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

In the urban canyon environment, the integer ambiguity is hard to be fixed completely mainly because of the multipath effects, hence partial ambiguity resolution (PAR) is developed. This paper systematically introduces a new model-driven PAR method considering elevation and C/N0. Firstly, the theory of partial ambiguity resolution, the elevation-C/N0 function, and the proposed elevation-C/N0 PAR method are deduced in detail. Secondly, the proposed elevation-C/N0 method is applied in the static and dynamic experiments. The performances of the proposed method are compared with the full ambiguity resolution method, traditional elevation-dependent method, and C/N0-dependent method. Comparisons indicate that the proposed elevation-C/N0 method outperforms other methods. The results show that no matter in the urban static experiment or the dynamic experiment, the ambiguity resolution and positioning solutions can be improved. [ABSTRACT FROM AUTHOR]

The fast and accurate solution of integer ambiguity is the key to achieve GNSS high-precision positioning. Based on the lattice theory of high-dimensional ambiguity solving, the reduction time consumption is much larger than the search time consumption, and it is especially important to improve the efficiency of the lattice basis reduction algorithm. The Householder QR decomposition with minimal column pivoting is utilized to pre-sort the basis vectors and reduce the number of basis vector exchanges during the reduction process by partial size reduction and relaxing the basis vector exchange condition to improve the reduction efficiency of the LLL algorithm. The improved algorithm is validated using simulated and measured data, respectively, and the performance advantages and disadvantages of the improved algorithm are evaluated from the perspectives of the extent of reduction basis orthogonality and the quality of reduction basis size reduction. The results show that the improved LLL algorithm can significantly reduce the number of basis vector exchanges and the reduction time consumption. The HSLLL and PSLLL algorithms with the Siegel condition as the basis vector exchange condition have a better reduction effect, but are slightly less stable. The PLLLR algorithm significantly improves the search ambiguity resolution efficiency, which is conducive to the rapid realization of ambiguity resolution. [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]

In the classic Precise Point Positioning (PPP) approach, observations of Global Navigation Satellite Systems (GNSS) are processed at the network level to generate satellite clocks and positions. This information can be used to enable accurate point positioning for a single GNSS receiver. In the PPP Real-Time Kinematic (PPP-RTK) approach, satellite phase biases are considered as well, enabling ambiguity resolution at the network and user levels. In this research, 30 s multi-frequency raw GPS, Galileo, and BDS-2/3 observations are processed at the network and user levels in a sequential Kalman filter. PPP-RTK enabling products are generated for up to five frequencies, and ambiguity resolution is performed at the network and user levels using a flexible ambiguity reparameterization approach, comparable to wide- and narrow-laning, which has shown to yield a significantly improved single epoch coordinate solution when multi-frequency observations are available. Different assumptions regarding the time stability of receiver and satellite phase biases have been made and compared. The availability of a precise user coordinate solution when multi-frequency and dual-frequency observations are processed is assessed and compared. A precise ambiguity-fixed solution is available in three epochs or fewer in 77% of all cases with an average of 24 visible satellites for static and kinematic receivers when multi-frequency observations are processed. When only dual-frequency observations are considered, a fixed solution is available in seven epochs or fewer in 71% of all cases. The fastest fixed solution was found in two epochs with multi-frequency observations and in six epochs with dual-frequency observations. Estimating a reference phase clock did not lead to an improvement in the coordinate solution. The findings indicate that a fixed solution can potentially be found faster than often suggested, with potential for further improvement when more satellites or regional atmospheric corrections are considered. [ABSTRACT FROM AUTHOR]

