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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]

Precise point positioning (PPP) uses precise satellite orbits, clock corrections and biases derived from a global network of reference stations to enable accurate positioning worldwide. Natural Resources Canada's Canadian Spatial Reference System (CSRS) PPP is a free Web service offering automated PPP processing. A critical factor limiting the adoption of PPP in many applications is the convergence time needed to reach centimeter‐level accuracies. To address this issue, CSRS‐PPP now implements PPP with ambiguity resolution (PPP‐AR). This feature required the development of new algorithms, such as sequential normal stacking for least‐squares filtering/smoothing, and the weighted integer decision concept for ambiguity validation. New satellite product lines (ultra‐rapid, rapid, final) also have been deployed to enable PPP‐AR processing with various latencies. This analysis demonstrates that sub‐centimeter horizontal accuracies can be obtained in less than one hour for both static and kinematic modes. Using product lines with longer latencies is beneficial, although improvements are typically within the reported uncertainties. [ABSTRACT FROM AUTHOR]

A frequency transfer model that is suitable for short baseline links is proposed herein. Based on a GPS single-differenced (SD) observation among two stations, the initial values and the corresponding variance of the SD ambiguity can be estimated. This can form the double-differenced (DD) ambiguity while defining the reference satellite, and can be fixed to an integer value by using the integer search method. After defining the values of the SD ambiguity datum for the reference satellite, the other SD ambiguities can be recovered; then, the final time difference of the two stations can be estimated using the known and fixed SD ambiguities. Validations performed using five different baseline links show that the new method has better accuracy and stability for precise time transfer than the traditional precise point positioning method, and it can be operated in conjunction with the broadcast ephemeris data, which is more convenient for real-time application. [ABSTRACT FROM AUTHOR]

Obtaining reliable GNSS uncalibrated phase delay (UPD) or integer clock products is the key to achieving ambiguity-fixed solutions for real-time (RT) precise point positioning (PPP) users. However, due to the influence of RT orbit errors, the quality of UPD/integer clock products estimated with a globally distributed GNSS network is difficult to ensure, thereby affecting the ambiguity resolution (AR) performance of RT-PPP. In this contribution, by fully utilising the consistency of orbital errors in regional GNSS network coverage areas, a method is proposed for estimating regional integer clock products to compensate for RT orbit errors. Based on Centre National d'Études Spatiales (CNES) RT precise products, the regional GPS/BDS integer clock was estimated with a CORS network in the west of China. Results showed that the difference between the estimated regional and CNES global integer clock/bias products was generally less than 5 cm for GPS, whereas clock differences of greater than 10 cm were observed for BDS due to the large RT orbit error. Compared with PPP using global integer clock/bias products, the AR performance of PPP using the regional integer clock was obviously improved for four rover stations. For single GPS, the horizontal and vertical accuracies of ambiguity-fixed PPP solutions were improved by 56.2% and 45.3% on average, respectively, whereas improvements of 67.5% and 50.5% in the horizontal and vertical directions, respectively, were observed for the combined GPS/BDS situation. Based on a regional integer clock, the RMS error of a kinematic ambiguity-fixed PPP solution in the horizontal direction could reach 0.5 cm. In terms of initialisation time, the average time to first fix (TTFF) in combined GPS/BDS PPP was shortened from 18.2 min to 12.7 min. In view of the high AR performance realised with the use of regional integer clocks, this method can be applied to scenarios that require high positioning accuracy, such as deformation monitoring. [ABSTRACT FROM AUTHOR]

To overcome the problem that a fixed estimator is contaminated by a system error for the ambiguity be misjudged in the GNSS precise positioning, a reliable integer float estimator is recommended. Accordingly, the method for determining a finite number of integer vectors based on a given reliability probability is proposed, the formula for calculating the variance matrix of the recommended estimator is derived, and the judgment method of the estimator's availability is proposed. The detailed process and the effect of the method are also demonstrated using examples to facilitate user application. [ABSTRACT FROM AUTHOR]

