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To obtain better zenith hydrostatic delay (ZHD) corrections for global navigation satellite system (GNSS) applications, seven types of Vienna mapping function 1 (VMF1) and VMF3-like ZHD models provided by the Vienna University of Technology (TU Wien, TUW), University of New Brunswick (UNB) and GeoForschungsZentrum Potsdam (GFZ) are evaluated. Firstly, we find that the conventional method for implementing VMF1/VMF3-like ZHD models has issues when applied over regions with highly variable topography. Therefore, we propose an improved implementation method (called Trop_vertical) based on an empirical model as well as a second version, called Trop_vertical-II, which further corrects for small residual biases. The results show that the Trop_vertical-II can effectively reduce the large errors reported in previous studies for complex terrains and yields an improvement in global accuracy of up to 50% over the conventional method. Then, the multisource ZHD models are evaluated and intercompared globally. The results reveal some deficiencies with the TUW-VMF1 over certain regions. The newly developed ZHD models from the TUW (TUW-VMF3) and GFZ (GFZ-VMF3) both achieve reliable performances globally, but there is a systematic difference (~ 2.9 mm) between them. The forecast VMF1/VMF3-like models can well capture the rapid ZHD variation in challenging weather conditions. Finally, the impacts of a priori ZHD errors on both GPS-only and GPS/GLONASS precise point positioning (PPP)-based zenith total delay (ZTD) and height solutions are examined globally. The results suggest that the sensitivities of PPP-ZTD/height solutions to a priori ZHD errors decrease by adding GLONASS data at high latitudes but increase at low latitudes.

High-precision localization through multi-sensor fusion has become a popular research direction in unmanned driving. However, most previous studies have performed optimally only in open-sky conditions; therefore, high-precision localization in complex urban environments required an urgent solution. The complex urban environments employed in this study include dynamic environments, which result in limited visual localization performance, and highly occluded environments, which yield limited global navigation satellite system (GNSS) performance. In order to provide high-precision localization in these environments, we propose a vision-aided GNSS positioning method using semantic information by integrating stereo cameras and GNSS into a loosely coupled navigation system. To suppress the effect of dynamic objects on visual positioning accuracy, we propose a dynamic-simultaneous localization and mapping (Dynamic-SLAM) algorithm to extract semantic information from images using a deep learning framework. For the GPS-challenged environment, we propose a semantic-based dynamic adaptive Kalman filtering fusion (S-AKF) algorithm to develop vision aided GNSS and achieve stable and high-precision positioning. Experiments were carried out in GNSS-challenged environments using the open-source KITTI dataset to evaluate the performance of the proposed algorithm. The results indicate that the dynamic-SLAM algorithm improved the performance of the visual localization algorithm and effectively suppressed the error spread of the visual localization algorithm. Additionally, after vision was integrated, the loosely-coupled navigation system achieved continuous high-accuracy positioning in GNSS-challenged environments.

The inter-satellite link (ISL) equipment of the third-generation BeiDou Navigation Satellite System (BDS-3) can enhance the accuracy of precise orbit determination (POD) for BDS-3 satellites. However, the hardware delays within ISL observations can impact the measurement accuracy of ISL observations. This study evaluates the characteristics of hardware delays in ISL observations for BDS-3 medium Earth orbit (MEO) satellites and investigates their effects on POD. Analysis shows that most links exhibit slow variations in hardware delays, with standard deviations (STD) of 6.4 cm and 3.6 cm over 45 days for the C19-C25 and C20-C21 links, respectively. Conversely, some links like C30-C23 and C30-C33 show more pronounced variations, with STD values reaching 17.7 cm and 14.1 cm within three days. Links involving satellites C23 and C30 display higher variability and significant jumps in hardware delays compared with other links. The larger variations in hardware delays of these links can be absorbed by other parameters, thereby affecting the accuracy of parameter estimation. To mitigate their impact on POD, a segmented estimation strategy for hardware delays is proposed. This strategy divides a single link into multiple segments based on a set interval length and estimates the hardware delay parameters for each segment separately, thereby absorbing the variations in hardware delays or unmodeled errors. The effectiveness of this strategy is demonstrated through ISL POD residual analysis, comparison with L-band orbit determination results, and validation using Satellite Laser Ranging (SLR) residuals. The root mean square (RMS) of ISL observation residuals decreased by approximately 44.3%, from 6.1 cm to 3.4 cm. Comparisons with L-band orbits confirmed an approximate 28.2% reduction in the 3D RMS of orbit discrepancies, from 26.5 cm to 19.0 cm. Additionally, the RMS of the overall SLR residuals showed a slight decrease. Overall, the improved segmented estimation strategy effectively reduces the influence of hardware delay variations on BDS-3 orbit determination, notably enhancing the orbit determination accuracy of BDS-3 satellites, especially for C23 and C30, which experience larger hardware delay fluctuations.