In this paper, we propose a partial ambiguity method of global navigation satellite system (GNSS) reliable positioning based on a robust estimation model to address the problems of the low reliability and availability of GNSS positioning in urban complex environments. First, the high-precision observations selected on the basis of the signal-to-noise ratio (SNR) were used to solve ambiguities. Then, the fixed ambiguities were used as constraints to solve the ambiguities of low-quality observations. The robust estimation method was used to reduce the impact of outliers for the ambiguity solutions. The robust estimation was also used to solve the position parameters to reduce the influence of the residual errors and uncorrected ambiguities for GNSS high-accuracy positioning. Static and dynamic data were used to evaluate the proposed algorithm. These experiments show that the proposed algorithm with the robust estimation can reduce the fixed time of ambiguity initialization, compared with the conventional algorithm without the robust estimation. The positioning accuracy and solution rate are similar regardless of whether the robust estimation is used in the GNSS unblocked environment. In blocked environments, the solution rate improves to more than 99%, and the three-dimensional (3D) position accuracy improves by more than 70% when the robust estimation is used. When the observation number of simulated small gross error accounts for 40.91% of total observations, the centimeter-level positioning accuracy can still be obtained via several robust estimation models. In the urban blocked environment, the IGG (Institute of Geodesy and Geophysics) III scheme has a better performance than other robust schemes discussed in this paper with regard to the positioning performance and computational efficiency. [ABSTRACT FROM AUTHOR]

Global navigation satellite system (GNSS) ambiguity resolution is the key to realize high-precision navigation and positioning applications. For some dynamic application scenes such as moving-baseline-based positioning and attitude determination, the baseline information of GNSS antennas can be measured in advance; such a priori information can contribute to integer ambiguity resolution, especially when it is in weak GNSS models. In this research, a baseline vector constrained ambiguity resolution method (VC-LAMBDA) is demonstrated theoretically and verified experimentally. The objective function of VC-LAMBDA method is derived firstly, and then the corresponding search algorithm is designed, with an adaptive search space strategy adopted to speed up the search efficiency. The VC-LAMBDA method extends the scalar baseline length constrained LAMBDA method (C-LAMBDA) to the three-dimensional vector case, and simplifies the nonlinearly constrained integer least-squares (ILS) problem to a linearly constrained ILS problem. Two groups of real-measured data with one vehicle platform and one aircraft platform are tested to evaluate the practical performance of VC-LAMBDA, also compared with standard LAMBDA and C-LAMBDA methods. The two experiments show consistent results that VC-LAMBDA performs better than C-LMABDA method in ambiguity fixed success rate, robustness and time consumption, and both the two baseline constraint methods are significantly superior than standard LAMBDA method when it is in weak GNSS models. [ABSTRACT FROM AUTHOR]

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

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

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]

Solution of the Global Navigation Satellite Systems (GNSS) phase ambiguity is considered as a global quadratic mixed integer programming task, which can be transformed into a pure integer problem with a given digit of accuracy. In this paper, three alternative algorithms are suggested. Two of them are based on local and global linearization via McCormic Envelopes, respectively. These algorithms can be effective in case of simple configuration and relatively modest number of satellites. The third method is a locally nonlinear, iterative algorithm handling the problem as {-1, 0, 1} programming and also lets compute the next best integer solution easily. However, it should keep in mind that the algorithm is a heuristic one, which does not guarantee to find the global integer optimum always exactly. The procedure is very powerful utilizing the ability of the numeric-symbolic abilities of a computer algebraic system, like Wolfram Mathematica and it is properly fast for minimum 4 satellites with normal configuration, which means the Geometric Dilution of Precision (GDOP) should be between 1 and 8. Wolfram Alpha and Wolfram Clouds Apps give possibility to run the suggested code even via cell phones. All of these algorithms are illustrated with numerical examples. The result of the third one was successfully compared with the LAMBDA method, in case of ten satellites sending signals on two carrier frequencies (L1 and L2) with weighting matrix used to weight the GNSS observation and computed as the inverse of the corresponding covariance matrix. [ABSTRACT FROM AUTHOR]

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

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

Global Navigation Satellite System (GNSS) attitude determination and positioning play an important role in many navigation applications. However, the two GNSS-based problems are usually treated separately. This ignores the constraint information of the GNSS antenna array and the accuracy is limited. To improve the performance of navigation, an integrated attitude and position determination method based on an affine constraint model is presented. In the first part, the GNSS array model and affine constrained attitude determination method are compared with the unconstrained methods. Then the integrated attitude and position determination method is presented. The performance of the proposed method is tested with a series of static data and dynamic experimental GNSS data. The results show that the proposed method can improve the success rate of ambiguity resolution to further improve the accuracy of attitude determination and relative positioning compared to the unconstrained methods. [ABSTRACT FROM AUTHOR]