This study explored differences between the two hemispheres in processing written words among deaf readers. The main hypothesis was that impoverished phonological abilities of deaf readers may lead to atypical patterns of hemispheric involvement. To test this, deaf participants completed a metalinguistic awareness test to evaluate their orthographic and phonological awareness. Additionally, they were asked to read biased or neutral target sentences ending with an ambiguous homograph, with each sentence followed by the request to make a rapid lexical decision on a target word presented either to the left (LH) or right hemisphere (RH). Targets were either related to the more frequent, dominant, meaning of the homograph, to the less frequent, subordinate, meaning of the homograph or were not related at all. An Inverse Efficiency Score based on both response latency and accuracy was calculated and revealed that deaf readers' RH perform better than their LH. In contrast to hearing readers who in previous studies manifested left hemisphere dominance when completed the same research design. The apparent divergence of deaf readers' hemisphere lateralization from that of hearing counterparts seems to validate previous findings suggesting greater reliance on RH involvement among deaf individuals during visual word recognition. [ABSTRACT FROM AUTHOR]

Knowledge of differential inter-systems phase/code biases are critical to integrate observations from several different Global Navigation Satellite Systems. Many studies on tightly-combined model have mostly focused on the overlapping frequencies and short baselines, and fewer have focused on non-overlapping frequencies and medium-long baselines. Considering differential inter-systems code biases and inter-frequency code biases, we propose a tightly combined real-time kinematic model by a reparameterization process for non-overlapping frequencies among GPS/GLONASS/BDS systems. Compared with the traditional double-difference ambiguity parameter, we use single-difference ambiguity as the parameter to be estimated, which is not affected by reference satellite switching and wavelength limitation. The paper first analyzes the stability of differential inter-systems code biases and inter-frequency code biases with several zero and ultra-short baselines. Then, the paper tests the positioning performance under occlusion environment. The experiment shows that the tightly-combined model is more robust than the loosely-combined model and the average time to first fix is shortened by approximately 22.4%. At last, the paper compares the positioning performance of tightly-combined model, loosely-combined model, and tightly-combined model after calibration under the medium and long baselines. The experiment shows that the tightly-combined model after calibration is better than the tightly-combined model and loosely-combined model in the ambiguity resolution rate, initialization speed and positioning accuracy, respectively. Compared with intra-system loosely-combined model, the positioning accuracy of tightly-combined model after calibration is improved by 42.1%, 25.5%, and 32.3% in the three-dimensional directions, respectively. [ABSTRACT FROM AUTHOR]

Precise point positioning with ambiguity resolution (PPP-AR) is a useful tool for high-precision geodetic and geophysical applications, while phase bias products are the prerequisite to implement PPP-AR. Wuhan University has been providing the final (the best operationally post-processing solution based) phase clock/bias products with a latency of two weeks since March of 2019, while a dedicated open-source software package PRIDE PPP-AR is released to leverage these products for high-precision positioning. In order to satisfy some both time and precision critical applications, such as rapid earthquake response, Wuhan University also released rapid (with comparable quality but with much shorter delivery latency) phase clock/bias products with a latency of less than 24 h and updated PRIDE PPP-AR in July 2019. We first introduce the phase clock/bias generation and validation schemes and the maintenance of routine products provision. Then, with 14 days (July 2 to July 15 in 2019) of GPS data collected from 146 globally distributed IGS (International GNSS Service) stations, we evaluated the positioning performance of the rapid products with respect to their final counterparts. It is found that positioning precision of PPP-AR using rapid products is comparable to that using final products, especially in kinematic positioning mode. When rapid products are used, the RMS of PPP-AR in static mode with respect to IGS weekly solutions can reach 1.7 mm, 1.8 mm and 5.5 mm in the east, north and up components, respectively. Furthermore, the RMS of epoch-wise positions with respect to daily solutions for the east, north and up components are 0.51 cm, 0.57 cm and 1.51 cm for PPP-AR with rapid products in kinematic mode. It demonstrates that the rapid phase clock/bias products can sufficiently meet the precision requirement of most geodetic and geophysical applications yet with much shorter time delay. Finally, we study the July 6th M7.1 2019 Ridgecrest, California earthquake using the rapid phase clock/bias products and demonstrate their comparable performance against the final products. [ABSTRACT FROM AUTHOR]

