Global Navigation Satellite System Solutions Research Articles

Coseismic slip model of the 14 January 2021 Mw 6.2 Mamuju-Majene earthquake based on static and kinematic GNSS solution

Abstract The Mw 6.2 Mamuju-Majene earthquake occurred on 14 January 2021, with the epicenter at 118.890°E, 2.972°S. The shaking caused severe damage in West Sulawesi, especially in the Mamuju and Majene cities. Most of the coseismic slip distribution of the Mamuju-Majene Earthquake is derived from the daily solutions, which might include early postseismic deformation. Therefore, we conducted a coseismic slip model using kinematic solution based on Global Navigation Satellite System (GNSS) to determine the best coseismic slip values and model distribution. Our analysis indicates that the coseismic displacement from the kinematic solution is higher than the static solution. The GNSS data was utilized for inversion analysis, considering two potential fault sources, they are the Makassar Strait Central Fault and the Mamuju Fault. We found a larger misfit between the observed data and the model generated on static and kinematic solutions along the Makassar Strait Central Fault. Based on the kinematic solution, the coseismic slip distribution represents that fault rupture spreading along a north-south orientation, while the static solution is centered in the northern part. The maximum coseismic slip from each kinematic and static solution is 0.29 m and 0.11 m, respectively. Meanwhile, the seismic moment generated from the kinematic solution is 1.5 × 1026 N m (equivalent to Mw 6.75), which is greater than the static solution of 2.4 × 1025 N m (equivalent to Mw 6.22).

A novel LiDAR-GNSS-INS Two-Phase Tightly Coupled integration scheme for precise navigation

Abstract. Recent advances in precise navigation have extensively utilized the integration of Global Navigation Satellite System (GNSS) and Inertial Navigation System (INS), particularly in the domain of intelligent vehicles. However, the efficacy of such navigation systems is considerably compromised by the reflection and multipath disruptions of non-light-of-sight (NLOS) signals. Light Detection and Ranging (LiDAR)-based odometry, an active perception-based sensor known for its precise 3D measurements, has become increasingly prevalent in augmenting navigation systems. Nonetheless, the assimilation of LiDAR odometry with GNSS/INS systems presents substantial challenges. Addressing these challenges, this study introduces a two-phase sensor fusion (TPSF) approach that synergistically combines GNSS positioning, LiDAR odometry, and IMU pre-integration through a dual-stage sensor fusion process. The initial stage employs an Extended Kalman Filter (EKF) to amalgamate the GNSS solution with IMU Mechanization, facilitating the estimation of IMU biases and system initialization. Subsequently, the second stage integrates scan-to-map LiDAR odometry with IMU mechanization to support continuous LiDAR factor estimation. Factor graph optimization (FGO) is then utilized for the comprehensive fusion of LiDAR factors, IMU pre-integration, and GNSS solutions. The efficacy of the proposed methodology is corroborated through rigorous testing on a demanding trajectory from an urbanized open-source dataset, with the system demonstrating a notable enhancement in performance compared to the state-of-the-art algorithms, achieving a translational Standard Deviation (STD) of 1.269 meters.

Maximum likelihood localization of a network of moving agents from ranges, bearings and velocity measurements

Localization is a fundamental enabler technology for many applications, like vehicular networks, IoT, and even medicine. While Global Navigation Satellite Systems solutions offer great performance, they are unavailable in scenarios like indoor or underwater environments, and, for large networks, the instrumentation cost is prohibitive. We develop a localization algorithm from ranges and bearings, suitable for generic mobile networks. Our algorithm is built on a tight convex relaxation of the Maximum Likelihood position estimator. To serve positioning to mobile agents, a horizon-based version is developed accounting for velocity measurements at each agent. To solve the convex problem, a distributed gradient-based method is provided. This constitutes an advantage over centralized approaches, which usually exhibit high latency for large networks and present a single point of failure. Additionally, the algorithm estimates all required parameters and effectively becomes parameter-free. Our solution to the dynamic network localization problem is theoretically well-founded and still easy to understand. We obtain a parameter-free, outlier-robust and trajectory-agnostic algorithm, with nearly constant positioning error regardless of the trajectories of agents and anchors, achieving better or comparable performance to state-of-the-art methods, as our simulations show. Furthermore, the method is distributed, convex and does not require any particular anchor configuration.