When precise positioning is carried out via GNSS carrier phases, it is important to make use of the property that every ambiguity should be an integer. With the known float solution, any integer vector, which has the same degree of freedom as the ambiguity vector, is the ambiguity vector in probability. For both integer aperture estimation and integer equivariant estimation, it is of great significance to know the posterior probabilities. However, to calculate the posterior probability, we have to face the thorny problem that the equation involves an infinite number of integer vectors. In this paper, using the float solution of ambiguity and its variance matrix, a new approach to rapidly and accurately calculate the posterior probability is proposed. The proposed approach consists of four steps. First, the ambiguity vector is transformed via decorrelation. Second, the range of the adopted integer of every component is directly obtained via formulas, and a finite number of integer vectors are obtained via combination. Third, using the integer vectors, the principal value of posterior probability and the correction factor are worked out. Finally, the posterior probability of every integer vector and its error upper bound can be obtained. In the paper, the detailed process to calculate the posterior probability and the derivations of the formulas are presented. The theory and numerical examples indicate that the proposed approach has the advantages of small amount of computations, high calculation accuracy and strong adaptability. [ABSTRACT FROM AUTHOR]

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

For Global Navigation Satellite System (GNSS) single frequency, single epoch attitude determination, this paper proposes a new reliable method with baseline vector constraint. First, prior knowledge of baseline length, heading, and pitch obtained from other navigation equipment or sensors are used to reconstruct objective function rigorously. Then, searching strategy is improved. It substitutes gradually Enlarged ellipsoidal search space for non-ellipsoidal search space to ensure correct ambiguity candidates are within it and make the searching process directly be carried out by least squares ambiguity decorrelation algorithm (LAMBDA) method. For all vector candidates, some ones are further eliminated by derived approximate inequality, which accelerates the searching process. Experimental results show that compared to traditional method with only baseline length constraint, this new method can utilize a priori baseline three-dimensional knowledge to fix ambiguity reliably and achieve a high success rate. Experimental tests also verify it is not very sensitive to baseline vector error and can perform robustly when angular error is not great. [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]

Integer ambiguity resolution is required to obtain precise coordinates for the global navigation satellite system (GNSS). Poorly observed data cause unfixed integer ambiguity and reduce the coordinate accuracy. Previous studies mostly used denoise filters and partial ambiguity resolution algorithms to address this problem. This study proposes a sequential ambiguity resolution method that includes a float solution substitution process and a double-difference (DD) iterative correction equation process. The float solution substitution process updates the initial float solution, while the DD iterative correction equation process is used to eliminate the residual biases. The satellite-selection experiment shows that the float solution substitution process is adequate to obtain a more accurate float solution. The iteration-correction experiment shows that the double-difference iterative correction equation process is feasible with an improvement in the ambiguity success rate from 28.4% to 96.2%. The superiority experiment shows significant improvement in the ambiguity success rate from 36.1% to 83.6% and a better baseline difference from about 0.1 m to 0.04 m. It is proved that the proposed sequential ambiguity resolution method can significantly optimize the results for poorly-observed GNSS data. [ABSTRACT FROM AUTHOR]

Global navigation satellite systems (GNSSs) play a key role in intelligent transportation systems such as autonomous driving or unmanned systems navigation. In such applications, it is fundamental to ensure a reliable precise positioning solution able to operate in harsh propagation conditions such as urban environments and under multipath and other disturbances. Exploiting carrier phase observations allows for precise positioning solutions at the complexity cost of resolving integer phase ambiguities, a procedure that is particularly affected by non-nominal conditions. This limits the applicability of conventional filtering techniques in challenging scenarios, and new robust solutions must be accounted for. This contribution deals with real-time kinematic (RTK) positioning and the design of robust filtering solutions for the associated mixed integer- and real-valued estimation problem. Families of Kalman filter (KF) approaches based on robust statistics and variational inference are explored, such as the generalized M-based KF or the variational-based KF, aiming to mitigate the impact of outliers or non-nominal measurement behaviors. The performance assessment under harsh propagation conditions is realized using a simulated scenario and real data from a measurement campaign. The proposed robust filtering solutions are shown to offer excellent resilience against outlying observations, with the variational-based KF showcasing the overall best performance in terms of Gaussian efficiency and robustness. [ABSTRACT FROM AUTHOR]