PPP (Precise Point Positioning) is a GNSS (Global Navigation Satellite Systems) positioning method that requires SSR (State Space Representation) corrections in order to provide solutions with an accuracy of centimetric level. The so-called RT-PPP (Real-time PPP) is possible thanks to real-time precise SSR products, for orbits and clocks, provided by IGS (International GNSS Service) and its associate analysis centers such as CNES (Centre National d'Etudes Spatiales). CNES SSR products also enable RT-PPP with integer ambiguity resolution. In GNSS related literature, PPP with ambiguity resolution (PPP-AR) in real-time is often referred as PPP-RTK (PPP – Real Time Kinematic). PPP-WIZARD (PPP - With Integer and Zero-difference Ambiguity Resolution Demonstrator) is a software that is made available by CNES. This software is capable of performing PPP-RTK. It estimates slant ionospheric delays and other GNSS positioning parameters. Since ionospheric effects are spatially correlated by GNSS data from active networks, it is possible to model and provide ionospheric delays for any position in the network coverage area. The prior knowledge ionospheric delays can reduce positioning convergence for PPP-RTK users. Real-time ionospheric models could benefit from highly precise ionospheric delays estimated in PPP-AR. In this study, we demonstrate that ionospheric delays obtained throughout PPP-AR estimation are actu ally ionospheric observables. Ionospheric observables are biased by an order of few meters caused by the receiver hardware biases. These biases prohibit the use of PPP-WIZARD ionospheric delays to produce ionospheric models. Receiver biases correction is essential to provide ionospheric delays while using PPP-AR based ionospheric observables. In this contribution, a method was implemented to estimate and mitigate receiver hardware biases influence on slant ionospheric observables from PPP-AR. In order to assess the proposed approach, PPP-AR data from 12 GNSS stations were processed over a two-month period (March and April 2018). A comparison between IGS ionospheric products and PPP-AR based ionospheric observables corrected for receiver biases, resulted in a mean of differences of −39 cm and 51 cm standard deviation. The results are consistent with the accuracy of the IGS ionospheric products, 2–8 TECU, considering that 1 TECU is ~16 cm in L1. In another analysis, a comparison of ionospheric delays from 5 pairs of short baselines GNSS stations found an agreement of 0.001 m in mean differences with 22 cm standard deviation after receiver biases were corrected. Therefore, the proposed solution is promising and could produce high quality (1–2 TECU) slant ionospheric delays. This product can be used in a large variety of modeling approaches, since ionospheric delays after correction are unbiased. These results indicate that the proposed strategy is promising, and could benefit applications that require accuracy of 1–2 TECU (~16–32 cm in L1). [ABSTRACT FROM AUTHOR]

In the context of processing GNSS (Global Navigation Satellite System) data, it is known that the estimation of the ionospheric delays decreases the strength of the observation model and makes significant the time required to fix the ambiguities namely in case of long baselines. However, considering the double-differenced (DD) ionospheric delays as stochastic quantities, the redundancy in this case increases and leads to the reduction of time of fixing the ambiguities. The approach developed in the present paper makes two considerations: 1) the DD ionospheric delays are assumed as stochastic quantities and, 2) the spatial correlation of errors is accounted for based on a simple model of correlation. A simulation is made and aims to study the effect of these two mentioned considerations on the performances of the three multifrequency GNSSs; modernized GPS, Galileo and BDS which are not yet in full capability. For each GNSS, dual-frequency combinations of frequencies as well as triple-frequency combination are investigated in the simulation. The performances studied include: the time to fix the ambiguities with high success rate and the precision of coordinates in static relative positioning with varying baseline length. A method is developed to derive what we call the spatial correlation model which approximately gives the covariance between the individual errors belonging to two stations. Furthermore, the stochastic models that follow from accounting and neglecting the spatial correlation are developed. The LAMBDA (Least-squares Ambiguity Decorrelation Adjustment) method is implemented for ambiguity decorrelation. The results show that the time to fix the ambiguities caused by accounting the spatial correlation is less than the time of fix without the spatial correlation. Also, a slight superiority of Galileo in terms of performances is seen compared to the other GNSS. For all the dualfrequency combinations investigated, when processing a baseline length of 500 km with accounted spatial correlation, the time needed to successfully fix the ambiguities lies between 5 and 9 min, whereas it becomes only between 2.5 and 3 min for all the triple-frequency combinations, this is with a sampling time of 5 s. In addition, for all different combinations, the coordinates precision is less than 8 mm even for 500 km. We think that these high performances result from: 1) the precise codes of future GNSS signals, 2) the high redundancy in the observations equation and, 3) taking into account the spatial correlation in the definition of the stochastic model. [ABSTRACT FROM AUTHOR]

