Search

The Modified Ambiguity Function Approach (MAFA) implicitly conducts the search procedure of carrier phase GNSS integer ambiguity resolution (IAR) in the coordinate domain using the integer least squares (ILS) principle, i.e. MAFA-ILS. One of the still open scientific problems is an accurate definition of the search region, especially in the context of instantaneous IAR. In doing so, the float solution results, which encompass float position (FP) and its variance-covariance (VC) matrix, must be improved as these are necessary for defining the search region. For this reason, the ambiguity parameters are separately regularized, and then the baseline parameters are conditioned on regularized float ambiguities. The conditional-regularized estimation is thus designed, obtaining the regularized FP (RFP) and its VC-matrix. This solution is promising because its accuracy is enhanced in the sense of mean squared error (MSE) thanks to the improved precision at the cost of regularized bias. The optimal regularization parameter (RP) values obtained for ambiguity parameters balance the contributions of improved precision and bias in the regularized float baseline solution's MSE. Therefore, the regularized search region is defined accurately in the coordinate domain to contain such approximate coordinates that more frequently give the correct ILS solution. It also contains fewer MAFA-ILS candidates, improving the search procedure's numerical efficiency. The regularized ILS estimator performs well with the presence of bias, increasing the probability of correct IAR in the coordinate domain. [ABSTRACT FROM AUTHOR]

Since 2020, the PPP-B2b service provided by BeiDou navigation satellite system (BDS) has achieved dynamic decimeter-level and static centimeter-level positioning accuracy in China and nearby regions, drawing significant attention from the GNSS community. However, despite these advancements, the service still faces a significant challenge with prolonged convergence times that limit its effectiveness in real-time applications. To address this issue, we present a novel solution by successfully extracting phase observable-specific bias (OSB) products compatible with the PPP-B2b service. These phase OSB products were extracted using one week of PPP-B2b corrections and GNSS multi-frequency observations from 19 evenly distributed reference stations across China. The results indicated that the PPP-B2b phase biases exhibited satisfactory short-term stability, as evidenced by an average standard deviation (STD) of 0.06 ns over several hours. After integrating phase OSB products, the user-end wide-lane/narrow-lane integer properties are restored, with BDS3 performing better than GPS. Numerical analysis shows that approximately 90% of the BDS3 narrow-lane fractional biases are less than 0.15 cycles, compared to approximately 74% for GPS. In terms of user-end positioning, the PPP-B2b service enables centimeter-level accuracy, although some fluctuations remain after convergence. However, in ambiguity-fixed solutions, which are enabled by the addition of phase OSB products, the positioning error sequences become quite stable, and the positioning accuracy significantly improves. Week-long data from 28 rover stations show horizontal accuracy improvements of 79.4% and 68.2% for the BDS3 and BDS3+GPS combined strategies, respectively, compared to ambiguity-float solutions. Additionally, the average convergence time for the horizontal and vertical components is significantly shortened from 26.1/14.1 min to 3.4/4.3 min, when phase OSB products are applied. [ABSTRACT FROM AUTHOR]

Real-time precise orbits of low earth orbit (LEO) satellites are becoming indispensable with the rapid development of real-time Earth observation application and LEO enhanced precise point positioning. Currently, GNSS-based precise orbit determination is a widely used method for LEO onboard navigation. However, the real-time LEO satellite orbits are usually obtained by ambiguity-float solution even when the GNSS augmentation corrections are considered. In this study, we perform LEO ambiguity-fixed multi-GNSS real-time precise orbit determination (RTPOD) based on square root information filter. One month of onboard GPS + Galileo observations from Sentinel-6A and real-time products of the Centre National d’Etudes Spatiales (CNES) are used to investigate the contribution of integer ambiguity resolution (IAR). The benefit of dual-system combination on LEO RTPOD is firstly evaluated. The combination of GPS and Galileo dual-system contributes to more visible GNSS satellites and better observation geometry for LEO RTPOD, which results in an evident accuracy improvement of 19% over GPS and a convergence time reduction of 43% and 41% compared to the GPS and Galileo solutions respectively. Considering the short arc of onboard GNSS observations and imperfections in GNSS real-time products, we propose a strict IAR quality control method to avoid fixing the ambiguity to the wrong values. The results indicate that the IAR quality control method we used can effectively reduce the wrong fixing risk and increase the robustness of the IAR solution. Using onboard GPS and Galileo observations, the 3D orbit accuracy of the ambiguity-fixed solution is significantly improved from 5.17 to 3.61cm, by 30%, compared to the ambiguity-float solution. Furthermore, the application of IAR also achieves a faster convergence to the centimeter-level orbit. [ABSTRACT FROM AUTHOR]

Factor graph optimization has been widely used for state estimation in robotic SLAM community. Extensive algorithms have been proposed for camera/LiDAR/INS based SLAM. However, GNSS positioning based on factor graph optimization is limited, which prevents the introduction of high precise GNSS to robotic SLAM community. The current implementations are focused on pseudorange or RTK based positioning. PPP with ambiguity resolution (AR) is the state-of-the-art positioning technique for the past decade. Therefore, the PPP AR based on factor graph optimization is proposed, in which the pseudorange and carrier phases factors are constructed from the error equations of raw observations, while the ambiguity resolution factor is built from the ambiguity resolution. Results from 80 MGEX stations show that the average accuracy of static PPP is improved from 1.25, 0.61 and 2.29 cm to 0.81, 0.5 and 2.1 cm, corresponding to improvements of 35.1%, 18.7% and 8.7% in east, north, and up directions, respectively. As for kinematic PPP, the average accuracy is improved from 2.62, 2.21 and 5.8 cm to 1.64, 1.74 and 5.37 cm, corresponding to improvements of 37.5%, 21.6% and 7.4% in east, north, and up directions, respectively. The kinematic PPP was also verified with real-world data collected from a moving vehicle. After the first ambiguity fixing, the accuracy of PPP is improved from 3.7, 2.1 and 10.1 cm to 1.6, 2.0 and 9.0 cm for east, north and up component, respectively, corresponding to improvements of 32%, 5% and 11%. The above results confirm the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this contribution, we introduce the ambiguity-resolved (AR) detector and study its distributional characteristics. The AR-detector is a new detector that lies in between the commonly used ambiguity-float (AF) and ambiguity-known (AK) detectors. As the ambiguity vector can seldomly be known completely, usage of the AK-detector is questionable as reliance on its distributional properties will then generally be incorrect. The AR-detector resolves the shortcomings of the AK-detector by treating the ambiguities as unknown integers. We show how the detector improves upon the AF-detector, and we demonstrate that the, for ambiguity-resolved parameter estimation, commonly required extreme success rates can be relaxed for detection, thus showing that improved model validation is also possible with smaller success rates. As such, the AR-detector is designed to work for mixed-integer GNSS models. [ABSTRACT FROM AUTHOR]

