In addition to the legacy B1I and B3I signals, the BeiDou global navigation satellite system (Beidou-3) are capable of transmitting B1C/B2a/B2b/B2 several new navigation signals. The multi-frequency signals of Beidou-3 are expected to benefit precise point positioning with ambiguity resolution (PPP AR). Currently, most international GNSS service (IGS) analysis center adopt the Beidou-3 B1I/B3I ionosphere-free (IF) combination to estimate the satellite orbit and clock products, the Beidou-3 B1C/B2a/B2b/B2 phase biases should be aligned with satellite B1I/B3I clocks. Therefore, in this paper, the multi-frequency phase observable-specific phase biases (OSB) estimation method is developed for Beidou-3 system, which is compatible with satellite B1I/B3I legacy clock. Experimenting on the Beidou-3 multi-frequency observations over 30 days from the globally distributed stations, the characteristics of the estimated Beidou-3 multi-frequency phase OSB and the positioning performance of the IF kinematic PPP AR with different frequency combination are assessed. After the OSB are used in the raw observations, the results demonstrate that the wide-lane ambiguities residuals within ± 0.25 cycle are approximately 97%, 94%, 97% and 93% for Beidou-3 B1I/B3I, B1C/B2b, B1C/B3I and B1C/B2a combinations, respectively. When the OSB and satellite B1I/B3I legacy clock are used in different dual-frequency combination PPP AR tests, over 94% of the corresponding narrow-lane ambiguities are within ± 0.25 cycle. In addition, owing to the low noise of the B1C/B2a combination, the positioning performance of B1C/B2a PPP AR outperforms that of the other frequency combinations. More specifically, in case of B1I/B3I PPP AR, almost 22.7 min is required to successfully achieve 10 cm for east, north and up components, while only 18.8 min is needed for B1C/B2a PPP AR. The results show that such phase OSB, along with Beidou-3 satellite B1I/B3I legacy clock, can fully recover the PPP ambiguities based on all available frequency choices and observable combinations. [ABSTRACT FROM AUTHOR]

The ultimate goal of PPP-RTK is to achieve rapid ambiguity resolution, which is influenced by the prior precision of the external ionospheric information. This study proposes a method for determining the precision of ionospheric corrections for each satellite. In this method, an 8 min piece-wise function linearly related to the spatial three-direction distance components (SDC) within the geocentric coordinate system is constructed. By exploiting the SDC model, the user can calculate the precision of the ionospheric corrections satellite by satellite. Using the German and French stations, we validate this method experimentally and compare it to a method with an 8 min piece-wise function constructed by the baseline length (BLL). The SDC model provides an accuracy better than 10 mm in modeling ionospheric correction precision for each GPS satellite, with an average improvement of 43% compared to the BLL model. In addition, the SDC model offers an accuracy of approximately 5 mm in the reference network with an inter-station distance of less than 100 km, which is about 15% better than that of the BLL model during the active ionospheric period. The SDC model exhibits advantages over ionospheric correction precision modeling, with an average improvement of 73.5% for a reference network with station spacing of 125–155 km. By adopting the adaptive ionospheric precision derived from the SDC model, the GPS/GPS + Galileo PPP-RTK achieves a horizontal error of 50 mm and a vertical error of 100 mm within an average of three to four epochs. Notably, the convergence time is significantly enhanced by 30% in reference networks with inter-station distances of 125–155 km, compared to that of the PPP-RTK solution generated with dynamic ionospheric correction precision from the BLL model for all observed satellites. [ABSTRACT FROM AUTHOR]

The fast motion of low Earth orbit (LEO) satellites provides rapid geometric changes in a short time, which can accelerate the initialization of precise point positioning (PPP). The rapid convergence of ambiguity parameters is conducive to the rapid success of ambiguity fixing. This paper presents the performance of single- and four-system combined PPP Ambiguity Resolution (AR), enhanced with an ambiguity-float solution LEO. Two LEO constellations were designed: L was a typical polar orbit constellation, with a higher number of visible satellites at high latitudes than at low and middle latitudes; and M was designed to compensate for the lack of visible satellites at low and middle latitudes. The ground observation data of the LEO satellites at the MGEX stations were simulated. Because the global navigation satellite systems (GNSSs) were fully operational, the GNSS data were real observation data from the MGEX stations. Based on the daily observation datasets collected at 258 stations in the global MGEX observation network over three days (from 1 January to 3 January 2022), in addition to the LEO simulation data, we evaluated the positioning performance of LEO ambiguity-float solution-enhanced PPP ambiguity resolution and compared it with LEO-enhanced PPP. The L+M mixed constellation was able to reduce the time to first fix (TTFF) of the four-system combined PPP-AR to 5 min, and four LEO satellites were sufficient to achieve this. L+M mixed constellation was able to reduce the convergence time of the four-system combined PPP to 2 min. Unlike PPP-AR, PPP required more LEO satellites for augmentation to saturate. [ABSTRACT FROM AUTHOR]

Due to the highly dynamic changes of the environment, the frequent loss of signal will seriously reduce the accuracy of realtime dynamic positioning. Meanwhile, the ambiguity resolution for medium/long baseline is more affected by atmospheric delay. To solve this problem, an Inertial Navigation System (INS) assisted Beidou Navigation System (BDS) medium/long baseline partial ambiguity resolution (PAR) method is designed. Firstly, constructing the BDS/INS tight integrated system that uses INS provided initial information to ambiguity resolution when the signal outages. Secondly, the atmospheric delay constraint is introduced to improve the precision of float ambiguity. Finally, the PAR based on the elevation angle information is applied to enhance fixed speed and accuracy. The vehicle experiments show that the proposed algorithm can quickly fix the ambiguity of medium/long baseline when the satellite signal outages for a short time, and improve the positioning accuracy of medium/long baseline in the dynamic environment. [ABSTRACT FROM AUTHOR]

