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Long-distance Real-Time Kinematic (RTK) positioning is crucial for applications in remote areas, such as maritime environments. Achieving 2–3 cm accuracy with RTK requires successful ambiguity resolution, which involves two main steps: identifying the best integer ambiguity candidate and confirming its validity. While previous research has largely concentrated on the first step, including the development of Cascading Ambiguity Resolution methods, and reducing tropospheric delay, studies on the validation of ambiguity for long-distance RTK are limited. This study conducts a thorough examination of ambiguity validation for long-distance RTK, focusing on two prevalent methods: the theoretical success rate and the R-ratio test. The results reveal several key insights. Firstly, the six commonly used bounds for the theoretical success rate are not an accurate reflection of the actual success rate, making them unsuitable for long-distance RTK applications. Secondly, the R-ratio test proves to be dependable when the threshold is set above 1.7, assuming there is a minimum observation period of one minute and at least ten satellites are visible. However, the probability of successfully resolving ambiguities with the R-ratio test does not surpass 50%. Additionally, if ambiguity resolution is not achieved within 20 min, simply prolonging the observation time is generally unproductive. To improve the performance of ambiguity resolution in practical situations that require extended observation times, this research proposes a novel ambiguity validation method. This new approach is based on the duration for which an integer ambiguity resolution candidate maintains the best status. This method aims to provide a reliable means of validating ambiguities in cases where the R-ratio test fails. [ABSTRACT FROM AUTHOR]

3D reconstruction plays an increasingly important role in modern photogrammetric systems. Conventional satellite or aerial-based remote sensing (RS) platforms can provide the necessary data sources for the 3D reconstruction of large-scale landforms and cities. Even with low-altitude UAVs (Unmanned Aerial Vehicles), 3D reconstruction in complicated situations, such as urban canyons and indoor scenes, is challenging due to the frequent tracking failures of camera frames and high data collection costs. Recently, spherical images have been extensively exploited due to the capability of recording surrounding environments using one camera exposure. Classical 3D reconstruction pipelines, however, cannot be used for spherical images. Besides, there exist few software packages for the 3D reconstruction of spherical images. Based on the imaging geometry of spherical cameras, this study investigates the algorithms for relative orientation using spherical correspondences, absolute orientation using 3D correspondences between the scene and spherical points, as well as cost functions for BA (bundle adjustment) optimization. Besides, an incremental SfM (Structure from Motion) workflow has been proposed for spherical images by using the above-mentioned algorithms. The proposed solution is finally verified by using three spherical datasets captured by both consumer-grade and professional spherical cameras. The results demonstrate that the proposed SfM workflow can achieve the successful 3D reconstruction of complex scenes and provide useful clues for the implementation in open-source software packages. The source code would be publicly available. [ABSTRACT FROM AUTHOR]

Spherical images have the advantage of recording full scenes using only one camera exposure and have been becoming an important data source for 3D reconstruction. However, geometric distortions inevitably exist due to the spherical camera imaging model. Thus, this study proposes a reliable feature matching algorithm for spherical images via the combination of local geometric rectification and CNN (convolutional neural network) learned descriptor. First, image patches around keypoints are reprojected to their corresponding tangent planes based on a spherical camera imaging model, which uses scale and orientation data from the keypoints to achieve both rotation and scale invariance. Second, feature descriptors are then calculated from the rectified image patches by using a pre-trained separate detector and descriptor learning network, which improves the discriminability by exploiting the high representation learning ability of the CNN. Finally, after classical feature matching with the ratio test and cross check, refined matches are obtained based on an essential matrix-based epipolar geometry constraint for outlier removal. By using three real spherical images and an incremental structure from motion (SfM) engine, the proposed algorithm is verified and compared in terms of feature matching and image orientation. The experiment results demonstrate that the geometric distortions can be efficiently reduced from rectified image patches, and the increased ratio of the match numbers ranges from 26.8% to 73.9%. For SfM-based spherical image orientation, the proposed algorithm provides reliable feature matches to achieve complete reconstruction with comparative accuracy. [ABSTRACT FROM AUTHOR]