On the Importance of Precise Positioning in Robotised Agriculture

The precision of agro-technical operations is one of the main hallmarks of a modern approach to agriculture. However, ensuring the precise application of plant protection products or the performance of mechanical field operations entails significant costs for sophisticated positioning systems. This paper explores the integration of precision positioning based on the global navigation satellite system (GNSS) in agriculture, particularly in fieldwork operations, seeking solutions of moderate cost with sufficient precision. This study examines the impact of GNSSs on automation and robotisation in agriculture, with a focus on intelligent agricultural guidance. It also discusses commercial devices that enable the automatic guidance of self-propelled machinery and the benefits that they provide. This paper investigates GNSS-based precision localisation devices under real field conditions. A comparison of commercial and low-cost GNSS solutions, along with the integration of satellite navigation with advanced visual odometry for improved positioning accuracy, is presented. The research demonstrates that affordable solutions based on the common differential GNSS infrastructure can be applied for accurate localisation under real field conditions. It also underscores the potential of GNSS-based automation and robotisation in transforming agriculture into a more efficient and sustainable industry.

Intelligent Environment-Adaptive GNSS/INS Integrated Positioning with Factor Graph Optimization

Global navigation satellite systems (GNSSs) applied to intelligent transport systems in urban areas suffer from multipath and non-line-of-sight (NLOS) effects due to the signal reflections from high-rise buildings, which seriously degrade the accuracy and reliability of vehicles in real-time applications. Accordingly, the integration between GNSS and inertial navigation systems (INSs) could be utilized to improve positioning performance. However, the fixed GNSS solution uncertainty of the conventional integration method cannot determine the fluctuating GNSS reliability in fast-changing urban environments. This weakness becomes solvable using a deep learning model for sensing the ambient environment intelligently, and it can be further mitigated using factor graph optimization (FGO), which is capable of generating robust solutions based on historical data. This paper mainly develops the adaptive GNSS/INS loosely coupled system on FGO, along with the fixed-gain Kalman filter (KF) and adaptive KF (AKF) being taken as comparisons. The adaptation is aided by a convolutional neural network (CNN), and the feasibility is verified using data from different grades of receivers. Compared with the integration using fixed-gain KF, the proposed adaptive FGO (AFGO) maintains the 100% positioning availability and reduces the overall 2D positioning error by up to 70% in the aspects of both root mean square error (RMSE) and standard deviation (STD).

A Statistical Approach for the Integration of Multi-Temporal InSAR and GNSS-PPP Ground Deformation Measurements.

Determining and monitoring ground deformations is critical for hazard management studies, especially in megacities, and these studies might help prevent future disaster conditions and save many lives. In recent years, the Golden Horn, located in the southeast of the European part of Istanbul within a UNESCO-protected region, has experienced significant changes and regional deformations linked to rapid population growth, infrastructure work, and tramway construction. In this study, we used Interferometric Synthetic Aperture Radar (InSAR) and Global Navigation Satellite System (GNSS) techniques to investigate the ground deformations along the Golden Horn coastlines. The investigated periods are between 2015 and 2020 and 2017 and 2020 for InSAR and GNSS, respectively. For the InSAR analyses, we used sequences of multi-temporal synthetic aperture radar (SAR) images collected by the Sentinel-1 and ALOS-2 satellites. The ground displacement products (i.e., time series and velocity maps) were then cross-compared with those achievable using the Precise Point Positioning (PPP) technique for the GNSS solutions, which can provide precise positions with a single receiver. In the proposed analysis, we compared the ground displacement velocities obtained by both methods by computing the standard deviations of the difference between the relevant observations considering a weighted least square estimation procedure. Additionally, we identified five circle buffers with different radii ranging between 50 m and 250 m for selecting the most appropriate coherent points to conduct the cross-comparison analysis. Moreover, a vertical displacement rate map was produced. The comparison of the vertical ground velocities derived from PPP and InSAR demonstrates that the PPP technique is valuable. For the coherent stations, the vertical displacement rates vary between -4.86 mm/yr and -23.58 mm/yr and -9.50 and -27.77 mm/yr for InSAR and GNSS, respectively.