Distance measurement based on the accumulated phase of intensity-modulated continuous-wave lasers is an established approach for pointwise geometry acquisition in uncontrolled conditions, enabling some of the most accurate Lidar/laser-scanning solutions. Inherently affected by cycle ambiguities due to the modulo 2 π phase observations, several modulation wavelengths are typically used in practical implementations to extend the measurement range. One of the main limitations of these systems arises from their inability to decouple mixed signals affected by different delays. This is especially relevant when the laser beam illuminates simultaneously two or more surfaces at significantly different distances, producing mixed-pixel measurements in which the estimated distance does not reliably correspond to any of the involved scatterers. Algorithms for detection and filtering of mixed pixels within point-cloud data have been proposed based on analyzing consistency across local neighborhoods. The resolution of multiple scatterers on individual measurements, however, has not been yet reported nor is provided by undisclosed commercial implementations. In this work, we analyze the problem of signal mixing in multi-wavelength phase-based distance estimation, and propose an algorithm for joint phase ambiguity resolution and mixed pixel detection based on mixed integer linear programming. We first analyze theoretically the performance limits of the proposed solution, demonstrating unbiasedness in the presence of noise and robustness in the presence of multiple scatterers. In addition, we investigate empirically the impact of noise, mixed measurements and choice of modulation wavelengths on the performance of the proposed algorithm. The results demonstrate the capacity of the presented approach, given an adequate wavelength selection, to provide unambiguous distance estimates under realistic noise conditions and to identify measurements affected by mixed pixels while approximating the position of the dominant scatterer. Aside from contributing to improving the reliability and resolution capability of Lidar and laser-scanning data, the proposed solution sets a promising step towards fully resolved multi-target distance measurement. [ABSTRACT FROM AUTHOR]

Objectives: BeiDou-3 navigation satellite system (BDS-3) has been fully completed and pro‐ vides reliable positioning, navigation, and timing services to global users. In order to achieve compatibility and interoperability with other global navigation satellite systems (GNSS), B1C and B2a signals have been modulated by BDS-3 based on BDS-2, which enable frequency multiplexing with E1 and E5a signals of Galileo. The inter-system biases (ISBs) are important for the fusion processing of different GNSS. Methods: This paper proposes an ISB estimation and application model based on the single-differenced observations and analyzes the ISBs between the overlapping frequencies of BDS-3 and Galileo. Based on several receivers of the new trackable BDS-3 signals, the characteristics of ISBs between BDS-3 and Galileo are revealed, and the real-time kinematic (RTK) positioning performance of BDS-3 and Galileo is analyzed. Results: The results show that the ISBs of B1C-E1 and B2a-E5a exist in different types of receivers but not in the same type of receivers. In addition, compared with BDS-3-only and Galileo-only, the combination of BDS-3 and Galileo has an improvement of more than 10% in both the success rate of ambiguity resolution and positioning accuracy. Conclusions: The multi-constellation RTK positioning performance with the introduction of ISBs is more advantageous than that of a single constellation [ABSTRACT FROM AUTHOR]

This study introduces a new scheme for resolving the ambiguity in a pulse‐Doppler radar. While ambiguity resolution is typically performed before tracking, the proposed approach, Track‐Before‐Resolving, is resolving ambiguity utilising tracking filters. A specific Doppler ambiguity resolution algorithm is provided for demonstrating that the Track‐Before‐Resolving method is useful. In order to resolve the ambiguity, which is equivalent to finding the ambiguity number, this algorithm investigates the maximum probability calculated in the multiple model estimation, each with a tracking filter of a different ambiguity number. Simulation shows that the proposed algorithm performs effectively, even at low SNR. [ABSTRACT FROM AUTHOR]

The real-time kinematic (RTK) technology has been widely used as the high-precision positioning method in the offshore area. However, RTK requires a bi-directional communication and groups measurement errors together, thereby limiting its mass-market applications. Combining the advantages of precise point positioning (PPP) and RTK, PPP-RTK has become one of the hotspot technologies in the mass market. In this contribution, we propose the uncombined multi-GNSS PPP-RTK model using uncalibrated phase delays (UPDs) estimated from the legacy ionosphere-free and Melbourne-Wübbena combination. With the UPDs estimated based on 14 regional stations, we conduct PPP ambiguity resolution (AR) at 3 augmentation stations and derive precise atmospheric corrections, i.e., RMS of zenith tropospheric and slant ionospheric correction can be up to 4.89 mm and 2.20 cm, respectively. After applying atmospheric correction, the correct fixed solution of four on-board kinematic experiments can be better than 95% and the positioning accuracy can be better than 5 cm in both horizontal and vertical direction, showing the encouraging performance similar to RTK in the offshore area. [ABSTRACT FROM AUTHOR]