Integrating global navigation satellite systems (GNSSs) with inertial navigation systems (INSs) has been widely recognized as an ideal solution for autonomous vehicle navigation. However, GNSSs suffer from disturbances and signal blocking inevitably, making the performance of GNSS/INSs degraded in the occurrence of measurement outliers. It has been proven that the sigma points-based Kalman filter (KF) performs better than an extended KF in cases where large prior uncertainty is present in the state estimation of a GNSS/INS. By modifying the sigma points directly, the resampling-free sigma point update framework (SUF) propagates more information excepting Gaussian moments of prescribed accuracy, based on which the resampling-free cubature Kalman filter (RCKF) was developed in our previous work. In order to enhance the adaptivity and robustness of the RCKF, the resampling-free SUF depending on dynamic prediction residue should be improved by suppressing the time-varying measurement outlier. In this paper, a robust observability-constrained RCKF (ROCRCKF) is proposed based on adaptive measurement noise covariance estimation and outlier detection, where the occurrence of measurement outliers is modelled by the Bernoulli variable and estimated with the state simultaneously. Experiments based on car-mounted GNSS/INSs are performed to verify the effectiveness of the ROCRCKF, and result indicates that the proposed algorithm outperforms the RCKF in the presence of measurement outliers, where the heading error and average root mean square error of the position are reduced from 1.96° and 6.38 m to 0.27° and 5.95 m, respectively. The ROCRCKF is robust against the measurement outliers and time-varying model uncertainty, making it suitable for the real-time implementation of GNSS/INSs in GNSS-challenged environments. [ABSTRACT FROM AUTHOR]

Atmospheric phase is the main factor affecting the accuracy of ground-based synthetic aperture radar. The atmospheric phase screen (APS) may be very complicated, due to the drastic changes in atmospheric conditions, and the conventional correction methods based on regression models cannot fit and correct it effectively. Partition correction is a feasible path to improve atmospheric phase correction (APC) accuracy for complicated APS, but the overfitting problem cannot be ignored. In this article, we propose a clustering partition method, based on the normal vector of APS, which can partition the complicated APS more reasonably, and then perform APC based on the partition results. APC, and simulation experiments on measurement data, suggests that the proposed method achieves higher accuracy than the conventional model-based methods for complicated APS and avoids severe overfitting, realizing the balance between accuracy and credibility. This article verifies the feasibility and effectiveness of using APS distribution information to guide the partition and conduct APC. [ABSTRACT FROM AUTHOR]

Ground-based multiple-input multiple-output synthetic aperture radar (MIMO-SAR) is a new type of deformation monitoring sensor that has the advantages of no mechanical motion and fast echo acquisition. Ground-based MIMO-SAR can significantly improve the data rate of deformation monitoring. In this paper, a fast imaging algorithm tailored for ground-based MIMO-SAR data is proposed, which can be applied in both far-field and near-field scenarios. First, the phase center approximation error of the non-collinear array in the near field is analyzed. Then, a fast imaging algorithm based on geometric transformation for the coherent synthesis of subimages is put forward. The algorithm uses the geometric transformation to convert the subaperture imaging results into the full aperture coordinate system, which avoids the point-by-point interpolation calculation and further reduces the computational cost of the subimage coherent synthesis algorithm. Simulations and experiments show that the algorithm can achieve high-precision focusing imaging, and its operation efficiency is significantly improved compared with the algorithm based on interpolation. [ABSTRACT FROM AUTHOR]