Phased Array Radio Navigation System on UAVs: In-Flight Calibration

Global Navigation Satellite Systems (GNSS) has been the primary positioning solution for Unmanned Aerial Vehicles (UAVs) due to their worldwide coverage, high precision and lightweight receivers. However, GNSS is prone to electromagnetic interference and malicious assaults, including jamming or spoofing because of its low signal-to-noise ratio (SNR). To ensure the continuity and protection of UAV operations, using redundant navigation systems is essential. In recent years, the phased array radio system (PARS) has established itself as a local navigation solution. PARS is robust towards malicious assaults because of an much higher SNR than GNSS regarding directed and encrypted transmission. An essential factor of PARS is that the orientation of the radio antenna at a ground station needs to be precisely determined to obtain the correct positioning of UAVs. This paper presents a method for extending a previously proposed calibration algorithm to estimate the ground antenna orientation with an inertial navigation system (INS) aided by redundant positioning sensors (GNSS, PARS or barometer) using a multiplicative extended Kalman filter (MEKF) so that the calibration can be activated during flights whenever GNSS is available. In other words, the proposed navigation system is essentially an aided-INS which switches between two modes depending on the availability of GNSS: calibration and GNSS aiding mode when GNSS is available (Mode 1) and PARS and barometer aiding mode when GNSS is unavailable (Mode 2). Considering that the navigation system needs to include the effect of Earth’s curvature for a long-distance flight, PARS horizontal measurement and the barometer measurement were treated independently, and the navigation equations were propagated in Earth Centred Earth Fixed (ECEF) frame. The independent treatment of barometer measurement, and the propagation in ECEF frame were also beneficial when using multiple ground antennas to have a common reference point and reference frame. The proposed method was validated using data (Inertial Measurement Unit (IMU), GNSS, PARS, Pixhawk autopilot (including barometer) measurements) collected during a field test. In the validation, GNSS was made available at the middle of the flight and the calibration mode was activated for 200s. The proposed navigation system successfully estimated the precise orientation of multiple ground antennas and the navigation solutions were verified using GNSS and Pixhawk autopilot solutions as ground truth.

Current deformation along the northern Caribbean plate boundary from GNSS measurements in Cuba

Global Navigation Satellite System (GNSS) measurements at episodic sites or continuously operating stations have been used in most actively deforming regions to determine strain rates, fault slip rates, and contribute to assessing regional seismic hazard. However, the central part of the northern Caribbean plate boundary in Cuba has so far been exempt from sufficient GNSS data to study these classic issues of plate boundary kinematics and the associated hazard. Here, we describe the first position-velocity GNSS solution for Cuba and its close surroundings, providing new information on the seismotectonics of the southern boundary of the North American plate. We find that (1) western and central Cuba are rigidly attached to the North American plate, with internal deformation – if any – that is <1 mm/yr, (2) eastern Cuba shows systematic east-trending residual velocities with respect to the North American plate at 2–4 mm/yr, (3) sites on the Cayman Ridge, although located <50 km from the Oriente fault, show negligible residual velocities with respect to the North American plate. A series of kinematic models shows that the data are best explained by a 10 mm/yr slip deficit between the Gonâve microplate and the North American plate accommodated on a vertical, left-lateral Oriente strike-slip fault with a 25 km locking depth along the eastern Cuban margin, and a much shallower locking depth further west along the Cayman Ridge segment of the Oriente fault, which is possibly creeping. The transition from deep to shallow locking coincides with a drastic change in seismicity distribution, possibly indicative of lateral variation in the stress state or fault rheology along the Oriente fault. Additional GNSS observations and longer time series will help consolidate these initial findings and determine whether and how other active faults may contribute to the seismotectonics of Cuba.

EVALUATION OF A GNSS/IMU/LIDAR-INTEGRATION FOR AIRBORNE LASER SCANNING USING RTKLIB PPK AND PPP GNSS SOLUTIONS

Abstract. Airborne laser scanning allows for efficient acquisition of accurate 3D data for large areas. Because georeferencing of the LiDAR data requires knowledge of the platform trajectory, the laser scanner system commonly comprises a global navigation satellite system (GNSS) receiver/antenna and an inertial measurement unit (IMU). The standard processing pipeline consists of GNSS/IMU integration, georeferencing, and subsequent adjustment of the laser data. Here, we consider a holistic GNSS/IMU/LiDAR-integration approach based on least-squares adjustment. The GNSS is loosely coupled, and the GNSS positions are obtained using either postprocessing kinematic or precise point positioning GNSS processing strategies using the open-source software RTKLib. In this contribution, we compare the resulting point clouds to those of a standard processing workflow and evaluate the impact of the different processing strategies on point cloud quality in terms of internal consistency and absolute accuracy for a airborne laser bathymetry (ALB) dataset. Although the GNSS solutions themselves differ strongly, both the PPK- and the PPP-derived point clouds show better strip differences (below 2.5 cm) and similar absolute accuracy (&lt;4 cm RMSE w.r.t. reference targets after correction of constant datum shift) compared to the reference solution.