To support real-time global navigation satellite systems (GNSS) precise applications, satellite clock corrections need to be precisely estimated at a high-rate update interval, which remains a challenge due to the rapid development of multi-GNSS constellations. In this study, we developed an undifferenced (UD) ambiguity resolution (AR) procedure to improve both the accuracy and computational efficiency for real-time multi-GNSS clock estimation realized by a square root information filter. In the proposed method, UD ambiguities are resolved after correcting the simultaneously estimated uncalibrated phase delays (UPD) and the fixed UD ambiguity parameters are eliminated immediately from the filter, so that the computational burden is significantly reduced. Moreover, based on the linear relationship between double-differenced (DD) and UD ambiguities, we investigated the difference between DD and UD AR in clock estimation. We found that the major reason why DD AR contributes little to the clock estimation while UD AR can speed up the convergence remarkably is that UD AR additionally provides a stable clock datum compared with DD AR. GNSS observations from about 100 globally distributed stations were processed with the proposed method to generate simulated real-time clocks and UPDs for GPS, Galileo, and BDS satellites over a one-month period. The results show that the percentage of wide-lane (WL) UPD residuals within ± 0.25 cycles and narrow-lane (NL) UPD residuals within ± 0.15 cycles are over 97.0% and 90.0%, respectively, which contributes to an ambiguity fixing rate of more than 90% for three systems. The mean daily standard deviation (STD) of the clocks of the UD-fixed solution with respect to Center for Orbit Determination in Europe 30 s final products is 0.021, 0.020, and 0.035 ns for GPS, Galileo, and BDS satellite, respectively, which is improved by 78.1%, 58.3%, and 79.8% compared to the float solution. Benefiting from the removal of fixed ambiguities, the average computation time per epoch was reduced from 3.88 to 1.05 s with a remarkable improvement of 72.9%. The quality of the satellite clock and UPD products was also evaluated by the performance of kinematic precise point positioning (PPP). The results show that fast and reliable multi-GNSS PPP-AR can be achieved with the derived UD-fixed clocks and UPDs, which outperforms that using DD-fixed clock and off-line UPD products with an average improvement of 7.9% and 19.9% in terms of convergence time and positioning accuracy, respectively. Furthermore, we demonstrated the effectiveness of the proposed UD AR method through a 7-day real-time clock estimation experiment. [ABSTRACT FROM AUTHOR]

The regional ionospheric corrections have become one of the critical parts of Precise Point Positioning (PPP)-based Real-Time-Kinematic (RTK) services to achieve fast positioning convergence. Several methods for regional ionospheric corrections supporting PPP-RTK have been developed and implemented over recent years, but little attention is given to the theoretical foundation of existing ionospheric correction methods and their performance comparison to find an optimal method in some sense. The optimality criterion of such methods should not only be based on the precision of the ionospheric correction itself, but also on its broadcasting strategies, and implementation aspects. This contribution studies ionospheric correction generation methods within the best linear unbiased predictor (BLUP) framework. Comparing the accuracy performances of the methods, we demonstrate that the Kriging method with trend, as a special case of BLUP, is the most appropriate method for large-scale networks (above 500 km). A strategy for the evaluation of the uncertainty of the grid-interpolated ionospheric corrections is also developed. In contrast to other empirical methods, this new method is rigorous in the sense that it avoids the underestimation of the uncertainty of predicted ionospheric corrections, especially when reference stations are close to a grid point. [ABSTRACT FROM AUTHOR]

The technology of precise point positioning – real time kinematic (PPP – RTK) can realize regional accurate positioning. However, poor quality atmospheric corrections can greatly impact the integer ambiguity resolution. The low reliability of interpolated corrections may arise from blocked transmission of the updated corrections, atmospheric disturbance, and when the user is located outside the service area. Therefore, to maintain a continuous ambiguity-fixed state in an inaccurate correction observation environment, we propose a novel stop-and-go (SAG) kinematic positioning method. Integer ambiguities inherited from the last epoch are used to estimate the ionospheric errors of the current epoch using an inversion calculation method. Unmodeled errors contained in the ionospheric corrections are also considered. We then experimentally compare the proposed method and traditional PPP – RTK and SAG methods with the results of the PPP-ambiguity resolution calculation using geomagnetic storm-influenced data. All indicators, including the number of fixed ambiguities, errors of corrections, successful fix rate, and correct fix rate, confirm the superiority of the proposed method. The proposed method achieves a horizontal correct fix rate of 98% and maintains the vertical correct fix rate above 96% throughout the day. It is proved that for most of the time the novel method can provide continuous ambiguity-fixed solutions for users in an inaccurate correction observation environment.

High-precision global navigation satellite system (GNSS) time transfer depends on the carrier phase observations, and ionospheric delay affects rapid integer ambiguity resolution. Therefore, this work applies the ionospheric-weighted single-differenced model. Experimental results indicate that for a time-link of 67.9 km, the time transfer accuracy of different single-system is better than 0.03 ns. Compared with single-system, multi-system demonstrates 8% to 14% improvement in accuracy and improvement of no more than 31% in frequency stability. Additionally, compared with the case without ionospheric constraint, imposing ionospheric constraints can improve performance of time transfer, but the gain decreases as the time-link length increases. [ABSTRACT FROM AUTHOR]

Troposphere augmentation is of great importance for global navigation satellite system (GNSS) real-time precise point positioning (PPP) service. This contribution focuses on the feasibility of modeling the regional troposphere by polynomial fitting and the benefits of precise tropospheric corrections for triple-frequency and multi-GNSS PPP and PPP with integer ambiguity resolution (PPP-IAR) during a period of typhoon weather. A modified optimal fitting coefficient (MOFC) method is proposed with the height-related parameters removed by a priori fitted exponential function. Two spatial scales of networks are chosen to verify the effect of the GNSS station distribution on troposphere modeling. The results show that the MOFC model can provide centimeter-level accuracy with average root mean square (RMS) of 2.1 and 2.2 cm for dense and sparse networks, respectively, while that of GPT2w and real-time VMF3-FC products are 6.6 and 3.3 cm during typhoon periods. PPP/PPP-IAR tests with zenith troposphere delay (ZTD) augmentation based on the MOFC model are conducted when a typhoon eye passes over. Accuracy improvements of 18.2 and 16.6% for vertical components are observed in BDS-only and BDS/Galileo/GPS PPP-IAR solutions with ZTD augmentation, while those for PPP float solutions are marginal. Additionally, 2-h positioning arcs for PPP float solutions and 1224 10-min arcs for PPP-IAR solutions confirm that ZTD augmentation plays an important role in convergence, especially for PPP-IAR solutions. The percentage of instantaneous convergence in BDS-only PPP-IAR solutions improves from 42.1, 44.0 and 18.9% to 51.3, 52.3 and 48.9% for the east, north and up components, respectively, indicating that decorrelation between ZTD and vertical coordinates can be achieved with MOFC ZTD corrections in the initial stage of positioning. The percentages further improved from 89.7, 89.5 and 74.6% to 94.1, 94.2 and 93.7% for BDS/Galileo/GPS PPP-IAR solutions. [ABSTRACT FROM AUTHOR]