Over the last decades, several approaches for GPS phase ambiguity resolution haven been proposed and analysed. For triple-frequency long-baseline relative positioning, the most commonly used approach is LAMBDA, which can resolve all ambiguities in one step. However, the main limitation of LAMBDA is that it is difficult to validate the ambiguity results when it is in high dimension. To address this issue, in this research, a new strategy based on the sequential least squares estimation is proposed and the characteristics of this strategy are analysed. The performance of the new strategy and the commonly used one were assessed and compared using simulated triple-frequency GPS observations. Due to the fact that the two key quantities for the validation of GPS ambiguity are the ratio test and success rate, these two types of values were used to analyse the reliability of the integer ambiguity resolution in this study. The numerical results suggest that the success rates of the two approaches have no significant difference. However, the ratio value of the new approach can be significantly decreased in the case where the ambiguities are correctly fixed. This can smartly improve the reliability of long-baseline relative positioning, and then improve the operational efficiency of coastal surveying. [ABSTRACT FROM AUTHOR]

The authors investigate the benefits for the precise point positioning (PPP) ambiguity resolution technique of using the GPS L1, L2 and L5; Galileo E1, E5a, E5b and E6; and BeiDou B1, B2 and B3 measurements. Data from 17 reference stations over a period of 31 consecutive days in 2018 were used. It was found that the four-frequency Galileo combination of E1+E5a+E5b+E6 provides the lowest geometric and ambiguity variance. In a kinematic test using triple- and four-frequency GNSS measurements, the solution convergence time can be shortened by an average of 5 minutes as compared to the triple-frequency GPS-only PPP case. [ABSTRACT FROM AUTHOR]

The current study aimed to elucidate the contributions of the subcortical basal ganglia to human language by adopting the view that these structures engage in a basic neurocomputation that may account for its involvement across a wide range of linguistic phenomena. Specifically, we tested the hypothesis that basal ganglia reinforcement learning (RL) mechanisms may account for variability in semantic selection processes necessary for ambiguity resolution. To test this, we used a biased homograph lexical ambiguity priming task that allowed us to measure automatic processes for resolving ambiguity toward high‐frequency word meanings. Individual differences in task performance were then related to indices of basal ganglia RL, which were used to group subjects into three learning styles: (a) Choosers who learn by seeking high reward probability stimuli; (b) Avoiders, who learn by avoiding low reward probability stimuli; and (c) Balanced participants, whose learning reflects equal contributions of choose and avoid processes. The results suggest that balanced individuals had significantly lower access to subordinate, or low‐frequency, homograph word meanings. Choosers and Avoiders, on the other hand, had higher access to the subordinate word meaning even after a long delay between prime and target. Experimental findings were then tested using an ACT‐R computational model of RL that learns from both positive and negative feedback. Results from the computational model simulations confirm and extend the pattern of behavioral findings, providing an RL account of individual differences in lexical ambiguity resolution. Going from cognitive theory to neural data to ACT‐R models, the authors relate brain activity in a lexical ambiguity priming task to brain processes that resolve ambiguity in word meanings. These detailed data were tested and found compatible to the results of an ACT‐R computational model of reinforcement learning (RL). The model confirms and extends the behavioral findings to provide a RL account of individual differences in lexical ambiguity resolution. [ABSTRACT FROM AUTHOR]

High-precision navigation using low-cost handsets has profound potential for mass-market applications, which has been being boosted by the release of raw GNSS data from Google Android smart devices. However, integer ambiguity fixing for centimeter-level GNSS positioning is prevented by the unaligned chipset initial phase biases (IPBs) found within Android carrier-phase data. In this study, we thus investigate the temporal behaviors of those chipset IPBs using zero baselines where smart devices are linked to external survey-grade antennas, and find that the IPBs are generally stable over time as the mean standard deviation of single-epoch IPB estimates derived from continuous carrier-phase data is as low as 0.04 cycles for all satellites. Unfortunately, these chipset IPBs differ randomly among satellites and change unpredictably if carrier-phase signals are re-tracked, discouragingly suggesting that the chipset IPBs cannot be pre-calibrated or even calibrated on the fly. We therefore have to presumably correct for them in a post-processing manner with the goal of inspecting the potential of Android GNSS ambiguity resolution if hopefully the IPBs can be gone. For a vehicle-borne Nexus 9 tablet with respect to a survey-grade receiver located 100–2000 m away, we achieve the first ambiguity-fixed solution within 321 s and finally 51.6% of all epochs are resolved; the ambiguity-fixed epochs can achieve a positioning accuracy of 1.4, 2.2 and 3.6 cm for the east, north and up components, respectively, showing an improvement of 30–80% compared to the ambiguity-float solutions. While all smart devices above are connected to external survey-grade antennas, we find that a Xiaomi 8 smartphone can be coupled effectively with a miniaturized portable patch antenna, and then achieve commensurate carrier-phase tracking and ambiguity-fixing performance to those of a commercial μ-blox receiver with its dedicated patch antenna. This is encouraging since a compact and inexpensive patch antenna paired with smart devices can promote the democratization of high-precision GNSS. [ABSTRACT FROM AUTHOR]