The full operational capability of the Chinese BeiDou Satellite Navigation System (BDS) has injected additional energy into the GNSS field. Along with the visibility of more BDS satellites, as well as the precise products generated by analysis centers, ambguity float and fixed Precise Point Positioning (PPP) performance with the complete BDS constellation are evaluated in this study. Inter-system biases (ISBs) between BDS-2 and BDS-3 are first evaluated, and Fractional Cycle Bias (FCB) with and without consideration of ISBs are assessed. Results show that when considering ISBs, the standard deviations of ambiguity residuals are smaller, thus the ISB parameter should be taken into consideration in BDS PPP. BDS-3 FCBs are more stable than those of BDS-2, at the same time, the ambiguity residuals are smaller for BDS-3 satellites. In terms of PPP performance, BDS-3 outperforms BDS-2 in positioning accuracy, convergence time and time to first fix. For the test data, the convergence time of BDS-2 static solution is 48.8 min, while for BDS-2 + 3 it is 19.7 min, representing an improvement of 59.6% when BDS-3 satellites are included. The positioning accuracy of static BDS-2, BDS-3 and BDS-2 + 3 PPP can reach the same millimeter-level after a long time of convergence, while kinematic solution with BDS-2 + 3 has the highest accuracy compared to BDS-2 and BDS-3, which could reach 1.7, 1.3 and 4.3 cm in East, North and Up components, respectively, in fixed solution. The performance of BDS PPP with the whole constellation is comparable with that of GPS and Galileo, and the PPP performance is promising with receiver updates for MGEX stations in the near future. [ABSTRACT FROM AUTHOR]

Ambiguity resolution (AR) is a core technology that helps to speed up convergence time and increase positioning accuracy for precise point positioning (PPP), and the performance of PPP-AR is based on the quality of ambiguity resolution products. Real-time PPP-AR becomes a reality as users can now obtain publicly accessible real-time observable-specific signal bias (OSB) products from the Centre National d'Etudes Spatiales (CNES). Therefore, an analysis of the quality of OSB products and an evaluation of the performance of PPP-AR are required to promote the application of real-time positioning. For a total of 31 days between day of year (DOY) 121 and 151 in 2021, observation data were collected from 90 stations, and the OSB products were used to assess the experiments. As for the quality of the OSB products, the data availability (DA) of the GPS and Galileo satellites was greater than 97%, whereas that of BDS was less than 60%; the maximum fluctuation value (MAX) and standard deviation (STD) of the GPS, Galileo, and BDS satellites were 0.045 and 0.012; 0.081 and 0.028; and 0.292 and 0.085 cycles, respectively. In terms of ambiguity residuals using the OSB products, the wide-lane (WL) residual percentages within ±0.25 cycles for the GPS, Galileo, BDS-2, and BDS-3 systems were more than 92%, and the narrow-lane (NL) residual percentages within ±0.25 cycles for the four systems were 92%, 89%, 79%, and 60%, respectively. With regard to the performance of PPP-AR, the GPS+Galileo solution showed the best performance in the kinematic positioning mode, in which the mean root mean square (RMS) of positioning accuracy was 1.06, 1.27, and 2.85 cm for the east (E), north (N), and up (U) components, respectively, and the mean convergence time reached 9.6 min. In the static positioning mode, the mean convergence times of the GPS-only and GPS+Galileo solutions were 11.4 min and 8.0 min, respectively, and both of their mean RMS for positioning accuracy reached 0.79, 0.95, and 1.48 cm for the E, N, and U components, respectively. However, the addition of BDS did not further enhance the performance of multi-GNSS PPP-AR in either the kinematic or static positioning mode due to the poor quality of the real-time BDS products. More importantly, a prediction method was proposed to avoid re-convergence and to enhance the reliability of PPP-AR in the event of short-time missing real-time OSB products and to improve the positioning accuracy and the ambiguity fixed rate. [ABSTRACT FROM AUTHOR]

Real-time precise orbit and clock products are necessary for Global Navigation Satellite System (GNSS) real-time precise applications. In the classical strategy, the real-time orbit is predicted from post-processed least-squares solutions and then the clock is estimated in real-time filtering, which are quite different and separate processes. We proposed an integrated filter method in which the satellite orbit and clock states are estimated simultaneously based on the undifferenced observation model. With the estimation of satellite and receiver uncalibrated phase delays (UPDs), the undifferenced ambiguities are resolved in real time, resulting in the ambiguity-fixed satellite orbit and clock solutions. One-month observations of 150 globally distributed stations from multi-GNSS experiment tracking network are processed using the proposed method. In the experiment, the RMS of wide-lane (WL) and narrow-lane (NL) UPD residuals is all less than 0.07 cycles and 92% of WL and NL UPD residuals are within ± 0.1 cycle, contributing to a high fixing success rate of more than 90% for both GPS and Galileo satellites. Comparison with the IGS and CODE final orbit products shows that ambiguity resolution (AR) brings about 45% and 44% improvements to 3D RMS of the filter-based orbit solutions, from 8.2 to 4.7 cm and 9.5 to 5.4 cm for GPS and Galileo satellites, respectively. For comparison, the prediction orbits of the IGU and GBU products in the same periods are also evaluated. The average 3D RMS of the ultra-rapid products in the same periods is 5.3 cm and 7.8 cm for GPS and Galileo satellites, respectively, which are larger than that of the filter orbits. Compared to the float solutions, the STDs of GPS and Galileo satellite clocks are improved by more than 40% after AR. In addition, both convergence time and accuracy of kinematic precise point positioning AR by using filter-based products are better than that of using ultra-rapid products. [ABSTRACT FROM AUTHOR]