The remarkably long distances covered by deep space probes result in extremely weak downlink signals, which poses great challenges for ground measurement systems. In the current climate, improving the comprehensive utilization of downlink signal power to increase the detection distance or enhance the measurement accuracy is of great significance in deep space exploration. Facing this problem, we analyze the delta Differential One-way Range (ΔDOR) error budget of the X-band of the China Deep Space Network (CDSN). Then, we propose a novel interferometry method that detunes one group of DOR beacons and reuses the clock components of regenerative pseudo-code ranging signals for interferometry delay estimation. The primary advantage of this method is its ability to enhance the power utilization efficiency of downlink signals, thereby facilitating more efficient tracking and measurement without necessitating additional design requirements for deep space transponders. Finally, we analyze and verify the correctness and effectiveness of our proposed method using measured data from CDSN. Our results indicate that the proposed method can save approximately 13% of the downlink signal power and increase the detection distance by about 6.25% using typical modulation parameters. Furthermore, if the relative power of other signal components remains unchanged, the power of the DOR tone can be directly increased by more than 100%, improving the deep space exploration ability more significantly. [ABSTRACT FROM AUTHOR]

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Precise Point Positioning (PPP) with Integer Ambiguity Resolution (IAR) is an effective way of improving the overall performance of the PPP technique both in terms of convergence time and accuracy. Even though PPP-IAR has seen a tremendous development in the last two decades, there is still room for improvement. Specifically, the search stage of candidate carrier phase ambiguities is characterized as an NP-hard problem that requires a long processing time, leading to limitation in the reliability of the identified optimal solution. A field that would have an impact on the search process of carrier phase ambiguities, and is addressed conceptually in this paper, is Artificial Intelligence (AI). [ABSTRACT FROM AUTHOR]

Objectives: Global navigation satellite system (GNSS) satellite chip shape distortions lead to individual biases in the pseudorange measurements. These biases are the results of the correlator's tracking response and thus depend on the correlator and front-end design of the receiver. As a result, different receivers are likely to exhibit inconsistent biases, called receiver-related pseudorange biases. The researches show that the receiver-related pseudorange biases cannot be absorbed by clock offset, which will affect GNSS precision applications. Methods: We estimate the receiver-related pseudorange biases of global positioning system (GPS)/BeiDou satellite navigation system (BDS) /Galileo satellite navigation system (Galileo) from 9 short/zero-baselines stations from the multi-GNSS experiment network using double difference method. The baselines are divided into three groups according to the combinations of two receivers of one baseline. Results: The results indicate that the receiver-related pseudorange biases of receivers with different manufacturers even the same manufacturers with different models cannot be neglected. For base‐lines with receivers from different manufacturers,the inconsistences of pseudorange biases can reach up to 160 cm. Conclusions: Among GPS, Galileo and BDS, Galileo shows the smallest pseudorange biases, while BDS in general is the largest. Furthermore, the stability of pseudorange biases is analyzed, the results suggest that estimated receiver-related pseudorange biases are quite stable with the standard deviation less than 12 cm for the three systems. We investigate the effect of receiver-related pseudorange biases on integer ambiguity resolution and pseudorange relative positioning, with the pseudorange biases correction, the root mean squares of fractional parts of double difference Melbourne ‐Wübbena combination are decreased by 17%, 22%, and 14% for GPS, BDS, Galileo, respectively. An improvement of pseudorange relative positioning accuracy is also confirmed, the 3D positioning errors of GPS, BDS, Galileo are reduced from 84.4, 77.3 and 60.0 to 80.1, 72.1 and 57.0 cm, respectively. [ABSTRACT FROM AUTHOR]

The precise point positioning (PPP)-based real-time-kinematic (RTK) method attracts increasing attention from both academia and industry because of its potential for high accuracy positioning with a shorter convergence time compared to the traditional PPP. Besides high accuracy, integrity monitoring (IM) is indispensable for safety–critical real-time land vehicle and aviation applications. As the traditional advanced receiver autonomous integrity monitoring (ARAIM) method is designed for (smoothed) pseudorange-based positioning, the complexity of multi-frequency multi-constellation PPP-RTK using carrier phase measurements has not been given sufficient consideration. This study proposes an IM scheme for multi-frequency multi-constellation uncombined PPP-RTK applying the ARAIM theory, with a new comprehensive threat model to accommodate not only pseudorange measurements, but also carrier phase measurements, and other fault events arising from the network corrections that support PPP-RTK. Characteristics of different types of faults are analyzed with the aid of numerical experiments. In addition, the impact of ambiguity-fixed solutions on PPP-RTK integrity performance is investigated. The authors have also conducted case studies, including static and real-kinematic positioning experiments. Experiments have demonstrated that fast convergence in accuracy and the position error bounds, or protection levels, with a given integrity risk, in horizontal position components of PPP-RTK could be achieved. For the open sky environments on a highway, the protection levels estimated by PPP-RTK solutions have the potential to meet the alert limit requirement for road transportation using ambiguity-fixed PPP-RTK positioning under the assumption that the risks of wrong ambiguity fixing are very small and can be ignored. [ABSTRACT FROM AUTHOR]

Real-time satellite clock offsets are key in realizing real-time precise point positioning (PPP). Typically, tens of minutes are required for re-convergence because many tropospheric and ambiguity parameters are estimated in the clock offset estimation when the interruption of observation data occasionally occurs. This contribution proposes a rapid re-convergence method for multi-global navigation satellite system (GNSS) real-time satellite clock offset estimation. In case of a few seconds of interruption, the dual-thread integer ambiguity resolution method is proposed. The float clock offset, uncalibrated phase delay, fixed and float ambiguities, clock offset with IAR, zenith wet delay (ZWD) and inter-system bias (ISB) are generated in a slow thread, in which the fixed and float ambiguities, ZWD and ISB are used in a quick thread to achieve rapid re-convergence. Observations from 60 globally distributed stations were processed using the proposed method. The experimental results show that rapid re-convergence, fast estimation and high-precision clock offsets can be achieved. The re-convergence time of clock offset estimation was 0.14, 0.15, 0.74, 0.36 and 2.48 min for the GPS, Galileo, BDS-2, BDS-3 and GLONASS, respectively. Most satellite clock offsets can realize instantaneous re-convergence. The clock offset standard deviations are 0.028, 0.024, 0.069, 0.043 and 0.125 ns, respectively. The computation times were 21.4 and 1.7 s for the slow and quick threads, respectively. Compared to the float PPP solutions, the positioning accuracy of the PPP-AR was improved by 53.9, 29.9 and 18.2% from 1.80 to 0.83 cm, 1.57 to 1.10 cm and 3.63 to 2.97 cm for the east, north and up components, respectively. In case of interruptions lasting from a few minutes to tens of minutes, the ZWD, ambiguities and ISB information before interruption are used in the clock offset estimation, and a strong constraint is imposed on the normal equation, i.e., a large value (e.g., 105) is used instead of the diagonal value of the normal equation matrix corresponding to each estimated parameter. Experimental results show that rapid re-convergence can be achieved for GPS and Galileo with an interruption of 10 min, whereas the rapid re-convergence cannot be achieved for BDS-2, BDS-3 and GLONASS because of the impact of satellite orbit accuracy, error model, and neglection of the inter-frequency bias, respectively. [ABSTRACT FROM AUTHOR]