Satellite chip shape distortions lead to signal tracking errors in pseudorange measurements, which are related to the receiver manufacturers, called receiver-related pseudorange biases. Such biases will lead to adverse effects for differential code bias (DCB) and satellite clock estimation, single point positioning (SPP) and precise point positioning (PPP) applications with pseudoranges. In order to assess the characteristics of receiver-related pseudorange biases for global positioning system (GPS), Galileo navigation satellite system (Galileo) and BeiDou navigation satellite system (BDS), seven short baselines from the Multi-GNSS experiment (MGEX) network are tested. The results demonstrate that there are significant inconsistences of pseudorange biases according to satellites, frequencies, receiver and antenna types. For the baselines using the same receivers of TRIMBLE, pseudorange biases are within ±0.2 ns with the same antennas, while they increase to ±0.6 ns with the different antennas. As for baselines with mixed receiver types, pseudorange biases can reach up to 2.5 ns. Among GPS/Galileo/BDS, Galileo shows the smallest pseudorange biases, and the obvious inconsistences of pseudorange biases are observed between BDS-2 and BDS-3, and Galileo in-orbit validation (IOV) satellites and full operational configuration (FOC) satellites. In order to validate receiver-related pseudorange biases, we carry out relative positioning experiments using short baselines. The results show that the RMS values of position errors are reduced 12.6% and 11.4% in horizontal and vertical components with biases correction. The impacts of receiver-related pseudorange biases on wide-lane (WL) ambiguity are also discussed. The results indicate that the percentage of the fractional parts within ±0.1 cycles have an obvious increase with the pseudorange biases correction, and RMS values of the fractional parts are reduced 28.9% and 67.6% for GPS and BDS, respectively. [ABSTRACT FROM AUTHOR]

The high precision positioning can be easily achieved by using real-time kinematic (RTK) and precise point positioning (PPP) or their augmented techniques, such as network RTK (NRTK) and PPP-RTK, even if they also have their own shortfalls. A reference station and datalink are required for RTK or NRTK. Though the PPP technique can provide high accuracy position data, it needs an initialisation time of 10–30 min. The time-relative positioning method estimates the difference between positions at two epochs by means of a single receiver, which can overcome these issues within short period to some degree. The positioning error significantly increases for long-period precise positioning as consequence of the variation of various errors in GNSS (Global Navigation Satellite System) measurements over time. Furthermore, the accuracy of traditional time-relative positioning is very sensitive to the initial positioning error. In order to overcome these issues, an improved time-relative positioning algorithm is proposed in this paper. The improved time-relative positioning method employs PPP model to estimate the parameters of current epoch including position vector, float ionosphere-free (IF) ambiguities, so that these estimated float IF ambiguities are used as a constraint of the base epoch. Thus, the position of the base epoch can be estimated by means of a robust Kalman filter, so that the position of the current epoch with reference to the base epoch can be obtained by differencing the position vectors between the base epoch and the current one. The numerical results obtained during static and dynamic tests show that the proposed positioning algorithm can achieve a positioning accuracy of a few centimetres in one hour. As expected, the positioning accuracy is highly improved by combining GPS, BeiDou and Galileo as a consequence of a higher amount of used satellites and a more uniform geometrical distribution of the satellites themselves. Furthermore, the positioning accuracy achieved by using the positioning algorithm here described is not affected by the initial positioning error, because there is no approximation similar to that of the traditional time-relative positioning. The improved time-relative positioning method can be used to provide long-period high precision positioning by using a single dual-frequency (L1/L2) satellite receiver. [ABSTRACT FROM AUTHOR]