The availability of GNSS raw measurements and the improved performance of mass-market GNSS chipsets for tracking multi-constellation dual-frequency signals have facilitated the development of smartphone high-precision GNSS positioning. However, the channel-dependent carrier phase biases within typical smartphone GNSS chipset prevent Android multi-GNSS ambiguity resolution. In this study, the channel-dependent biases were investigated for the Android GLONASS G1, BDS B1I, Galileo E5a and QZSS L1 carrier phase observations. They destroy the integer property of GNSS ambiguities and result in varying GLONASS inter-frequency bias (IFB) rates. As a result, Android multi-GNSS double-difference ambiguity resolution is hindered and the traditional method of correcting for a constant GLONASS IFB rate is no longer applicable. We propose an on-the-fly phase biases correction method, which introduces reliability verification by resolving only the bias-free ambiguities and estimating the phase bias corrections on-the-fly by gain filtering. In this way, GPS/GLONASS/Galileo/BDS/QZSS dual-frequency ambiguities are resolved for a representative Xiaomi Mi 8 smartphone. For a ~ 13 km short baseline, when the smartphone is connected to an external survey-grade antenna, the time to first fix was 50 s and the fixing rate was 99.21% with the root mean square (RMS) of positioning errors of 1.32, 1.48 and 1.92 cm for the east, north and up components, respectively. Compared with dual-frequency GPS and five-constellation GNSS without phase biases correction, the ambiguity-fixing rate was improved by 30.4% and 99.2%, and the positioning accuracy was improved by 93.4% and 41.8%, respectively. In the case of the smartphone's embedded antenna, the ambiguity-fixing rate of five-constellation GNSS dropped to about 60% due to multipath, but the positioning precision of its ambiguity-fixed solutions was still at centimeter level, which was less than one-tenth of its float solutions. Therefore, the implementation of multi-GNSS ambiguity resolution will further boost the potential of high-precision GNSS positioning for smartphones. [ABSTRACT FROM AUTHOR]

To compare and evaluate the performance of different multi-GNSS fractional cycle biases (FCBs) products and precise point positioning (PPP) ambiguity resolution. We compare the stability and positioning performance of the School of Geodesy and Geomatics (SGG) and CNES GPS\Galileo FCBs products. The results show that similar stability and high consistency are observed between the two products, the difference of PPP ambiguity resolution bias between them is in the level of millimetre. And it is found that the epoch-interval of narrow-lane FCBs can be enlarged from 15 min to 30-180 min, to ease the transmission pressure on the transmission link. [ABSTRACT FROM AUTHOR]

Objectives: Precise point positioning (PPP) combines the advantages of standard point positioning (SPP) and relative positioning, which can achieve centimeter level positioning. With the development of BeiDou satellite navigation system (BDS), more and more BDS satellites begin to provide global positioning, navigation and timing services, which also promotes the development of multi⁃frequency and multi⁃system PPP. For a long time, because of the atmospheric delay and hardware delay of satellite and receiver, the ambiguity of PPP is not an integer. PPP needs a long time to converge, which greatly limits its application. The ambiguity can be restored to integer and the convergence time can be shortened with the help of fractional cycle bias (FCB). Methods: In order to improve the effect of precise point positioning⁃am biguity resolution (PPP⁃AR) of BDS as a whole, we estimate the FCBs of GPS and BDS based on the observation data from August 1 to August 31 in 2020 of globally distributed stations. The single difference between satellites is used to eliminate the influence of hardware delay at the receivers, and the single difference ambiguity vector is solved by the whole network adjustment to obtain the FCB estimation of each satellite. Results: The results of the time series of BDS⁃3 wide lane (WL) and narrow lane (NL) FCBs show that the WL FCBs has long term stability, the change of BDS 3 WL FCBs in 31 days is less than 0.2 weeks, and the change of GPS WL FCBs is less than 0.1 weeks. The FCBs of BDS⁃3 NL can keep stable for a period of time, and the change is less than 0.1 weeks. The percentages of GPS WL and NL FCBs residuals within 0.15 weeks are 99.8% and 99.3% respectively, and the percentages of BDS 3 are 99.7% and 98.1% respectively. In order to reflect the improvement effect of FCBs on PPP, static and dynamic PPP⁃AR tests were carried out at 8 stations around the world. The results show that under the static condition, the average fixed time and convergence time of BDS⁃3 are 31.5 min and 24.9 min respectively, which is 24.8% shorter than the float PPP. The errors in E, N and U directions are 1.03 cm, 0.60 cm and 1.72 cm respectively, and the fixed rate is 89.8%. Under the dynamic condition, the average fixed time and convergence time of BDS⁃3 are 33.3 min and 50.7 min respectively, which is 17.4% shorter than the float PPP. The errors in E, N and U directions are 2.57 cm, 2.29 cm and 3.71 cm respectively, and the fixed rate is 83.9%. Conclusions: PPP⁃AR can shorten the convergence time of PPP to a certain extent, but the improvement of positioning accuracy is not obvious after complete convergence. BDS 3 FCBs stability is limited by precision products and observation data, and its PPP⁃AR is slightly worse than GPS. [ABSTRACT FROM AUTHOR]