A Survey on IoT Positioning Leveraging LPWAN, GNSS, and LEO-PNT

Location data is an important piece of information in many Internet of Things (IoT) applications. Global Navigation Satellite Systems (GNSS) have been established as the standard for large-scale localization. However, the rapidly increasing need to locate IoT devices in recent years has exposed several shortcomings of traditional GNSS approaches. These limitations include the weak signal propagation in indoor and dense environments, the inability to calculate or obtain a location remotely, and a high energy consumption. Therefore, several industries have shown an increasing demand for alternative and innovative positioning solutions that are more suited in an IoT context. Hence, we conduct a survey on state-of-the-art, large-scale and energy-efficient positioning techniques for IoT applications. More specifically, we analyze the performance of terrestrial-based Low Power Wide Area Network (LPWAN) techniques, novel GNSS solutions, and innovative positioning techniques leveraging Low Earth Orbit (LEO) satellite constellations. A comparison is made in terms of 16 dimensions including energy consumption, positioning accuracy, coverage, and scalability. The analysis shows that interoperability between technologies is key to enable energy-efficient communication and positioning applications in the emerging market of satellite IoT.

A Cost-Effective GNSS Solution for Continuous Monitoring of Landslides

The development of low-cost dual-frequency global navigation satellite system (GNSS) receivers in recent years has enabled the use of these devices in numerous applications. In the monitoring of natural hazards, such as landslides, these devices can be considered suitable sensors. In this work, dual-frequency GNSS receivers and antennas were used for setting up near-real-time continuous low-cost GNSS monitoring systems (LGMSs) under field conditions. The SimpleRTK2B board, which integrates the u-blox ZED-F9P dual-frequency GNSS chip and the survey-calibrated GNSS antenna are the main components of the GNSS system. The LGMS was installed and tested for six months in the Laze landslide located in the northwestern part of Slovenia. A total of four GNSS systems were deployed, three of which were located in pillars in the landslide itself and one in a stable area. Open-source software was used to postprocess the acquired data, providing daily coordinates in static relative and precise point positioning (PPP) positioning modes. The results of six months of near-real-time monitoring showed that the Laze landslide was stable during this period, with only minor changes in the vertical component. The trend of decreasing ellipsoid height was evident at all stations, although it was in the range of a few millimeters. To validate the results in static relative positioning mode, the coordinate differences between low-cost and high-end geodetic GNSS instruments were estimated and found to be in the range of 5 mm or less, while the difference between horizontal and spatial positions was less than 7 mm for all stations. The same data were processed in PPP, vertical displacements were not detected as in the static relative positioning mode due to the lower accuracy of the method itself. Considering the six-month performance of a low-cost GNSS system under field conditions, it can be emphasized that these devices are capable of performing near real-time continuous monitoring of slow movements with high accuracy and decreased costs. In addition, an experimental test was performed to identify the size of detected displacements in real-time kinematic (RTK). Based on the achieved results, it was concluded that 20 mm spatial displacements are detectable with LGMSs in RTK considering only 15 s of observations.

Fusion of GNSS Pseudoranges with UWB Ranges Based on Clustering and Weighted Least Squares.

Global navigation satellite systems (GNSSs) and ultra-wideband (UWB) ranging are two central research topics in the field of positioning and navigation. In this study, a GNSS/UWB fusion method is investigated in GNSS-challenged environments or for the transition between outdoor and indoor environments. UWB augments the GNSS positioning solution in these environments. GNSS stop-and-go measurements were carried out simultaneously to UWB range observations within the network of grid points used for testing. The influence of UWB range measurements on the GNSS solution is examined with three weighted least squares (WLS) approaches. The first WLS variant relies solely on the UWB range measurements. The second approach includes a measurement model that utilizes GNSS only. The third model fuses both approaches into a single multi-sensor model. As part of the raw data evaluation, static GNSS observations processed with precise ephemerides were used to define the ground truth. In order to extract the grid test points from the collected raw data in the measured network, clustering methods were applied. A self-developed clustering approach extending density-based spatial clustering of applications with noise (DBSCAN) was employed for this purpose. The results of the GNSS/UWB fusion approach show an improvement in positioning performance compared to the UWB-only approach, in the range of a few centimeters to the decimeter level when grid points were placed within the area enclosed by the UWB anchor points. However, grid points outside this area indicated a decrease in accuracy in the range of about 90 cm. The precision generally remained within 5 cm for points located within the anchor points.