Ambiguity resolution enabled precise point positioning (PPP-AR or PPP-RTK) without atmospheric corrections requires the user to estimate tropospheric and ionospheric delay parameters. The presence of the unconstrained ionosphere parameters impedes fast and reliable ambiguity resolution, so a time-to-first-fix of around 30 min for GPS-only solutions is generally reported, which can, to some extent, be reduced when combining multiple GNSS. In this contribution, we investigate the capabilities of almost instantaneous PPP-RTK, using only a few observation epochs at a sampling interval of 30 s, with the ionosphere-float model. The considered key elements are (a) the MSE-optimal best integer-equivariant estimator, (b) a combination of dual-frequency GPS, Galileo, BDS, and QZSS, (c) an area with good visibility of BDS and QZSS, and (d) a proper weighting of the PPP-RTK corrections. We provide a formal and simulation-based analysis of kinematic and static PPP-RTK with perfect, i.e., deterministic, clock and bias corrections as well as corrections computed from only a single reference station. The results indicate that, on average, one can expect centimeter-level positioning results with just slightly more than two epochs already with single-station corrections. This is confirmed with real four-system GNSS data, for which the availability of two-epoch centimeter-level horizontal positioning results is 99.7% during an exemplary day. [ABSTRACT FROM AUTHOR]

Precise Point Positioning (PPP) with Integer Ambiguity Resolution (IAR) is an effective way of improving the overall performance of the PPP technique both in terms of convergence time and accuracy. Even though PPP-IAR has seen a tremendous development in the last two decades, there is still room for improvement. Specifically, the search stage of candidate carrier phase ambiguities is characterized as an NP-hard problem that requires a long processing time, leading to limitation in the reliability of the identified optimal solution. A field that would have an impact on the search process of carrier phase ambiguities, and is addressed conceptually in this paper, is Artificial Intelligence (AI).

With the availability of Global Navigation Satellite Systems raw measurements in smartphones, high-precision positioning using smartphones has become possible in recent years. Integer ambiguity resolution (IAR) is critical for smartphone precise positioning, which would be more difficult in smartphones and affected by various factors. In this paper, we will numerically study the effect factors for integer property of phase ambiguities, data quality, IAR efficiency and positioning accuracy for the smartphone. The results show that integer property of phase ambiguities and data quality are governed not only by the smartphone brands and embedded antennas, but also by the mobile operating system and smartphone attitudes. In general, the different constant offsets exist for the different frequency ambiguities, and the ambiguities are fixable once the corresponding offsets are calibrated. With the operating system of EMUI 9.0, the ambiguities are fixable for Xiaomi Mi8 but not for Huawei Mate20. However, with the updated operating system of EMUI 9.0.1, the ambiguities of Huawei Mate20 become fixable. Besides the smartphone brands and embedded antennas, the smartphone attitudes significantly affect the data quality, such as carrier-to-noise density ratio (C/N0) values, data availability and observation precisions, thus affecting the ambiguity fixing rate and positioning accuracy. The ambiguity fixing rates differ from attitudes by 17%, and generally, the upward attitude has the best performance. Finally, the kinematic positioning results indicate that only the meter-level accuracy is obtained with an embedded antenna, while the centimeter to decimeter-level accuracy is achievable with the external antenna. [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]

The BeiDou Navigation Satellite System (BDS) is fully operational and provides positioning, navigation, and timing services to users worldwide. To comprehensively evaluate the BeiDou-3 Navigation Satellite System (BDS-3) global real-time kinematic (RTK) positioning performance, five sets of IGS/MEGX stations with different baseline lengths are selected in this research, and the visibility of current BDS-3, BDS-2+BDS-3, and Global Positioning System (GPS) system satellites are analyzed. The single frequency, dual-frequency, and triple-frequency positioning accuracy as well as ambiguity fixing rate under short baseline and long baseline are also analyzed. The experimental results show that the positioning accuracies of B1C, BII, L1, and B3I single-frequency bands were about the same, while for band B2a it was lower. For the short baseline dual-frequency RTK positioning mode, the accuracy of BDS-3 (B1C/B2a), BDS-3 (B1I/B3I), triple-frequency BDS-3 (B1C/B2a/B3I), and GPS (L1L2) is comparable and slightly better than that of BDS-3 (B1I/B3I). With the increase in baseline length, the advantages of dual-frequency BDS-3 (B1C/B2a) and triple frequency BDS (B1C/B2a/B3I) are more obvious, with triple-frequency BDS-3 (B1C/B2a/B3I) having the best positioning accuracy. In terms of ambiguity fixing performance, dual-frequency BDS-2+BDS-3 (B1I/B3I) and dual-frequency GPS (L1L2) have the highest ambiguity fixing rate. The ambiguity fixing rate of dual-frequency BDS-3 (B1C/B2a) and triple-frequency BDS-3 (B1C/B2a/B3I) can be higher than 90% within 100 km. In the case of positioning using only the BDS-3 system, the triple-frequency BDS-3 (B1C/B2a/B3I) is superior to both the dual-frequency BDS-3 (B1I/B3I) and dual-frequency BDS-3 (B1C/B2a) in terms of both positioning accuracy and ambiguity fixing rate. The BDS-2+BDS-3 (B1I/B3I) dual-frequency RTK, which has reached a level comparable to GPS, can provide global users with real-time centimeter-level differential positioning services. [ABSTRACT FROM AUTHOR]

The strength of the GNSS precise positioning model degrades in cases of a lack of visible satellites, poor satellite geometry or uneliminated atmospheric delays. The least-squares solution to a weak GNSS model may be unreliable due to a large mean squared error (MSE). Recent studies have reported that Tikhonov’s regularization can decrease the solution’s MSE and improve the success rate of integer ambiguity resolution (IAR), as long as the regularization matrix (or parameter) is properly selected. However, there are two aspects that remain unclear: (i) the optimal regularization matrix to minimize the MSE and (ii) the IAR performance of the regularization method. This contribution focuses on these two issues. First, the “optimal” Tikhonov’s regularization matrix is derived conditioned on an assumption of prior information of the ambiguity. Second, the regularized integer least-squares (regularized ILS) method is compared with the integer least-squares (ILS) method in view of lattice theory. Theoretical analysis shows that regularized ILS can increase the upper and lower bounds of the success rate and reduce the upper bound of the LLL reduction complexity and the upper bound of the search complexity. Experimental assessment based on real observed GPS data further demonstrates that regularized ILS (i) alleviates the LLL reduction complexity, (ii) reduces the computational complexity of determinate-region ambiguity search, and (iii) improves the ambiguity fixing success rate. [ABSTRACT FROM AUTHOR]