With the increasing number of available satellites from multi‐global navigation satellite systems (GNSS) and their applications in complicated environments, an increased number of faults in measurements are inevitable. Fault detection and exclusion (FDE) is an effective way to reject observation faults in order to guarantee the integrity of a GNSS positioning and navigation system. We propose a modified between‐receiver single‐differencing (SD)‐based FDE algorithm for real‐time kinematic (RTK) positioning. First, a modified between‐receiver SD model‐based FDE is proposed for testing the estimated float ambiguities. This is helpful in rejecting observations with unreliable float ambiguities and obtaining reliable double‐differencing (DD) integer ambiguities, denoted as the SD float model in the sequel. Second, DD ambiguities are resolved by the DD model and used to update the previous SD float ambiguity. After that, a modified SD fix model, taking the DD ambiguities as the known parameters, is further developed to detect any unreliable or fault‐resolved ambiguities. To verify the modified SD model‐based FDE algorithm, a kinematic vehicle test is conducted. The fault detection test statistics of the SD float model and the SD fix model, time‐to‐first‐fix, ambiguity‐fix rate, SD residuals, and positioning performances are examined. The results show that the modified FDE method can detect and exclude fault satellites accurately and effectively, which is verified by the SD residuals of fault satellites. The ambiguity‐fix rate of the proposed modified FDE algorithm is improved by approximately 3% with 70 more epochs of fixes. Regarding the 3D positioning performance, the modified proposed SD‐based FDE algorithm can achieve 54.11%, 57.78%, and 73.11% improvements for standard deviation, root mean square, and mean bias, respectively, when compared with the processing strategy without the use of the proposed FDE. [ABSTRACT FROM AUTHOR]

The carrier-based kinematic-to-kinematic relative positioning can obtain the precise baseline between two moving stations, which greatly expands the application field of dynamic relative positioning. However, the relative positioning performance is degraded greatly with low fixation rate of ambiguity with low-cost receivers. Especially, in the complex dynamic environment, ambiguity resolution effect is influenced by the satellite signal blocked, multipath outlier, and abnormal state prediction. Aiming at the problems, a novel inertial navigation system–aided robust adaptive filtering ambiguity resolution model is proposed. In addition, a hierarchical filtering strategy is developed to eliminate ambiguity parameters in BeiDou navigation satellite system/inertial navigation system tightly coupled integrated system. Finally, the precise relative position can be calculated with the "best" ambiguity solution. Both experiments with static data and field vehicle test were carried out to evaluate the algorithm efficiency in different data configurations. The results indicate that IRAFAR-TCRP method can effectively suppress the influence of observation outliers and model prediction abnormalities, which improves the success rate of ambiguity resolution, raises the accuracy as well as the continuity of relative positioning. The success rate of ambiguity resolution with single-frequency BeiDou navigation satellite system can reach 90% in the gross error and abnormal disturbance environments and centimeter-level accuracy can be achieved. [ABSTRACT FROM AUTHOR]

In this article we present a critical overview of the various investigations carried out to date on the subject/object asymmetry in the comprehension of relative clauses in Spanish. We review the findings reached so far through different experimental techniques and offer an overview of what these discoveries contribute to the discussion of the main theoretical proposals on sentence comprehension. We focus on four aspects of relative clauses in Spanish that can enrich the hypotheses that we have so far: (i) the structural ambiguity, (ii) the variety of relative types in Spanish (headed, false-free and free), (iii) the order of constituents and (iv) the animacity information and the gender, number and case of the nominals of the relatives. Thus, we try to identify what we know, what remains to be understood, and what are the most relevant directions of research in Spanish in order to inform contemporary theoretical models. [ABSTRACT FROM AUTHOR]

In two experiments, we examine how proficient second language speakers integrate verb bias and plausibility information during online sentence comprehension. Spanish–English speakers and native English speakers read sentences in English in which a post-verbal noun phrase (NP) could be interpreted as a direct object or a sentential subject. To examine the role of verb bias, the post-verbal NP was preceded by a verb that is preferentially followed by a direct object (DO-bias verbs) or a sentential complement (SC-bias verbs). To assess the role of plausibility, the semantic fit between the verb and the post-verbal NP was either congruent or incongruent with the direct object interpretation. The results show that both second language speakers and native speakers used verb bias information to assign a grammatical role to the post-verbal ambiguous NP with small differences. Syntactic revision of an initially incorrect DO interpretation was facilitated by the presence of an implausible NP. [ABSTRACT FROM AUTHOR]

For long baseline in a network, the traditional combined ionosphere-free (IF) + wide-lane (WL) strategy is commonly used, but the residual tropospheric delays and larger noise hamper the basic ambiguity resolution (AR). With the completion of the BeiDou global navigation satellite system (BDS-3) and the quad-frequency signals provided by BDS-3 satellites, we can construct more combinations that are conducive to ambiguity resolution. Compared with ionosphere-free linear combinations, we estimated ionospheric delay using three independent WL observations, and formed an ionosphere-weighted model using uncombined code and phase observations, which proved to be quite effective. Based on the real quad-frequency BDS-3 observations of two CORS (Continuously Operating Reference Stations) and two user stations, we processed eight days of data to study the formal and empirical ambiguity success rates and user positioning errors. The rounding success rate of WL ambiguity was significantly improved with ionospheric correction. The success rate of the basic ambiguity increased from 94.4 and 96.1% to 98.0% using the quad-frequency ionosphere-weighted (QFIW) model compared with the double-frequency ionosphere-free (DFIF) model and the triple-frequency geometry-based (TFGB) model. Furthermore, the user E/N/U positioning accuracy improved by 20.6/31.5/13.1% and 6.3/22.9/5.8%, respectively. [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 previous study has shown that children use recent input to adapt their syntactic predictions and use these adapted predictions to infer the meaning of novel words. In the current study, we investigated whether children could use this mechanism to disambiguate words whose interpretation as a noun or a verb is ambiguous. We tested 2‐ to 4‐year‐old French children using the phrase la petite followed by a homophone that could be interpreted as either a noun or a verb. We assigned the children to a noun condition or a verb condition. Before the test, those in the noun condition were exposed to sentences where la petite predicted nouns, and those in the verb condition to sentences where la petite predicted verbs. At testing, 3‐ to 4‐year‐olds, but not 2‐year‐olds, from the verb condition looked at the verb interpretation longer than did the children in the noun condition. This suggests a progression in children's ability to rely on input to adapt their predictions in language comprehension. [ABSTRACT FROM AUTHOR]