Effect of Large Height Difference on Global Positioning System Solutions from a Commercially Available Software Package

Commercially available global navigation satellite system (GNSS) processing software is user-friendly and can be used in a wide variety of positioning applications from establishing geodetic control over large regions to deformation monitoring on a local scale. It is important to study the accuracy of positioning from commercial software for presurvey planning. Previously, this was done in several studies; however, none of them focused on the effect of large height differences in positioning solutions. It is known in the literature that large height differences on a baseline degrade GNSS solutions. In this study, we investigate the effect using TOPCON MAGNET v 4.0.1 through analysis of continuously operating reference stations (CORS) in California, US. Because the effect of height differences on global positioning system (GPS) baseline components has not yet been properly quantified, the positioning accuracy standards given in the surveying guidelines may not be appropriate and are often overoptimistic. When the height difference was less than about 300 m, the root mean square error was about 2–3 mm for the horizontal components and about 20 mm for the vertical component for baseline lengths of 10–20 km. However, for a height difference of 1,500 m, the error became 5–8 mm for the horizontal and 70 mm for the vertical components. In all cases, the vertical error was greater than the horizontal by a factor of 5–9, which is much greater than the expected 2–4 for GNSS. These results are likely only applicable to the version of the MAGNET software used in this study.

Comparison of GRACE/GRACE-FO Spherical Harmonic and Mascon Products in Interpreting GNSS Vertical Loading Deformations over the Amazon Basin

We compute the vertical displacements in the Amazon Basin using the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) observations, including both the gravity spherical harmonic (SH) solutions from the Center for Space Research (CSR), GeoForschungsZentrum (GFZ) and Jet Propulsion Laboratory (JPL) and mascons from CSR, JPL and Goddard Space Flight Center (GSFC). The correlation coefficients, annual amplitude and root mean squares (RMS) reductions are calculated to assess the agreements between the GRACE/GRACE-FO and Global Navigation Satellite System (GNSS) vertical displacements at 22 selected GNSS stations. For the six GRACE/GRACE-FO products (i.e., CSR SH, GFZ SH, JPL SH, CSR mascon, GSFC mascon and JPL mascon), the mean annual amplitude reductions are 77.6%, 76.4%, 76.3%, 78.6%, 78.5% and 76.6%, respectively, the corresponding mean RMS reductions are 63.2%, 61.7%, 62.3%, 64.9%, 65.3% and 63.8%, respectively, and the mean correlation coefficients are all over 0.93. On the whole, mascon solutions agree slightly better with GNSS solutions than SH solutions do. The CSR SH and the GSFC mascon solutions show the best agreements with the GNSS solution among the 3 SH and 3 mascon products, respectively. We estimate GRACE/GRACE-FO noises using the three-cornered hat (TCH) method and find that the CSR SH and GSFC mascons also have the smallest noise variances among the SH and mascon products, respectively. By analyzing the GNSS stations from the central and southern Amazon Basin, we find that: (1) the RMS reductions when the mascon solutions are removed from GNSS height series are slightly larger than those using the SH solutions in the center, while in south all the RMS reductions are fairly close; (2) for both SH solutions and mascon solutions, the correlation coefficients in the center are slightly larger than those in the south, but conversely, the mean annual amplitude reductions in the center are much smaller than those in the south.

Tropospheric parameters from multi-GNSS and numerical weather models: case study of severe precipitation and flooding in Germany in July 2021

Storms and floods are the most frequent natural disaster in western and central Europe. Due to climate change, intensive storms with prolonged rain episodes will continue to cause even more destructive flooding. The good understanding and forecasting of such events are thus of uttermost importance. One of the ways to improve weather forecasts is the assimilation of external data, such as the global navigation satellite systems (GNSS). In this study, a preparation of the multi-GNSS tropospheric products—zenith total delays, tropospheric gradients and slant total delays—for future operational assimilation is shown. For a severe precipitation event in July 2021 in Germany, the GNSS parameters from three systems—GPS, GLONASS and Galileo—are compared to three Numerical Weather Models (NWMs)—ERA5 reanalysis of ECMWF, ICON run by the German Weather Service and GFS run by the US Weather Service. The flood that followed the rainfall was the deadliest natural disaster in Germany since 1962. The results show that all considered GNSS solutions have a similar level of agreement with the NWMs. However, for the flood region in western Germany, the biases from the multi-GNSS solutions are smaller compared to the GPS-only solution. From the models, ICON has the highest agreement with the GNSS data for all considered tropospheric parameters. The best agreement with the ICON is probably due to its high horizontal resolution and, thus, low representative errors and the fine tuning of DWD’s regional model for the specific region (Germany).