Global navigation satellite system (GNSS) differential code bias (DCB) and topside ionosphere vertical electron content (VEC) can be estimated using onboard data from low-earth-orbit (LEO) satellites. These satellites provide the potential to make up for the lack of ground-based stations in the oceanic and polar regions and establish a high-precision global ionosphere model. In order to study the influences of different LEO-topside VEC processing methods on estimates, we creatively analyzed and compared the results and accuracy of the DCBs and LEO-topside VEC estimates using two topside VEC solutions—the SH-topside VEC (spherical harmonic-topside vertical electron content) and EP-topside VEC (epoch parameter-topside vertical electron content) methods. Some conclusions are drawn as follows. (1) Using GRACE-A data (400 km in 2016), the monthly stabilities (STDs) of GPS satellite DCBs and LEO receiver DCBs using the EP-topside VEC method are better than those using the SH-topside VEC method. For JASON-2 data (1350 km), the STD results of GPS DCBs using the SH-topside VEC method are slightly superior to those using the EP-topside VEC method, and LEO DCBs using the two methods have similar STD results. However, the root mean square (RMS) results for GPS DCBs using the SH-topside VEC model relative to the Center for Orbit Determination in Europe (CODE) products are slightly superior to those using the EP-topside VEC method. (2) The peak ranges of the actual GRACE-A-topside VEC results using the SH-topside VEC and EP-topside VEC methods are within 42 and 35 TECU, respectively, while the peak ranges of the JASON-2-topside VEC results are both within 6 TECU. Additionally, only the SH-topside VEC model results are displayed due to the EP-topside VEC method not modeling VEC. Due to the difference in orbital altitude, the results and distributions of the GRACE-topside VECs differ from those of the JASON-topside VECs, with the former being more consistent with the ground-based results, indicating that there may be different height structures in the LEO-topside VECs. In addition, we applied the IRI-GIM (International Reference Ionosphere model–Global Ionosphere Map) method to compare the LEO-based topside VEC results, which indicate that the accuracy of GRACE-A-topside VEC using the EP-topside VEC method is better than that using the SH-topside VEC method, whereas for JASON-2, the two methods have similar accuracy. Meanwhile, we note that the temporal and spatial resolutions of the SH-topside VEC method are higher than those of the EP-topside VEC method, and the former has a wide range of usability and predictive characteristics. The latter seems to correspond to the single-epoch VEC mean of the former to some extent.