• BDS-3 quad-frequency phase OSB for all frequency ambiguity resolution is estimated. • The B1C/B2a/B3I combination achieved the highest positioning accuracy for the PPP-WAR. • The B1C/B2a combination of BDS-3 has a faster convergence speed than B1I/B3I. • Antenna phase center must be carefully handled as it threatens multi-frequency PPP-AR. In addition to the legacy of B1I and B3I signals, the BeiDou Global Navigation Satellite System (BDS-3) also broadcasts the new navigation signals B1C and B2a, which brings new challenges and opportunities for multi-frequency precise point positioning (PPP) ambiguity resolution. The observable-specific signal biases (OSBs) provide flexible frequency choice for multi-frequency ambiguity resolution. This work implemented an approach of BDS-3 quad-frequency OSBs estimation, making the generated OSBs suitable for ambiguity resolution using any frequency combinations. Besides, the benefits of B1C and B2a signals for wide-area decimeter-level and centimeter-level point positioning with ambiguity resolution are also investigated in depth. The BDS-3 B1C/B1I/B2a/B3I measurement data of 110 stations over one month were used to estimate the quad-frequency phase OSBs, and 20 different stations were selected for PPP verification. The results indicate that the BDS-3 quad-frequency phase OSBs are relatively stable, with a standard deviation of less than 0.06 cycle. The B1C/B2a/B3I combination achieved the highest positioning accuracy for instantaneous triple-frequency PPP wide-lane ambiguity resolution, with root-mean-square of 0.15 m, 0.17 m and 0.51 m in the east, north and up directions, respectively. Moreover, the use of B1C/B2a instead of the traditional frequency B1I/B3I as the WL combination improved the single-epoch PPP accuracy. Furthermore, after solving the narrow-lane ambiguity, the median convergence time of B1C/B2a for the kinematic and static mode was 26.5 min and 14.5 min, which was shortened by 29.3 % and 27.5 % compared to the results of the B1I/B3I combination, respectively. [ABSTRACT FROM AUTHOR]

Precise point positioning (PPP) has been recognized as a powerful tool for various geophysical applications. However, the long convergence time required to resolve a reliable ambiguity impedes its further application in time-critical scenarios. Although PPP ambiguity resolution (AR) can shorten the convergence time, its performance is subject to the quality of float ambiguity estimates and the uncalibrated phase delay (UPD), which can be contaminated by multipath errors. Furthermore, the observation residuals derived from PPP are very likely to be affected by the common-mode error (CME), thereby deteriorating the multipath modeling accuracy. The principal component analysis (PCA) is employed to mitigate the CME effect, and the multipath is modeled using a multipath hemispherical map (MHM). Consequently, the narrow-lane (NL) UPDs with multipath correction have better temporal stability and residual distributions than those without correction. Compared with sidereal filtering (SF), the MHM 0.5 has comparable residual variance reduction percentages, indicating its capability of capturing high-frequency multipath. For static PPP AR, the averaged time to first fix (TTFF) can be reduced by 24.2% to about 26 min and the convergence time can be achieved within 16.2 min after multipath correction. The pseudorange multipath correction significantly contributes to shortening the TTFF and convergence time. Reducing the resolution of MHM increases the risk of extending the TTFF. For kinematic PPP AR with MHM 0.5 , the convergence time exhibits a remarkable improvement when compared with that of the uncorrected case (21.7 min versus 40.2 min), and 20% of the stations achieve convergence within 10 min. Meanwhile, a few stations only take one minute to achieve convergence. The contribution of the multipath correction to the fixing rate is comparatively small. After applying MHM 0.5 , the kinematic positioning accuracies are improved by 35.7%, 12.6%, and 24.4% to 1.26, 1.39, and 2.73 cm for the east, north, and up components, respectively. • Mitigating of common-mode error can ameliorate the multipath modeling accuracy. • NL UPD estimates with multipath correction have better temporal stability and residual distributions. • Correcting pseudorange multipath is beneficial for shortening the TTFF and convergence time. • Multipath correction can significantly improve the performance of real-time PPP AR. [ABSTRACT FROM AUTHOR]

• Observable-specific signal bias (OSBs) transformation for multi-frequency is deduced. • Inter-frequency clock bias and antenna phase center must be consistent with OSBs. • Quad-frequency is conductive to shorten the convergence time of BDS-3 kinematic PPP. • Quad-system multi-frequency PPP-AR achieve millimeter-level in horizontal direction. With the completion of the BeiDou Global Navigation Satellite System (BDS-3), more available frequencies have brought opportunities for precise point positioning ambiguity resolution (PPP-AR). This research theoretically deduced the multi-frequency PPP-AR model and the rule of observable-specific signal bias (OSBs) transformation. Then 34 International GNSS Service stations were selected to investigate the multi-frequency BDS-3 and multi-GNSS PPP-AR. The results suggested that the OSBs products provided by Centre National D'Etudes Spatiales (CNES) have absorbed the impact of inter-frequency clock bias and could be directly added to the original observations to restore the integer characteristics of the multi-frequency ambiguity. Meanwhile, the antenna phase center correction should keep consistent when using the CNES OSBs to restore the Melbourne-Wübbena ambiguity. The BDS-3 quad-frequency ambiguity-fixed convergence time was 39.0 and 25.1 min for kinematic and static PPP, which was shortened by nearly 15.0 and 3.4 min than the dual-frequency ambiguity-fixed solution. The quad-system multi-frequency PPP-AR showed the optimal state, which was 0.66, 0.76 and 2.66 cm for kinematic mode while 0.31, 0.31 and 1.02 cm for static mode in east, north, and up directions, respectively. [ABSTRACT FROM AUTHOR]