Ambiguity resolution at Continuously Operating Reference Station (CORS) network sites is the key step in the whole processing chain of Network Real Time Kinematic (NRTK). An appropriate ambiguity-resolution speed is important, and single-epoch ambiguity resolution has not been realized yet, especially for large-scale CORS. We attempt to realize single-epoch ambiguity resolution for a large-scale CORS network by neglecting tropospheric delay through forming difference between satellites with close mapping functions whether they belong to the same or different GNSSs. As only two frequency bands are shared among GPS, Galileo and BeiDou, the biggest challenge is how to get this single-epoch ambiguity solution for wide-lane combinations of L1 and L5 when the difference is formed between satellites of different GNSSs. The proposed method includes five steps for ambiguity resolution for different combinations: extra wide-lane, wide-lane, inter-GNSS wide-lane, subset narrow-lane and narrow-lane. The single-epoch ambiguity-resolution performance is assessed based on GNSS observations from two long-distance baselines formed with IGS stations, BRUX-REDU and BAUT-LEIJ, separated by distances of approximately 104 km and 151 km, respectively. The numerical results show that the fixing rate of the single-epoch ambiguity resolution can reach more than 90%, so for a large-scale CORS network, single-epoch ambiguity resolution is feasible and can be realized in the future. [ABSTRACT FROM AUTHOR]

Ionospheric disturbances affect Global Positioning System (GPS) performance in terms of accuracy and integrity, especially over the equatorial region. During the period of the disturbances, GPS receivers suffer from a high noise level. Not taken into account by the current stochastic model, the ionospheric disturbances degrade GPS positioning accuracy. In addition, non-Gaussian tails are observed in the distribution of the noise during the period of the disturbances; therefore the integrity of GPS can also be affected. This paper develops a statistical solution that is able to mitigate effects of ionospheric disturbances on GPS accuracy and integrity using a commercial dual frequency receiver. The Rate of Total Electron Content (TEC) change Index (ROTI), a parameter derived from the dual frequency receiver, is used to group the levels of ionospheric disturbances. The standard deviations of the pseudorange noise under different groups are evaluated. By incorporating both the ROTI and the satellite elevation, a modified stochastic model is proposed to reduce the effect of the disturbed observation on the positioning accuracy. The performance of the model is evaluated by a test and an inflated sigma for each group is recommended for over-bounding anomalies of observations to protect the user against threats from ionospheric disturbances. This technique, together with results in this paper, can be applied to mitigate the effects of ionospheric disturbances on GPS. [ABSTRACT FROM PUBLISHER]

COMPASS or BeiDou is the new satellite navigation system under construction in China. In this paper, the standalone performance of COMPASS is compared to the Global Positioning System (GPS), including: Single Point Positioning (SPP), differential positioning (DGPS and Differential COMPASS) and single epoch ambiguity resolution and positioning. Based on the results, it was found that COMPASS SPP performance is clearly worse than that of GPS, due to larger broadcast orbit and satellite clock errors, especially the latter. Differential positioning performance of COMPASS and GPS are essentially similar, with GPS marginally better. COMPASS single epoch ambiguity resolution performance is obviously better than that of GPS due to more observed satellites and the single epoch positioning performance of COMPASS and GPS are similar. [ABSTRACT FROM PUBLISHER]

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

Traditional coseismic displacement retrieval generally uses real-time kinematic (RTK) and precise point positioning (PPP) services. However, both RTK and real-time PPP need a network link to transmit the corrected data. Although the network link may be interrupted when an earthquake happens, the PPP-B2b service broadcasted by geostationary orbit (GEO) satellites will not be affected. Its service range mainly covers China and the surrounding areas. In this research, the PPP method with PPP-B2b service based on constrained coordinates is proposed and overcomes the limitation of the network link and long convergence time. First, the accuracy of orbits and clock offsets for the PPP-B2b service is evaluated and compared with real-time service (RTS). Then, the simulated experiments are carried out using the PPP method with PPP-B2b service based on constrained coordinates, which tests the accuracy by calculating the coordinate displacement of the measurement station. The results show that the accuracy of PPP-B2b orbits in the radial direction is within 0.1 m. Moreover, regarding the accuracy of clock offsets, the PPP-B2b service is no more than 3.5 cm. This validates the feasibility of replacing RTS products with PPP-B2b. In the 15 min simulated experiments, the root mean square (RMS) of horizontal and vertical directions is maintained within 3 cm. [ABSTRACT FROM AUTHOR]