Inspired by excellent precision of carrier phase positioning, this paper presents a new carrier phase positioning technique for 5G new radio cellular networks with a focus on clock synchronization and integer ambiguity resolution. A carrier-phase based clock offset estimation method is first proposed to achieve precise clock synchronization among base stations, and proved to achieve the Cramér–Rao Lower Bound (CRLB) asymptotically. A fusion method is developed to fuse the estimated positions of a mobile station (MS) based on time-difference-of-arrival, with the estimated position changes based on the temporal changes of carrier phase measurements. While circumventing the integer ambiguities of the carrier phase measurements, the fusion method provides quality interim estimates of the MS positions, at which the measurements can be linearized to resolve the integer ambiguities. As a result, precise MS positions can be obtained based on the disambiguated carrier phase measurements. Numerical simulations show that the proposed carrier phase positioning can achieve a centimeter-level accuracy in wireless cellular networks. [ABSTRACT FROM AUTHOR]

This paper presents a formulation of snapshot positioning as a mixed-integer least-squares problem. In snapshot positioning, one estimates a position from code-phase (and possibly Doppler-shift) observations of global navigation satellite system (GNSS) signals without knowing the time of departure (timestamp) of the codes. Solving the problem allows a receiver to determine a fix from short radio-frequency snapshots missing the timestamp information embedded in the GNSS data stream. This is used to reduce the time to first fix in some receivers, and it is used in certain wildlife trackers. This paper presents two new formulations of the problem and an algorithm that solves the resulting mixed-integer least-squares problems. We also show that the new formulations can produce fixes even with huge initial errors, much larger than permitted in Van Diggelen's widely-cited coarse-time navigation method. [ABSTRACT FROM AUTHOR]

Stochastic models are essential for precise navigation and positioning of the global navigation satellite system (GNSS). A stochastic model can influence the resolution of ambiguity, which is a key step in GNSS positioning. Most of the existing multi-GNSS stochastic models are based on the GPS empirical model, while differences in the precision of observations among different systems are not considered. In this paper, three refined stochastic models, namely the variance components between systems (RSM1), the variances of different types of observations (RSM2) and the variances of observations for each satellite (RSM3) are proposed based on the least-squares variance component estimation (LS-VCE). Zero-baseline and short-baseline GNSS experimental data were used to verify the proposed three refined stochastic models. The results show that, compared with the traditional elevation-dependent model (EDM), though the proposed models do not significantly improve the ambiguity resolution success rate, the positioning precision of the three proposed models has been improved. RSM3, which is more realistic for the data itself, performs the best, and the precision at elevation mask angles 20°, 30°, 40°, 50° can be improved by 4⋅6%, 7⋅6%, 13⋅2%, 73⋅0% for L1-B1-E1 and 1⋅1%, 4⋅8%, 16⋅3%, 64⋅5% for L2-B2-E5a, respectively. [ABSTRACT FROM AUTHOR]

Precise ionospheric information, as like precise satellite orbits, clocks, and code/phase biases, is a critical factor for achieving fast integer ambiguity resolution in precise point positioning (PPP-AR). This study develops an ionosphere-weighted (IW) undifferenced and uncombined PPP real-time kinematic (PPP-RTK) network model using code and phase observations. We introduce between-station single-differenced ionospheric delay pseudo-observations to take advantage of the similar characteristics of ionospheric delays between two receivers tracking the same satellite. The estimable ionospheric parameters are commonly affected by the differential code bias referring to a particular receiver assigned as pivot, which facilitates the ionospheric interpolation at the user side. Then, the kinematic positioning performance of the IW PPP-RTK user model is analyzed and compared with those of PPP-AR without ionospheric corrections, RTK, and IW-RTK models during low and high solar activity days. The results show that for the PPP-RTK model, the positioning errors converge to thresholds of 2 cm for the horizontal components and 5 cm for the vertical component within 20 epochs, and the positioning errors become stable after an initialization of 20 epochs with root-mean-squared (RMS) values of approximately 0.47, 0.58 and 1.66 cm for the east, north and up components, respectively, which are superior to those of the other three models. Owing to the high ionospheric disturbance influence, the RMS values of the east and up components increase by approximately double and the mean time-to-first-fix increases by 61.5% for the PPP-RTK case. [ABSTRACT FROM AUTHOR]

In this contribution, we extend the principle of integer bootstrapping (IB) to a vectorial form (VIB). The mathematical definition of the class of VIB-estimators is introduced together with their pull-in regions and other properties such as probability bounds and success rate approximations. The vectorial formulation allows sequential block-by-block processing of the ambiguities based on a user-chosen partitioning. In this way, flexibility is created, where for specific choices of partitioning, tailored VIB-estimators can be designed. This wide range of possibilities is discussed, supported by numerical simulations and analytical examples. Further guidelines are provided, as well as the possible extension to other classes of estimators. [ABSTRACT FROM AUTHOR]

Precise knowledge of orbit represents a fundamental requirement for the earth observing satellite missions to achieve their advanced objectives. The integer ambiguity resolution (IAR) has proved to be a key to utmost accuracy in space navigation. Generally, there are two typical IAR methods widely used in the orbit determination of low Earth orbit (LEO) satellites, the classical double‐difference (DD) IAR and new single‐difference (SD) IAR. Based on one‐year observations of Gravity Recovery and Climate Experiment Follow‐On (GRACE‐FO) and Sentinel‐3 missions, this study is dedicated to a comprehensive analysis of the differences of the products used, implementation details and ambiguity fixing performance for different IAR methods in LEO precise orbit determination (POD), and discusses how these differences influence the orbit solutions. The results show that the orbit accuracy improvement contributed by the ambiguity fixing varies with the adopted IAR methods. SD IAR can contribute to a representative reduction of 1–4 mm in satellite laser ranging (SLR) residuals compared to the float solutions. The application of bias products from different analysis centers leads to marginal differences for the ambiguity fixing. For DD IAR method, the different ways to form the double‐difference ambiguity yield different performances in POD. The DD IAR of space‐ground baselines can achieve a comparable performance to SD IAR, while the benefit of ambiguity fixing is largely weakened when forming space‐space baseline. Furthermore, we also analyze the contribution of the ambiguity fixing to the accuracy and robustness of the kinematic orbit and discuss its great potential for the future applications. Plain Language Summary: Obtaining accurate orbit information of low Earth orbit satellite is an essential prerequisite for the geodetic and remote sensing missions to support their operation. Today, the onboard Global Navigation Satellite System (GNSS) technology has been commonly recognized as the optimal way to produce high‐quality orbit for these Earth‐observation satellites. However, due to the existence of hardware delays in both signal transmitter and receiver, the inherent accuracy of carrier phase signal is not fully exploited. Removing the effects of these errors plays a key to achieve the ultimate accuracy of GNSS‐based orbit. Nevertheless, different methods of separating these hardware delays from GNSS observations eventually lead to accuracy discrepancy in satellite orbit recovery. Our study focuses on the several commonly used methods of eliminating the hardware delays in the precise orbit determination. We present a detailed analysis about the differences between these methods lying in the implementation details and performance, and discuss how these differences impact the orbit solutions. Using a wider set of Earth‐observation missions and data over a longer time span than before, we aim to answer the question which method is optimal or most appropriate for the recovery of satellite orbit and make suggestion for the future mission. Key Points: The differences in the implementation, fixing performance and accuracy between several ambiguity fixing methods in low Earth orbit (LEO) precise orbit determination (POD) are discussedThe single‐receiver integer ambiguity resolution represents the currently optimal choice for LEO PODWith the integer ambiguity fixing method, the kinematic orbit exhibits a great potential for the future applications [ABSTRACT FROM AUTHOR]