• There are two different error sources: one relates to the error propagation law and the other to the systematic bias of the interpolation model. • We verify the existence of systematic errors in the interpolation model. • We discuss the spatial changes in systemic errors of the interpolation model. • A algorithm for estimating the stochastic model of atmospheric corrections is proposed. Regional Augmented Precise Point Positioning (RA-PPP) is a method used to support PPP-Real Time Kinematic (PPP-RTK) based on state space representation. In case of RA-PPP, uncalibrated phase delays and undifferenced ionospheric and tropospheric corrections generated by the reference station network are interpolated at the rover in real time. This study proposes a set of algorithms for estimating the uncertainties of atmospheric corrections that are compatible for use with the RA-PPP model. There are two different error sources of interpolated atmospheric corrections: one relates to the error propagation law and the other to the systematic bias of the interpolation model. We discuss the spatial changes in systemic errors of the interpolation model and present a new interpolation method and its use in calculating the uncertainties of interpolated atmospheric corrections. In addition, we verify the existence of systematic errors in the interpolation model and discuss the correlation between zenith tropospheric delay and slant ionospheric corrections. The results of PPP ambiguity resolution experiments using GPS/Galileo observations are presented. For a reference station network with an interstation distance of more than 110 km, when the proposed method is used, the rate of successfully fixing ambiguities reaches 67.8% in 5 min, and the fixing rate is higher than 90%. It is considered that our method has enhanced applicability for use with large networks and in complex environments. [ABSTRACT FROM AUTHOR]

The network real-time kinematic (RTK) technique uses continuously operating reference stations (CORS) within a geographic area to model the distance dependent errors, allowing users in the area to solve ambiguities. A key step in network RTK is to fix ambiguities between multiple reference stations. When a new satellite rises or when maintenance happens, many unknown parameters are involved in the mathematical model, and traditional methods take some time to estimate the integer ambiguities reliably. The purpose of this study is the single-epoch ambiguity resolution on small-scale CORS network with inter-station distance of around 50 km. A new differencing scheme is developed to explore the full potential of multi-frequency Global Navigation Satellite System (GNSS). In this scheme, a differencing operation is formed between satellites with the closest mapping functions. With the new differencing scheme, tropospheric error can be mostly neglected after the correction, as well as the double-differencing operation. Numerical tests based on two baselines of 49 km and 35 km show that the success rate of ambiguity resolution can reach more than 90%. The single-epoch ambiguity resolution for reference stations brings many benefits to the network RTK service, for example, the instantaneous recovery after maintenance or when a new satellite rises. [ABSTRACT FROM AUTHOR]

In the face of a complex observation environment, the solution of the reference station of the ambiguity of network real-time kinematic (RTK) will be affected. The joint solution of multiple systems makes the ambiguity dimension increase steeply, which makes it difficult to estimate all the ambiguity. In addition, when receiving satellite observation signals in the environment with many occlusions, the received satellite observation values are prone to gross errors, resulting in obvious deviations in the solution. In this paper, a new network RTK fixation algorithm for partial ambiguity among the reference stations is proposed. It first estimates the floating-point ambiguity using the robust extended Kalman filtering (EKF) technique based on mean estimation, then finds the optimal ambiguity subset by the optimized partial ambiguity solving method. Finally, fixing the floating-point solution by the least-squares ambiguity decorrelation adjustment (LAMBDA) algorithm and the joint test of ratio (R-ratio) and bootstrapping success rate index solver. The experimental results indicate that the new method can significantly improve the fixation rate of ambiguity among network RTK reference stations and thus effectively improve the reliability of positioning results. [ABSTRACT FROM AUTHOR]

• We manipulated lexical cues and the plausibility of structurally ambiguous sentences. • 5-year olds rapidly used lexical cues to resolve ambiguity during comprehension. • 5-year olds made little use of plausibility to resolve ambiguity. • During comprehension, adults relied almost exclusively on plausibility. Both 5-year-old children and adults infer the structure of a sentence as they are hearing it. Prior work, however, has found that children do not always make use of the same information that adults do to guide these inferences. Specifically, when hearing ambiguous sentences like "You can tickle the frog with the feather," children seem to ignore the aspects of the referential context that adults rely on to resolve the ambiguity—e.g., are there two frogs in the scene, one with a feather and one without? Or is there only one frog to be tickled by using a feather? The present study explored two hypotheses about children's failure to use high-level, top-down context cues to infer the structure of these ambiguous sentences: First, children may be less likely to use any top-down cue during comprehension. Second, children may only have difficulties with top-down cues that are unreliable predictors of which syntactic structure is being used. Thus, to disentangle these hypotheses, we conducted a visual world study of adults' and children's ambiguity resolution, manipulating a more reliable top-down cue (the plausibility of the interpretation) and pitting it against a robust bottom-up cue (lexical biases). We find that adults' and children's final interpretations are influenced by both sources of information: adults, however, give greater weight to the top-down cue, whereas children primarily rely on the bottom-up cue. Thus, children's tendency to make minimal use of top-down information persists even when this information is highly valid and dominates adult comprehension. We propose that children have a systematic propensity to rely on bottom-up processing to a greater degree than adults, which could reflect differences in the architecture of the adult and child language comprehension systems or differences in processing speed. [ABSTRACT FROM AUTHOR]