The BeiDou-3 system uses the BeiDou Global broadcast Ionospheric delay correction Model (BDGIM) to describe global vertical total electron content (VTEC) distributions and provide ionospheric delay mitigations in single-frequency positioning. The transmission of BDGIM correction parameters in the navigation message of BeiDou-3 started in mid-2015. The limited coverage of BeiDou-3 transmitted BDGIM parameters inhibits the evaluation of model performance during different levels of solar conditions. As such, we present a method to re-estimate BDGIM correction parameters and generate model parameters during the period 2010–2017 using a small global network of 20 global navigation satellite system (GNSS) stations. Tests covering the eight years demonstrate that BDGIM can reduce the ionospheric error to less than 25% for 98% of the examined samples when compared to global ionospheric maps (GIMs) provided by the International GNSS Service (IGS), and for 90% when compared to the observed VTECs from Jason-2/3 altimetry missions. Overall, BDGIM reduces residual ionospheric delays by 10–20% compared to the ionospheric correction algorithm (ICA) of the global positioning system (GPS), the empirical International Reference Ionosphere (IRI) 2016, and our fitted NeQuick-C model. The root-mean-square (RMS) error of BDGIM increases by 32 and 21% in comparison with GIM-derived and Jason-2 observed VTECs during the geomagnetic storm in March 2015, indicating the significant degradation of model performance during the disturbed geomagnetic period.

Observable-specific bias (OSB) parameterization allows observation biases belonging to various signal types to be flexibly addressed in the estimation of ionosphere and global navigation satellite system (GNSS) clock products. In this contribution, multi-GNSS OSBs are generated by two different methods. With regard to the first method, geometry-free (GF) linear combinations of the pseudorange and carrier-phase observations of a global multi-GNSS receiver network are formed for the extraction of OSB observables, and global ionospheric maps (GIMs) are employed to correct ionospheric path delays. Concerning the second method, satellite and receiver OSBs are converted directly from external differential code bias (DCB) products. Two assumptions are employed in the two methods to distinguish satellite- and receiver-specific OSB parameters. The first assumption is a zero-mean condition for each satellite OSB type and GNSS signal. The second assumption involves ionosphere-free (IF) linear combination signal constraints for satellites and receivers between two signals, which are compatible with the International GNSS Service (IGS) clock product. Agreement between the multi-GNSS satellite OSBs estimated by the two methods and those from the Chinese Academy of Sciences (CAS) is shown at levels of 0.15 ns and 0.1 ns, respectively. The results from observations spanning 6 months show that the multi-GNSS OSB estimates for signals in the same frequency bands may have very similar code bias characteristics, and the receiver OSB estimates present larger standard deviations (STDs) than the satellite OSB estimates. Additionally, the variations in the receiver OSB estimates are shown to be related to the types of receivers and antennas and the firmware version. The results also indicate that the root mean square (RMS) of the differences between the OSBs estimated based on the CAS- and German Aerospace Center (DLR)-provided DCB products are 0.32 ns for the global positioning system (GPS), 0.45 ns for the BeiDou navigation satellite system (BDS), 0.39 ns for GLONASS and 0.22 ns for Galileo.

Following the continuous and stable regional service of BDS2, the BDS3 officially announced its global service in July 2020. To fully take advantage of the new multi-frequency BDS3 signals in ionosphere sensing and positioning, it is essential to understand the characteristics of the differential code bias (DCB) of new BDS3 signals and BDS performance in global ionospheric maps (GIMs) estimation. This article presents an evaluation of the characteristics of 13 types of BDS DCBs and the accuracy of BDS-based GIM based on the data provided by the International GNSS Service (IGS) and International GNSS Monitoring and Assessment System (iGMAS) for the first time. The GIMs and DCBs are estimated by the APM (Innovation Academy for Precision Measurement Science and Technology) method in a time efficient manner, which can be divided into two main steps. The first step is to produce GIMs based on BDS observations at the B1I, B2I and B3I signals, and the second step is to estimate DCBs among the other frequency bands by removing the ionospheric delay using the precomputed GIMs. Good agreement is found between the APM-based satellite DCB estimates and those from the Chinese Academy of Sciences (CAS) and the German Aerospace Center (DLR) at levels of 0.26 ns and 0.18 ns, respectively. The results, spanning one month, show that the stability of BDS DCB estimates among different frequency bands are related to the contributed observations, and the receiver DCB estimates represent larger STD values than the satellite DCB estimates. The differences in receiver DCB estimates between BDS2 and BDS3 are found to be related to the types of receivers and antennas and firmware version, and the bias of the JAVAD receivers reaches 1.03 ns. The results also indicate that the difference in the single-frequency standpoint positioning (SPP) accuracy using GPS-based and BDS-based GIMs for ionospheric delay corrections is less than 0.03 m in both the horizontal and vertical directions.