The Ambiguity Dilution of Precision (ADOP) is a well-known scalar measure that can be used to infer the strength of the Global Navigation Satellite System (GNSS) model of the carrier phase ambiguities involved in precise relative GNSS positioning. Odijk and Teunissen (2008a) derived closed-form expressions for single-baseline GNSS models that allow verifying the factors affecting the ambiguity resolution as well as the probability of its correct resolution as integer values. However, this weighted-ionosphere ADOP closed form assumes that the standard deviation of the ionosphere delay is dependent on a function associated with the baseline length. This means that a baseline of the same length at different locations around the world and in different moments in time would have the same standard deviation, which in practice is not true. This becomes even worse in regions like Brazil, where the ionospheric anomalies are more intense and frequent, especially in periods of high solar activity. In this work, a new method for calculating the ionospheric delay standard deviation that considers the ionospheric scintillation S4 index is proposed to improve the closed-form ADOP performance. Experiments with a baseline of 280 m located in Presidente Prudente, Brazil (magnetic latitude of around −13°), were carried out. The results showed that in periods of both weak and strong ionospheric scintillation, the introduction of S4 into the ionospheric delay standard deviation was beneficial for ADOP. The average improvement of the ADOP closed form was of around 72% in the analyzed period of weak scintillation and of 35% in the period of strong scintillation. In addition, the results showed that in periods of strong scintillation, relative positioning accuracy is around 100 times worse, up to 30 m, when compared to periods of weak ionospheric scintillation. [ABSTRACT FROM AUTHOR]

Multi-constellation GNSS (multi-GNSS) and multi-frequency signals open new prospects for fast ambiguity resolution (AR) of precise point positioning (PPP). Currently, all the BDS and Galileo satellites are capable of transmitting signals on three or more frequencies. In this contribution, we investigate the triple-frequency PPP ambiguity resolution with B1, B2 and B3 observations from BDS satellites and E1, E5a and E5b observations from Galileo satellites and evaluate the contribution of BDS + Galileo combination to triple-frequency PPP AR. The uncalibrated phase delay (UPD) products are estimated based on triple-frequency observations, and the temporal characteristic as well as the residual distributions are analyzed. Our results show that the extra-wide-lane (EWL) and wide-lane (WL) UPDs for BDS and Galileo satellites are both stable during the 30 days and the daily narrow-lane (NL) UPD series are also steady with no obvious fluctuation. The Galileo UPDs exhibit better performance than BDS UPDs due to the high-quality observations. It is also interesting to find that the EWL UPD corrections for all Galileo satellites are very close to the zero. With the precise UPD products, the triple-frequency PPP AR with BDS and Galileo observations was implemented in both static and kinematic modes. Compared to the ambiguity-float solution, the performance can be significantly improved by triple-frequency PPP AR with the positioning accuracy improved by 30–70% in both static and kinematic modes. Moreover, the triple-frequency PPP fixed solutions also present better performance than the dual-frequency PPP fixed solutions in terms of time to the first fix and positioning accuracy, especially for the Galileo-only and BDS + Galileo solutions. And the fusion of multi-GNSS (BDS and Galileo) can further improve the position estimations compared to the single system with more satellites and better spatial geometry. [ABSTRACT FROM AUTHOR]