Low-cost integrated INS/GNSS using adaptive H∞ Cubature Kalman Filter

AbstractWe proposed an adaptive H-infinity Cubature Kalman Filter (AH∞CKF) to improve the navigation accuracy of a highly manoeuvrable unmanned aerial vehicle (UAV). AH∞CKF fuses the Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS) measurements. Traditional state estimation filters like extended Kalman filters (EKF) and cubature Kalman filters (CKF) assume Gaussian noises. However, their performance degrades for non-Gaussian noises and system uncertainties encountered in real-world applications. Thus, designing filters robust to noise and distribution is crucial. AH∞CKF combines H∞CKF design with an added adaptive factor to adjust the state estimation covariance matrix according to measurements by exploiting the square root method to yield more numerically stable results (SrAH∞CKF). We conducted multiple dynamically rich flight tests to validate our claims using a UAV equipped with a commercially well-known GNSS solution. Results show that the SrAH∞CKF state estimation outperforms EKF and CKF methods on average by 90% in various statistical measures.

A Novel Low-Cost GNSS Solution for the Real-Time Deformation Monitoring of Cable Saddle Pushing: A Case Study of Guojiatuo Suspension Bridge

Extreme loadings, a hostile environment and dangerous operation lead to the unsafe state of bridges under construction, especially large-span bridges. Global Navigation Satellite Systems (GNSS) tend to be the best choice for real-time deformation monitoring due to the significant advantage of automation, continuation, all-weather operation and high precision. Unfortunately, the traditional geodetic GNSS instrument with its high price and large volume is limited in its applications. Hence, we design and develop low-cost GNSS equipment by simplifying the monitoring module. The performance of the proposed solution is evaluated through an experimental dynamic scenario, proving its ability to track abrupt deformation down to 3–5 mm. We take Chongqing Guojiatuo Suspension Bridge in China as a case study. We build a real-time low-cost GNSS monitoring cloud platform. The low-cost bridge GNSS monitoring stations are located at the top of the south and north towers, midspan upstream and downstream respectively and the reference station is located in the stable zone 400 m away from the bridge management buildings. We conducted a detailed experimental assessment of low-cost GNSS on 5 April and a real-time deformation detection experiment of the towers and main cables during the dynamic cable saddle pushing process on 26 February 2022. In the static experiment, the standard deviation of the residual using the multi-GNSS solution is 2 mm in the horizontal direction and 5 mm in the vertical direction. The multi-GNSS solution significantly outperforms the BDS/GPS single system. The dynamic experiment shows that, compared with the movement measured by the robotic total station, the horizontal error of the south tower and north tower measured by low-cost GNSS is below 0.005 m and 0.008 m respectively. This study highlights the potential of low-cost GNSS solutions for Structural Health Monitoring (SHM) applications.

IMU-Aided Precise Point Positioning Performance Assessment with Smartphones in GNSS-Degraded Urban Environments

The tracking of satellite signals with the passive linearly polarized embedded global navigation satellite system (GNSS) antenna of smartphones in dynamic scenarios is susceptible to the changing multipath and obstructions in urban environments, which lead to a significant decrease in the availability and reliability of GNSS solutions. Accordingly, based on the characteristics of smartphone GNSS and inertial measurement unit (IMU) sensors data in GNSS-degraded environments, we established an IMU-aided uncombined precise point positioning (PPP) mathematical model that is suitable for smartphones. To enhance the reliability of initial alignment in dynamic mode, the step function variances depending on carrier-to-noise density ratio were established with the variances of GNSS measurements, and the inertial navigation system (INS) parameters were initialized while both the velocity of smartphones and the position dilution of precision (PDOP) reached corresponding thresholds. Considering the measurement noise and observations gaps of smartphones, the robust Kalman filter (RKF) with equivalent variance matrix was used for parameter estimation to improve the convergence efficiency of the coupled PPP/INS model. Experimental results indicated that the proposed PPP/INS method can effectively improve the positioning performance of smartphones in GNSS-degraded environments. Compared with the conventional smartphone PPP scheme, the PPP/INS horizontal errors in the eastern and western areas of the long trajectory experiment decreased by 49.37% and 48.29%, respectively. Meanwhile, the trajectory deviation of smartphones can remain stable in the tunnel where GNSS signals are blocked.