An assessment of standalone GLONASS RTK performance is provided using its FDMA and CDMA signals. The new integer-estimable GLONASS FDMA model (Teunissen 2019), which guarantees the integer-estimability of its ambiguities, is employed. We introduce the combined integer-estimable GLONASS FDMA+CDMA model and compare its strength against the FDMA model for instantaneous integer ambiguity resolution and positioning. Various combinations of GLONASS signals are considered including FDMA L1, FDMA+CDMA L1+L3, FDMA L1+L2 and FDMA+CDMA L1+L2+L3. To provide insight into the current RTK performance of GLONASS, we used observations of a short baseline to analyze the integer ambiguity resolution success rate and positioning precision, formally and empirically. To provide insight into the future RTK performance of GLONASS, we present a formal analysis of the integer ambiguity resolution success rate and ADOP, assuming that all the GLONASS satellites transmit FDMA L1, L2 and CDMA L3 signals. A formal analysis of standalone GLONASS ambiguity resolution based on current and future GLONASS constellation is then presented for different locations around the world. [ABSTRACT FROM AUTHOR]

GNSS observation outage occurs inevitably in various situations, e.g., automobile driving in urban environments. Although the ambiguity resolution (AR) significantly shortens the initialization time of precise point positioning (PPP), frequent re-initialization of PPP AR may be needed due to outages. The inertial navigation system (INS) can be used for acquiring highly accurate position information during GNSS outages. In the previous studies, the GPS PPP/INS with the ambiguity resolution model is proposed, and the experimental results confirm that the INS could facilitate the re-fixing of the interrupted GNSS ambiguity. Multiple GNSS can also be used to shorten the PPP convergence time. We compare the contribution of multi-GNSS and the INS to the ambiguity re-fixing during GNSS outage. Results show that the multi-GNSS, e.g., Galileo, GLONASS and BDS, without ambiguity resolution has little contribution to the re-fixing of GPS ambiguity in PPP/INS, while INS can provide highly accurate positioning results during the GNSS outages. The higher the accuracy of the predicted INS positioning, the lower the contribution of multi-GNSS to the re-fixing of the ambiguity in the PPP/INS. The finding is verified by a theoretical analysis, carborne experiment and shipborne experiment. Experiment results show that the re-fixing time is 43 s for GPS PPP and MEMS-grade INS coupled system in GNSS outage of 1 s. The re-fixing time of GPS is slightly changed when adding the multi-GNSS, e.g., Galileo, GLONASS and BDS, without the ambiguity resolution. However, by performing ambiguity resolution to the added GNSS system, the re-fixing time of PPP/INS is significantly reduced from 43 to 4 s. The reason is that, although the multi-GNSS provides little improvement on the accuracy of the ambiguity, it enlarges the number of the ambiguity parameter. The possibility of ambiguity resolution is increased due to the large candidate set of the ambiguity, which reduces re-fixing time. [ABSTRACT FROM AUTHOR]

The tropospheric delay is one of many error sources that affect the Global Navigation Satellite System (GNSS) positioning solutions. The widely used troposphere models assume a homogeneous atmosphere so that only the zenith delay needs to be determined and is mapped through an elevation-dependent mapping function. This procedure is to reduce the computational burden and keep the positioning model full-rank. However, this assumption fails for a realistic description of the troposphere, which is always asymmetrical at a certain elevation angle, especially during a weather event when the weather conditions are very complex. These imperfectly modelled tropospheric delays may influence the positioning accuracy and integer ambiguity resolution performance. In this case, this contribution aims to investigate the effects of the model errors due to the asymmetrical troposphere on GNSS estimations. The Numerical Weather Prediction (NWP) model is applied to generate the actual ray-tracing tropospheric delay in Western Europe, and the tropospheric model errors are calculated in a normal weather condition and a weather event condition by comparing the slant delay calculated from the NWP model and the mapping function. Case studies on the same GNSS station are conducted in two weather conditions: a normal troposphere condition and a weather event with heavy rainfall. The results based on the case studies show that the troposphere in the normal weather condition is nearly homogeneous that the azimuthal-dependent discrepancies of the tropospheric delay are less than 1 c m at a very low elevation angle; meanwhile, the discrepancies between different azimuthal angles can reach to more than 25 c m in the weather event. A single-frequency Single Point Positioning (SPP) model and a Precise Point Positioning (PPP) model that preserves the integer property of ambiguity are chosen for studying the estimation biases caused by the troposphere model errors. It turns out that almost all horizontal positioning biases of SPP and PPP are less than 1 c m in the normal weather condition; however, the scales of the horizontal and 3 D biases are concentrated in 1 to 10 c m in the weather event for these two models. This contribution also contains the study of the actual integer ambiguity resolution success rate in the presence of the tropospheric model errors by applying the Monte Carlo simulation, and the success rates of PPP in the normal weather condition are consistent with the theoretical values calculated with the ideal troposphere which is totally symmetrical. However, the actual success rates in the weather event are extremely low at some epochs due to the tropospheric model errors, which means that wrong fixing may occur since the theoretical values cannot take into account these model errors. Note that the horizontal tropospheric gradients are not involved in the processing, which means that an optimistic performance might be expected if the gradients are considered. [ABSTRACT FROM AUTHOR]