In multi-GNSS integration, fixing inter-system double-difference ambiguities to integers is still a challenge due to the existence of inter-system biases (ISB) when mixed types of GNSS receivers are used. It has been shown that when ISB is known, the inter-system ambiguities can be fixed and the reliability of ambiguity fixing can be improved significantly, especially under poor conditions when the number of observed satellites is small. In traditional methods, the intra-system ambiguity is fixed first; then, the ISB is estimated to ultimately fix the inter-system ambiguity. In our work, we use the particle filter-based method to estimate the ISB parameter and fix the inter-system ambiguities to integers at the same time. This method shows higher reliability and higher ambiguity fixing rate. Nevertheless, the existing particle filter approach for ISB parameter estimation is a one-dimensional algorithm. When satellites from three or more systems are observed, there are two or more ISB parameters. We extend the current one-dimensional particle filter approach to multi-dimensional case and estimate multi-ISB parameters in this study. We first present a multi-dimensional particle filter approach that can estimate multi-ISB parameters simultaneously. We also show that the RATIO values can be employed to judge the quality of multi-dimensional ISB values. Afterward, a two-dimensional particle filter approach is taken as an example to validate this approach. For example, in the experiment of GPS L5, Galileo E5a and QZSS L5 integration with 6 satellites using the IGS baseline SIN0-SIN1, only three ambiguities are resolved to integer when the ISBs are unknown. The integer ambiguity fixing rate is 41.0% with 53% of the ambiguity-fixed solutions having positioning errors larger than 3 cm. However, when our approach is adopted, the number of integer ambiguity parameters increases to five. The integer ambiguity fixing rate increases to 99.7% with 100% of ambiguity-fixed solutions having positioning errors smaller than 3 cm. [ABSTRACT FROM AUTHOR]

Autonomous driving represents one of the emerging applications that require both high-precision positions and highly critical timeliness to reach stringent safety standards. We develop a method to potentially achieve global instantaneous decimeter-level positioning by virtue of tightly coupled multi-GNSS triple-frequency observations contributing to precise point positioning (PPP). Inter-system phase biases (ISPBs) for two wide-lane observables are first computed for each station to form inter-GNSS resolvable ambiguities, and then correspondingly two wide-lane fractional-cycle biases (FCBs) are computed for each satellite to recover the integer property of single-station ambiguities. With both ISPB and FCB products, we can accomplish tightly coupled multi-GNSS PPP wide-lane ambiguity resolution (PPP-WAR) using only a single epoch of triple-frequency observations on a global scale. To verify this method, we used 1 month of GPS/BeiDou/Galileo/QZSS data from 107 globally distributed stations and 1 h of such multi-GNSS data collected on a vehicle moving in an urban area. We found that both ISPB and FCB products could be estimated every 24 h with high precisions of around or below 0.1 cycles; 83–98% of their day-to-day variations fell within 0.1 cycles, facilitating their precise predictions for real-time applications. Using these corrections, we achieved both instantly and reliably ambiguity-fixed solutions at 91.2% of all epochs at the 107 stations on average; the resultant single-epoch positions reached a mean accuracy of 0.22 m, 0.18 m and 0.63 m for the east, north and up components, respectively, in case of abundant triple-frequency observations from over 15 satellites. Similarly, for the vehicle-borne test, we obtained instantaneous PPP-WAR solutions at 99.31% of all epochs and achieved a positioning accuracy of 0.29, 0.35 and 0.77 m for the east, north and up components, respectively, which improved significantly the identification of road lanes as opposed to other single-epoch solutions. Finally, we expect that the prospect of instantaneous PPP-WAR in aiding driverless vehicles can be more promising if, whenever possible, integrated with inertial sensors and/or smoothed through multi-epoch data. [ABSTRACT FROM AUTHOR]

Abstract Ambiguity fixing to integer numbers of the phase measurements has been proven to ameliorate the accuracy of GNSS data processing. Until now there are two strategies to achieve ambiguity resolution; by forming double differences and by using undifferenced phase measurements. In this article, the potentiality of using the latter method for fixing the phase ambiguities for the Galileo system combined with GPS measurements in a Multi-GNSS solution is proved. The integer property of the Galileo phase clocks is demonstrated. GPS and Galileo phase fixed orbit and "integer" clock products are compared to the float solutions. Both orbit overlaps and orbit validation using satellite laser ranging (SLR) validation methods showed that there is an improvement mainly in the normal and the along track direction. [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]

Single-frequency GPS ambiguity resolution on-the-fly has the problem that normal equation is ill-posed. Using epoch-differenced coordinate information between neighboring epochs can mitigate the ill-condition problem to some extent, as a result, the accuracy of the float ambiguity solution will be improved and the convergence time of ambiguity will be shortened. In order to further improve the ambiguity fixing effciency of epoch-differenced method, the epoch-differenced coordinate pseudo-observation error equation and its new variance matrix is reconstructed. The experimental results show that, compared with the previous algorithm with epoch-differenced coordinate information, the new method has higher stability and efficiency. [ABSTRACT FROM AUTHOR]