Evaluation of the Multipath Environment Using Electromagnetic-Absorbing Materials at Continuous GNSS Stations.

To date, no universal modelling technique is available to mitigate the effect of site-specific multipaths in high-precision global navigation satellite system (GNSS) data processing. Multipaths affect both carrier-phase and code/pseudorange measurements, and the errors can propagate and cause position biases. This paper presents the use of an Eccosorb AN-W-79 microwave-absorbing material mounted around a GNSS antenna that reflects less than dB of normal incident energy above a frequency of 600 MHz. To verify the feasibility and effectiveness of the Eccosorb, we installed two close stations by continuously operating multi-GNSS (BeiDou, GLONASS, Galileo and GPS) in a challenging location. One station is equipped with the Eccosorb AN-W-79, covering a square area of 3.35 m around the antenna, and the second station operates without it. The standard deviation reductions from single point positioning estimates are significant for all the individual GNSS solutions for the station equipped with microwave-absorbing material. The reductions are as follows: for GPS, between 15% and ; for Galileo, between 22% and ; for GLONASS, ; and for BeiDou, . Furthermore, we assess the influence of multipaths by analysing the linear combinations of code and carrier phase measurements for various GNSS frequencies. The Galileo code multipath shows a reduction of more than for the station with microwave-absorbing material. For GLONASS, particularly for the GLOM3X and GLOM1P code multipath combinations, the reduction reaches , depending on the observation code types. For BeiDou, the reduction is more than , and for GPS, it reaches between and . The Eccosorb AN-W-79 microwave-absorbing material shows convincing results in reducing the code multipath noise level. Again, using microwave-absorbing material leads to an improvement between and in carrier phase cycle slips. The carrier-phase multipath contents on the post-fit residuals from the processed GNSS solutions show a relative RMS reduction of for Galileo and for GLONASS and GPS when using the microwave-absorbing material. This study also presents power spectral contents from residual signal-to-noise ratio time series using Morlet wavelet transformation. The power spectra from the antenna with the Eccosorb AN-W-79 have the smallest magnitude, demonstrating the capacity of microwave-absorbing materials to lessen the multipath influence while not eliminating it.

Farklı troposfer modellerinin gerçek zamanlı çoklu-GNSS PPP performansına etkisi

With the initialization of IGS (International GNSS Service) real-time service products, real-time Precise Point Positioning (PPP) applications have been a popular topic within the GNSS (Global Navigation Satellite Systems) users. The impact of the troposphere on GNSS signals is one of the most crucial error sources regarding the real-time PPP solution. In the PPP technique, the dry component of tropospheric delay is usually corrected by means of empirical models, while its wet component is estimated as an unknown parameter in the adjustment process. Hence, the troposphere model employed in the PPP solution has a considerable impact on the performance of the obtained solution. Therefore, the main objective of this study is to investigate the impact of different troposphere models on the performance of real-time multi-GNSS PPP. As a part of this study, four different troposphere models, where Saastamoinen and Hopfield models that are most frequently used in GNSS solutions are used together with GPT (Global Pressure and Temperature) 2 and 3 models separately, were constituted. In this context, the observation dataset acquired from a total of 16 different IGS stations over a ten-day period of December 19-28, 2021, were processed utilizing four different troposphere models. In addition to the positioning performance, PPP solutions were also analyzed in terms of zenith total delay (ZTD) estimation. The results show that the best positioning performance can be obtained when the Saastamoinen model is used in combination with GPT3. The three-dimensional positioning accuracy acquired from the corresponding solution is 2.72 cm, which is better than the closest solution by a ratio of 9.2%. Besides, in terms of the ZTD estimation, the best performance is achieved again in the case when the Saastamoinen model is used in combination with GPT3. For the related solution, the accuracy of ZTD estimation is calculated as 1.24 cm and this value indicates a better performance by a ratio of 10.2% compared with the closest solution.