The integer ambiguity resolution (AR) of carrier phase is significant for Global Navigation Satellite System (GNSS) precise positioning. However, in kinematic case, single-epoch AR methods based on alone GNSS are usually not reliable due to the instable pseudorange accuracy. Moreover, the computation of classical AR method Least Squares Ambiguity Decorrelation Adjustment (LAMBDA) is large. Thus, the inertial measurement unit (IMU) is introduced, a new inertial-aided AR method that directly rounds the float ambiguity of BeiDou triple-frequency combined observations, which is characterized by long wavelength, low carrier-phase noise and ionospheric delay, is proposed. The mathematical model of the new method is derived first. Then the impacts of the carrier-phase noise, ionospheric delay and inertial navigation system (INS) position error on the AR success ratio of combined observation are analyzed through probabilistic approach. Based on above investigation, the combinations (0, −1, 1), (1, 4, −5) and (4, −2, −3) are selected to resolve the original ambiguity. A vehicular integrated navigation test is performed to demonstrate the proposed method. The results show that the average AR success ratios of the three selected combinations, whose float ambiguity errors are 0.041, 0.146, 0.279 cycle respectively, are above 97.25% without regard to low-elevation C05. With respect to positioning accuracy based on our AR method when compared with IE software, the east, north, up error RMS of position are 0.042, 0.024, 0.069 m, respectively. In terms of the AR recover after the BeiDou signals outage, as long as 62 s BeiDou signal complete outage, all the ambiguities of all satellites could be re-fixed immediately. Besides, during the 90 s signals partial outage, the AR is not influenced by the position error, since the float ambiguity errors are all below half-cycle. The research of this contribution demonstrates the effectiveness of the proposed new method, which indicates it is applicable to kinematic positioning, even in BDS degraded and denied environments. [ABSTRACT FROM AUTHOR]

GNSS observations stochastic model influences all subsequent stages of data processing, from the possibility to reach the optimal parameters estimation, to the reliability and quality control of the solution. Nowadays, an uncontrolled use of GNSS stochastic models is common for both data processing and simulation missions, especially in commercial GNSS software packages. As a result, the variance–covariance matrices that are derived in the processing are inadequate and cause incorrect interpretations of the results. A proper method to evaluate the reliability of the stochastic model is needed to reflect the confidence level in statistic testing and simulation mission efforts. In this contribution, a novel method for evaluating the statistical nature of GNSS stochastic model is presented. The method relies on the deterministic nature of the integer ambiguity variable to examine and express the expected multinormal distribution of the double-difference adjustment results. The suggested method was used with a controlled experiment and 24 h of observations data to investigate how the statistical nature of the stochastic model is affected by different baseline lengths. The results indicate that as the baseline length increases, the stochastic model is less predictable and exposed to irregularities in the observation's precision. Additionally, the reliability of the integer ambiguity resolution success rate (SR) was tested as part of the stochastic model evaluation. The results show a dramatic degradation in the SR prediction level when using an inadequate stochastic model, which suggests using extra caution when handling this parameter unless high-confidence reliable stochastic model is available. [ABSTRACT FROM AUTHOR]

The triple-frequency linear combination with a low noise, a long wavelength, and a weak ionosphere is beneficial to effectively eliminate or weaken the common errors, advance the reliability of cycle slip detection and repair, and speed up the convergence time of fixed ambiguity. By establishing the Galileo triple-frequency carrier linear combination model, three types of linear combinations are derived: Geometry-free (GF) combinations, minimum noise (MN) combinations, and ionosphere-free (IF) combinations. The geometric relationships of these linear combinations are displayed in the form of image. The results indicate that the angle formed by the IF combinations and the MN combinations is between 75.02° and 86.01°, which also illustrates that it is more difficult to meet the carrier phase combinations with a low noise and a weak ionosphere. Moreover, to guarantee the integer cycle characteristics of ambiguity, the combination coefficient must be an integer. Galileo triple-frequency linear combination is solved utilizing the extremum method. To sum up, the sum of the coefficients of the extra wide lane (EWL) combinations and wide lane (WL) combinations is zero, and the sum of the coefficients of the narrow lane (NL) combinations is one. (0, 1, −1) is the optimal triple-frequency linear combination in Galileo. Three independent linear combinations are selected separately from the EWL, WL, and NL to jointly solve the integer ambiguity. Further, it creates a prerequisite for high-precision and real-time kinematic positioning. [ABSTRACT FROM AUTHOR]

The multi-GNSS fusion makes positioning more reliable and accurate. Considering the signal difference of different systems, GPS + Galileo + QZSS + BDS tightly combined double-difference model (TCDDM), including function and stochastic model, is proposed. The proposed model fully utilizes the overlapping frequency signals of various systems, and thus to enhance positioning model when DISBs are known beforehand. The observations of 3 ultra-short (1~10 m) and 3 short (4~10 km) baselines were processed by self-programming software, and the single-epoch single-frequency RTK performance using different system-combined models was evaluated by ambiguity-fixed correctness rate (ACR) and positioning accuracy. It demonstrated that three- and four-system TCDDM were superior to their corresponding loosely combined double-difference model (LCDDM) for ACR and positioning accuracy especially at high cut-off elevation. Moreover, four-system TCDDM had the best RTK performance obtaining average ACRs of 100% and 97.6% even at 25° cut-off elevation for ultra-short and short baseline, respectively. [ABSTRACT FROM AUTHOR]

The use of the GLONASS legacy signals for real-time kinematic positioning is considered. Due to the FDMA multiplexing scheme, the conventional CDMA observation model has to be modified to restore the integer estimability of the ambiguities. This modification has a strong impact on positioning capabilities. In particular, the ambiguity resolution performance of this model is clearly weaker than for CDMA systems, so that fast and reliable full ambiguity resolution is usually not feasible for standalone GLONASS, and adding GLONASS data in a multi-GNSS approach can reduce the ambiguity resolution performance of the combined model. Partial ambiguity resolution was demonstrated to be a suitable tool to overcome this weakness (Teunissen in GPS Solut 23(4):100, 2019). We provide an exhaustive formal analysis of the positioning precision and ambiguity resolution capabilities for short, medium, and long baselines in a multi-GNSS environment with GPS, Galileo, BeiDou, QZSS, and GLONASS. Simulations are used to show that with a difference test-based partial ambiguity resolution method, adding GLONASS data improves the positioning performance in all considered cases. Real data from different baselines are used to verify these findings. When using all five available systems, instantaneous centimeter-level positioning is possible on an 88.5 km baseline with the ionosphere weighted model, and on average, only 3.27 epochs are required for a long baseline with the ionosphere float model, thereby enabling near instantaneous solutions. [ABSTRACT FROM AUTHOR]

The integer characteristics of the undifferenced ambiguity can be recovered after the correction of fractional cycle biases (FCB), which can significantly shorten the initialization time of precise point positioning (PPP). In the former work, the ambiguity resolution model of the client end needs to be consistent with the FCB products server. However, the client may face the problem that inconsistent FCB products are provided and cannot be used to fix the ambiguity. We propose a new method for client of undifferenced and uncombined PPP ambiguity resolution based on FCB product of ionosphere-free combination PPP model. The hardware delay in server of ionosphere-free combination FCB (IF FCB) and undifferenced and uncombined FCB (L1L2 FCB) are deduced in detail. Constructing the narrow-lane ambiguity by using the raw ambiguity and the wide-lane ambiguity, the FCB product of the ionosphere-free combination PPP model is used to fix the ambiguity step by step. A globally distributed network consisting of about 118 MGEX stations is selected as the server end. Two types of FCB products, i.e., IF FCB and L1L2 FCB, are generated. 50 additional MGEX stations in global are selected as client end for performance assessment. The experimental results show that the new method for client of UU PPP model based on the IF FCB products has a comparable performance with the traditional method based on L1L2 FCB products, which improves the utilization of FCB products. [ABSTRACT FROM AUTHOR]