Precise Point Positioning (PPP), as a global precise positioning technique, suffers from relatively long convergence times, hindering its ability to be the default precise positioning technique. Reducing the PPP convergence time is a must to reach global precise positions, and doing so in a few minutes to seconds can be achieved thanks to the additional frequencies that are being broadcast by the modernized GNSS constellations. Due to discrepancies in the number of signals broadcast by each satellite/constellation, it is necessary to have a model that can process a mix of signals, depending on availability, and perform ambiguity resolution (AR), a technique that proved necessary for rapid convergence. This manuscript does so by expanding the uncombined Decoupled Clock Model to process and fix ambiguities on up to three frequencies depending on availability for GPS, Galileo, and BeiDou. GLONASS is included as well, without carrier-phase ambiguity fixing. Results show the possibility of consistent quasi-instantaneous global precise positioning through an assessment of the algorithm on a network of global stations, as the 67th percentile solution converges below 10 cm horizontal error within 2 min, compared to 8 min with a triple-frequency solution, showing the importance of having a flexible PPP-AR model frequency-wise. In terms of individual datasets, 14% of datasets converge instantaneously when mixing dual- and triple-frequency measurements, compared to just 0.1% in that of dual-frequency mode without ambiguity resolution. Two kinematic car datasets were also processed, and it was shown that instantaneous centimetre-level positioning with a moving receiver is possible. These results are promising as they only rely on ultra-rapid global satellite products, allowing for instantaneous real-time precise positioning without the need for any local infrastructure or prior knowledge of the receiver's environment. [ABSTRACT FROM AUTHOR]

Precise point positioning with ambiguity resolution (PPP-AR) based on multiple global navigation satellite system (multi-GNSS) constellations is an important high-precision positioning tool. However, some unmodeled satellite and receiver biases (such as errors in satellite attitude) make it difficult to fix carrier-phase ambiguities. In order to fix ambiguities of eclipsing satellites, accurate integer clock and satellite attitude products (i.e., attitude quaternion) have been provided by the International GNSS Service (IGS). Nevertheless, the quality of these products and their positioning performance in multi-GNSS PPP-AR have not been investigated yet. Using the PRIDE PPP-AR II software associated with the corresponding rapid satellite orbit, integer clock and attitude quaternion products of Wuhan University (WUM), we carried out GPS/BDS PPP-AR using 30 days of data in an eclipsing season of 2020. We found that about 75% of GPS, 60% of BDS-2 and 57% of BDS-3 narrow-lane ambiguity residuals after integer clock corrections fall within ±0.1 cycles in the case of using nominal attitudes. However, when using attitude quaternions, these percentages will rise to 80% for GPS, 70% for BDS-2 and 60% for BDS-3. GPS/BDS daily kinematic PPP-AR after integer clock and nominal attitude corrections can usually achieve a positioning precision of about 10, 10 and 30 mm for the east, north and up components, respectively. In contrast, the counterparts are 8, 8 and 20 mm when using attitude quaternions. Compared with the case of using attitude quaternions only at the network end for the integer clock estimation, using attitude quaternions only at the user end shows a pronounced improvement of 15% in the east component and less than 10% in the north and up components. Therefore, we suggest PPP users apply integer clock and satellite attitude quaternion products to realize more efficient ambiguity fixing, especially in satellite eclipsing seasons. [ABSTRACT FROM AUTHOR]

The use of carrier phase data is the main driver for high-precision Global Navigation Satellite Systems (GNSS) positioning solutions, such as Real-Time Kinematic (RTK). However, carrier phase observations are ambiguous by an unknown number of cycles, and their use in RTK relies on the process of mapping real-valued ambiguities to integer ones, so-called Integer Ambiguity Resolution (IAR). The main goal of IAR is to enhance the position solution by virtue of its correlation with the estimated integer ambiguities. With the deployment of new GNSS constellations and frequencies, a large number of observations is available. While this is generally positive, positioning in medium and long baselines is challenging due to the atmospheric residuals. In this context, the process of solving the complete set of ambiguities, so-called Full Ambiguity Resolution (FAR), is limiting and may lead to a decreased availability of precise positioning. Alternatively, Partial Ambiguity Resolution (PAR) relaxes the condition of estimating the complete vector of ambiguities and, instead, finds a subset of them to maximize the availability. This article reviews the state-of-the-art PAR schemes, addresses the analytical performance of a PAR estimator following a generalization of the Cramér–Rao Bound (CRB) for the RTK problem, and introduces Precision-Driven PAR (PD-PAR). The latter constitutes a new PAR scheme which employs the formal precision of the (potentially fixed) positioning solution as selection criteria for the subset of ambiguities to fix. Numerical simulations are used to showcase the performance of conventional FAR and FAR approaches, and the proposed PD-PAR against the generalized CRB associated with PAR problems. Real-data experimental analysis for a medium baseline complements the synthetic scenario. The results demonstrate that (i) the generalization for the RTK CRB constitutes a valid lower bound to assess the asymptotic behavior of PAR estimators, and (ii) the proposed PD-PAR technique outperforms existing FAR and PAR solutions as a non-recursive estimator for medium and long baselines. [ABSTRACT FROM AUTHOR]