The differential global navigation satellite system (DGNSS) is an enhancement system that is widely used to improve the accuracy of single-frequency receivers. However, distance-dependent errors are not considered in conventional DGNSS, and DGNSS accuracy decreases when baseline length increases. In network real-time kinematic (RTK) positioning, distance-dependent errors are accurately modelled to enable ambiguity resolution on the user side, and standard Radio Technical Commission for Maritime Services (RTCM) formats have also been developed to describe the spatial characteristics of distance-dependent errors. However, the network RTK service was mainly developed for carrier-phase measurements on professional user receivers. The purpose of this study was to modify the local-area DGNSS through the use of network RTK corrections. Distance-dependent errors can be reduced, and accuracy for a longer baseline length can be improved. The results in the low-latitude areas showed that the accuracy of the modified DGNSS could be improved by more than 50% for a 17.9 km baseline during solar active years. The method in this paper extends the use of available network RTK corrections with high accuracy to normal local-area DGNSS applications. [ABSTRACT FROM AUTHOR]

Global navigation satellite systems (GNSS) can attain centimeter level positioning accuracy, which is conventionally provided by real-time precise point positioning (PPP) and real-time kinematic (RTK) techniques. Corrections from the data center or the reference stations are required in these techniques to reduce various GNSS errors. The time-relative positioning approach differs from the traditional PPP and RTK in the sense that it does not require external real-time corrections. It computes the differences in positions of a single receiver at different epochs using phase observations. As the code observations are not used in this approach, its performance is not affected by the noise and multipath of code observations. High reliability is another advantage of time-relative precise positioning because the ambiguity resolution is not needed in this approach. Since the data link is not required in the method, this approach has been widely used in remote areas where wireless data link is not available. The main limitation of time-relative positioning is that its accuracy degrades over time between epochs because of the temporal variation of various errors. The application of the approach is usually limited to be within a time interval of less than 20 min. The purpose of this study was to increase the time interval of time-relative positioning and to extend the use of this method to applications with a longer time requirement, especially in remote areas without wireless communication. In this paper, the main error sources of the time-relative method are first analyzed in detail, and then the approach to improve the accumulated time relative positioning method is proposed. The performance of the proposed method is assessed using both static and dynamic observations with a duration as long as several hours. The experiments presented in this paper show that, among the four scenarios tested (i.e., GPS, GPS/Galileo, GPS/Galileo/BeiDou, and GPS/Galileo/BeiDou/GLONASS), GPS/Galileo/BeiDou performed best and GPS/Galileo/BeiDou/GLONASS performed worst. The maximum positioning errors were mostly within 0.5 m in the horizontal direction, even after three hours with GPS/Galileo/BeiDou. It is expected that the method could be used for positioning and navigation for as long as several hours with decimeter level horizontal accuracy in remote areas without wireless communication. [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]

Real-time precise point positioning (RTPPP) is a popular positioning method that uses a real-time service (RTS) product to mitigate various Global Navigation Satellite Systems (GNSS) errors. However, communication links are not available in the ocean. The use of a communication satellite for data transmission is so expensive that normal users could not afford it. The BeiDou short-message service provides an efficient option for data transmission at sea, with an annual fee of approximately 160 USD. To perform RTPPP using BeiDou short messages, the following two challenges should be appropriately addressed: the maximum size of each BeiDou message is 78 bytes, and the communication frequency is limited to once a minute. We simplify the content of RTS data to minimize the required bandwidth. Moreover, the orbit and clock corrections are predicted based on minute-interval RTS orbital and clock corrections. An experiment was conducted to test the performance of the proposed method. The numerical results show that the three-dimensional positioning precision can reach approximately 0.4 m with combined GPS + GLONASS and approximately 0.2 m with combined GPS + GLONASS + Galileo + BeiDou. [ABSTRACT FROM AUTHOR]

The geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites of the Beidou navigation satellite system are maneuvered frequently. The broadcast ephemeris can be interrupted for several hours after the maneuver. The orbit-only signal-in-space ranging errors (SISREs) of broadcast ephemerides available after the interruption are over two times larger than the errors during normal periods. To shorten the interruption period and improve the ephemeris accuracy, we propose a two-step orbit recovery strategy based on a piecewise linear thrust model. The turning points of the thrust model are firstly determined by comparison of the kinematic orbit with an integrated orbit free from maneuver; afterward, precise orbit determination (POD) is conducted for the maneuvered satellite by estimating satellite orbital and thrust parameters simultaneously. The observations from the IGS Multi-Global Navigation Satellite System (GNSS) Experiment (MGEX) network and ultra-rapid products of the German Research Center for Geosciences (GFZ) are used for orbit determination of maneuvered satellites from Sep to Nov 2017. The results show that for the rapidly recovered ephemerides, the average orbit-only SISREs are 1.15 and 1.0 m 1 h after maneuvering for GEO and IGSO respectively, which is comparable to the accuracy of Beidou broadcast ephemerides in normal cases. [ABSTRACT FROM AUTHOR]

Different approaches have been developed to monitor the integrity of the Global Positioning System (GPS). The individual approaches rely on conservative error bounds and faces great challenges in meeting stringent integrity requirements set by the International Civil Aviation Organization (ICAO). These approaches, in fact, do not compete with one another but complement one another. We propose the vertical integration of the Satellite-Based Augmentation System (SBAS) and a local monitor station in this study. When the SBAS data deviate from the local monitor, users are informed to revert to the error bounds that are directly determined from SBAS data. Otherwise, the validation criterion that the error of the SBAS corrected solution is within a threshold is exploited to tighten the SBAS error bounds. The algorithm to integrate the SBAS with the independent monitor station is described, and its performance is evaluated based on simulations and real observations. The test results show that the vertical protection level (VPL) is reduced on average from 17.60 to 11.27 m, i.e., a 30.3% reduction in VPL while the integrity is guaranteed. [ABSTRACT FROM AUTHOR]

The Chinese BeiDou Navigation Satellite System (BDS) has been an important constitute of the Global Navigation Satellite System (GNSS), and the combination of GPS and BDS shows significant improvements when compared with single GPS system for real-time kinematic (RTK) positioning, and improves on availability and fixing rates, especially in the East Asian area. While network RTK might have different types of receivers, both for global and regional networks, different types of receiver may adopt different internal multipath mitigation methods and other techniques that result in different pseudorange characteristics, especially for a multipath. Then, the performance of wide-lane ambiguity resolution (WL AR) is affected. In this study, we first analyze and compare the characteristics of BDS dual-frequency observations for different types of receivers, including Trimble, Leica, Javad, and Septentrio, based on multipath (MP) observables, and then we assess their influence on double-differenced (DD) WL AR. The numerical results show that an obvious low-frequency component exists in MP observables of BDS geostationary earth-orbit satellites (GEOs) for Leica receivers, while its high-frequency measurement noise is very small. For geosynchronous orbit satellites (IGSOs) and medium earth-orbit satellites (MEOs), a slight fluctuation can also be observed that is similar to that of GPS satellites, except for the satellite-included code bias. In Trimble, Javad, and Septentrio receivers, the MP series are dominated by high-frequency measurement noise, both for GEOs and non-GEOs, except for satellite-included code bias. Furthermore, the characteristic of Leica receivers for BDS GEOs seriously affects WL AR and, even for a short baseline, it takes a long time for WL ambiguities to converge, or not converge for many GEO-related DD WL ambiguities, while Trimble, Javad, and Septentrio receivers perform well for short and medium baselines. Then, a time-difference method is proposed to mitigate the multipath of BDS GEOs for a Leica receiver. After applying the proposed method, WL ambiguity fixing rates of GEO-related satellite pairs are improved significantly and the convergence time is shortened from several hours to ten minutes. [ABSTRACT FROM AUTHOR]