The benefits of an increased number of global navigation satellite systems (GNSS) in space have been confirmed for the robustness and convergence time of standard precise point positioning (PPP) solutions, as well as improved accuracy when (most of) the ambiguities are fixed. Yet, it is still worthwhile to investigate fast and high-precision GNSS parameter estimation to meet user needs. This contribution focuses on integer ambiguity resolution-enabled Precise Point Positioning (PPP-RTK) in the use of the observations from four global navigation systems, i.e., GPS (Global Positioning System), Galileo (European Global Navigation Satellite System), BDS (Chinese BeiDou Navigation Satellite System), and GLONASS (Global'naya Navigatsionnaya Sputnikova Sistema). An undifferenced and uncombined PPP-RTK model is implemented for which the satellite clock and phase bias corrections are computed from the data processing of a group of stations in a network and then provided to users to help them achieve integer ambiguity resolution on a single receiver by calibrating the satellite phase biases. The dataset is recorded in a local area of the GNSS network of the Netherlands, in which 12 stations are regarded as the reference to generate the corresponding corrections and 21 as the users to assess the performance of the multi-GNSS PPP-RTK in both kinematic and static positioning mode. The results show that the root-mean-square (RMS) errors of the ambiguity float solutions can achieve the same accuracy level of the ambiguity fixed solutions after convergence. The combined GNSS cases, on the contrary, reduce the horizontal RMS of GPS alone with 2 cm level to GPS + Galileo/GPS + Galileo + BDS/GPS + Galileo + BDS + GLONASS with 1 cm level. The convergence time benefits from both multi-GNSS and fixing ambiguities, and the performances of the ambiguity fixed solution are comparable to those of the multi-GNSS ambiguity float solutions. For instance, the convergence time of GPS alone ambiguity fixed solutions to achieve 10 cm three-dimensional (3D) positioning accuracy is 39.5 min, while it is 37 min for GPS + Galileo ambiguity float solutions; moreover, with the same criterion, the convergence time of GE ambiguity fixed solutions is 19 min, which is better than GPS + Galileo + BDS + GLONASS ambiguity float solutions with 28.5 min. The experiments indicate that GPS alone occasionally suffers from a wrong fixing problem; however, this problem does not exist in the combined systems. Finally, integer ambiguity resolution is still necessary for multi-GNSS in the case of fast achieving very-high-accuracy positioning, e.g., sub-centimeter level. [ABSTRACT FROM AUTHOR]

This paper presents a PREcise and Fast Method of Ambiguity Reinitialization/Resolution (PREFMAR) for L1 and L2 in GPS measurements. The method determines N L 1 and N L 2 ambiguities based on the ambiguity functions: Ψ (N L 1 ) N L 1 N L 2 and Ψ (N L 2 ) N L 2 N L 1 . These ambiguity functions have been described in detail in this work. The developed method of ambiguity initialization and reinitialization in relative positioning can use Global Positioning System (GPS) measurements from only two satellites and one measurement epoch. To resolve N L 1 and N L 2 ambiguities, a variance-covariance (VC) matrix of the float solution is not needed. The size of the search area in the PREFMAR method depends on code and phase accuracy as well as on the GNSS signal frequencies. Therefore, the search area is specific for every double or triple Global Navigation Satellite Systems (GNSS) data frequency. However, this part of the research only presents the ambiguity search area for L1 and L2 of GPS measurements. Additionally, a numerical example has been analyzed in detail with the use of the PREFMAR method and a float solution ( N ˜ L 1 , N ˜ L 2 ). Finally, the elaborated algorithms were successfully tested on real L1 and L2 GPS measurements for instantaneous ambiguity reinitialization. The PREFMAR method allows instantaneous ambiguity reinitialization if all satellites lose contact with a GNSS antenna, for short and long baselines. Therefore, the PREFMAR has a great potential for precise real-time kinematic GNSS navigation. [ABSTRACT FROM AUTHOR]