This paper investigates the performance of pulsar-based navigation in deep space mission applications. The noise properties of X-ray based and radio-baspulsar measurements are examined and compared. A closed form parametric covariance analysis tool was developed in this study. It provides a rough estimate of the navigation performance associated with a deep space cruise that makes use of ion thrusters and sequential pulsar observations. In addition, the flight trajectory of the Dawn spacecraft was used to form a hypothetical deep space mission scenario that utilizes pulsars as navigation beacons. This simulated scenario accounts for clock uncertainty, pulsar timing noise, maneuver execution errors, sequential observation and interruptions between pulsar observations. A particle filter was implemented to reduce the large initial position uncertainty by resolving the number of pulsar wavelengths between the spacecraft and the Solar System Barycenter. The resulting position and velocity uncertainties from the particle filter can be used to initialize an Extended Kalman Filter, which estimates the spacecraft position and velocity for steady state operations. [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]

Real-time kinematic (RTK) ambiguity resolution can be improved by engaging multiple reference antennas. The baseline information between the antennas can be taken as true values and used as a hard-constraint; or it can be regarded as weighted, a priori measurements, and used as a softconstraint. In this contribution, a comparison between the two constraints is made to explicate their difference in RTK ambiguity resolution for some specific applications, in which the coordinates of the reference antennas cannot be accurately calibrated in advance. The functional and stochastic models of the hard and soft-constrained RTK positioning are given. The float ambiguity precision of the unconstrained, the hard and the soft-constrained cases is compared. The closed-formulae of the ambiguity dilution of precision (ADOP) for the unconstrained and the hard-constrained models are derived, and they are proven to be the upper and lower bound of the soft-constrained ADOP, respectively. A simulated and a real data show that, with the hard or soft-constraints, the single-frequency ambiguity resolution success rate, as well as the performance in time-to-first-fix (TTFF), is improved significantly. When there is a bias smaller than 6 cm in the a priori baseline vectors between the reference antennas, the two constraints have a comparable performance in ambiguity success rate. Also, a sharp increase in the hard-constrained TTFF is observed at the same time. When the bias gets larger, the hard-constrained ambiguity success rates are decreased drastically. In contrast, the soft-constraint maintains a relatively good performance, showing a much greater tolerance for bias.

A global navigation satellite system (GNSS) receiver with multi-antenna using clock synchronization technology is a powerful piece of equipment for precise attitude determination and reducing costs. The single-difference (SD) can eliminate both the satellites and receiver clock errors with the common clock between antennas, which benefits the GNSS short-baseline attitude determination due to its lower noise, higher redundancy and stronger function model strength. However, the existence of uncalibrated phase delay (UPD) makes it difficult to obtain fixed SD attitude solutions. Therefore, the key problem for the fixed SD attitude solutions is to separate the SD UPD and fix the SD ambiguities into integers between antennas. This article introduces the one-step ambiguity substitution approach to separate the SD UPD, through which we merge the SD UPD parameter with the SD ambiguity of the reference satellite ambiguity as the new SD UPD parameter. Reconstructing the other SD ambiguities, the rank deficiency can be remedied by nature, and the new SD ambiguities can have a natural integer feature. Finally, the fixed SD baseline and attitude solutions are obtained by combining the ambiguity substitution approach with integer ambiguity resolution (IAR). To verify the effect of the ambiguity substitution approach and the advantages of the SD observables with a common clock in practical applications, we conducted static, kinematic, and vehicle experiments. In static experiments, the root mean squared errors (RMSEs) of the yaw and pitch angles obtained by the SD observables with a common clock were improved by approximately 80% and 93%, respectively, compared to double-difference (DD) observables with a common clock in multi-day attitude solutions. The kinematic results show that the dispersion of the SD-Fix in the pitch angle is two times less that of the DD-Fix, and the standard deviations (STDs) of the pitch angle for SD-Fix can reach 0.02°. Based on the feasibility, five bridges with low pitch angles in the vehicle experiment environment, which the DD observables cannot detect, were detected by the SD observables with a common clock. The attitude angles obtained by the SD observables were also consistent with the fiber optic gyroscope (FOG) inertial navigation system (INS). This research on the SD observables with a common clock provides higher accuracy.

In the past few years, Global Navigation Satellite Systems (GNSS) based attitude determination has been widely used thanks to its high accuracy, low cost, and real-time performance. This paper presents a novel 3-D GNSS attitude determination method based on Riemannian optimization techniques. The paper first exploits the antenna geometry and baseline lengths to reformulate the 3-D GNSS attitude determination problem as an optimization over a non-convex set. Since the solution set is a manifold, in this manuscript we formulate the problem as an optimization over a Riemannian manifold. The study of the geometry of the manifold allows the design of efficient first and second order Riemannian algorithms to solve the 3-D GNSS attitude determination problem. Despite the non-convexity of the problem, the proposed algorithms are guaranteed to globally converge to a critical point of the optimization problem. To assess the performance of the proposed framework, numerical simulations are provided for the most challenging attitude determination cases: the unaided, single-epoch, and single-frequency scenarios. Numerical results reveal that the proposed algorithms largely outperform state-of-the-art methods for various system configurations with lower complexity than generic non-convex solvers, e.g., interior point methods. [ABSTRACT FROM AUTHOR]

The global BeiDou navigation satellite system (BDS-3) has been in operation recently and many related applications have been already compatible with BDS-3 satellites. Most applications still use the empirical stochastic models for combined regional BeiDou navigation satellite system (BDS-2) and BDS-3 positioning. However, BDS-3 has different satellite design, and the empirical stochastic models may not describe the observation precisions and the correlation characteristics of BDS-3 signals well and finally degrade the positioning performance. Hence, in this contribution, the variance-covariance component estimation is applied to calculate the precisions of observations and their spatiotemporal correlations as well as the cross-correlations for BDS-2 and BDS-3 multi-frequency signals. With the retrieved stochastic model, the performance of integer ambiguity resolution and positioning are then numerically demonstrated on short baseline. The results show that the observation precisions are in general elevation-dependent for both BDS-2 and BDS-3 except for BDS-2 geostationary earth orbit (GEO) satellites. For both BDS-2 and BDS-3, the spatial correlations are adequately small to be ignored in practical data processing. For the receivers we used, the cross-correlations are found significantly amongst the BDS-2 multi-frequency phase signals. Moreover, the temporal correlations differ between different frequencies and observations. The combined BDS-2 and BDS-3 can improve the ambiguity resolution success rate and positioning accuracy. [ABSTRACT FROM AUTHOR]