The signal-in-space ranging errors (SISREs), which are mainly dominated by clock errors, are computed for 18 BeiDou-3 (BDS-3) medium earth orbit satellites by comparing broadcast ephemeris values against precise values provided by Wuhan University from January 1 to December 31, 2019. For clock errors, a weighted least-square estimation method is carried out to eliminate the common clock error datum among all satellites. A standard deviation of 0.30 m indicates that the BDS-3 satellite clocks have good stability. However, as opposed to the near-zero means shown in the radial, along-track and cross-track directions of the orbit errors, satellite-specific nonzero means appear in the clock errors for most satellites and result in an RMS of 0.53 m for the whole satellite constellation. Dominated by the clock errors, the global average SISREs have an RMS of approximately 0.54 m, which demonstrates that the BDS-3 signal-in-space accuracy is at the same level as that of GPS. Super-Gaussian probability distributions fit the orbit and clock errors; however, the tails are not obviously heavier than that of a Gaussian distribution. Although the distribution of worst-case SISREs is bimodal, it could be overbounded by a Gaussian distribution with a mean of zero and a standard deviation of the user ranging accuracy (URA) with a certain confidence. To display Gaussian distribution models with different overbounding abilities, different URAs are estimated under various confidence levels based on actual SISRE samples. If the integrity risk is set to 10−5, the range of estimated URA values is 0.29–0.67 m for all satellites.

With the increasing demand for high-precision positioning, integrated navigation technology has become a key approach to achieving accurate and reliable location tracking in modern intelligent mobile platforms. While previous studies have explored the application of various sensor combinations, there is still a lack of systematic analysis regarding the integration of the four major sensors: GNSS, INS, vision, and LiDAR. This study analyzes 5193 academic articles published between 2000 and 2024 in the Web of Science database, employing bibliometric analysis, network analysis, and content analysis to evaluate the development and application of these four sensors in integrated navigation systems. By reviewing the evolution of integrated navigation technology, the study examines four typical integration modes: GNSS/INS, INS/visual, GNSS/INS/visual, and GNSS/INS/visual/LiDAR, discussing their complementarity, fusion algorithm optimization, and emerging application scenarios. Despite significant progress in improving navigation accuracy and environmental adaptability, challenges persist in sensor cooperation and real-time processing capabilities in complex environments. The study concludes by summarizing existing research findings and identifying gaps, with future research focusing on optimizing multisensor fusion algorithms, enhancing system adaptability, improving error models, and enhancing sensor performance in adverse environmental conditions.

Continuous and stable precision satellite clock offsets are an important guarantee for real-time precise point positioning (PPP). However, in real-time PPP, the estimation of a satellite clock is often interrupted for various reasons such as network fluctuations, which leads to a long time for clocks to converge again. Typically, code biases are assumed to stay constant over time in clock estimation according to the current literature. In this contribution, it is shown that this assumption reduces the convergence speed of estimation, and the satellite clocks are still unstable for several hours after convergence. For this reason, we study the influence of different code bias extraction schemes, that is, taking code biases as constants, extracting satellite code biases (SCBs), extracting receiver code biases (RCBs) and simultaneously extracting SCBs and RCBs, on satellite clock estimation. Results show that, the time-varying SCBs are the main factors leading to the instability of satellite clocks, and considering SCBs in the estimation can significantly accelerate the filter convergence and improve the stability of clocks. Then, the products generated by introducing SCBs in the clock estimation based on undifferenced observations are applied to PPP experiments. Compared with the original undifferenced model, clocks estimated using the new method can significantly accelerate the convergence speed of PPP and improve the positioning accuracy, which illustrates that our estimated clocks are effective and superior.