Position Dilution Of Precision Research Articles

REAL-TIME WATER LEVEL MONITORING USING LOW-COST GNSS RECEIVER

Abstract. Developing an accurate water level monitoring system is one of the measures to mitigate the effects of water-related hazards such as river flooding. While current monitoring systems in the country are efficient in terms of accurate and immediate data delivery, these systems can be costly. This study assesses the Global Navigation Satellite System (GNSS) performance of low-cost receiver systems for water level monitoring using real-time kinematic (RTK) solution. A total of 10 days’ valid observation were analyzed to compare the two base-rover receiver setups: 1) low-cost base to low-cost rover (LC-LC) and 2) survey-grade base to low-cost rover (SG-LC) grounded on accuracy, integrity, continuity, availability, and cost. Accuracy results show LC-LC=5.81 cm and SG-LC=5.37 cm mean difference of RTK from in-situ readings. In terms of RTK and post-processing kinematic (PPK) difference for integrity criterion, the RTK SG-LC setup has a lower range of RMS of 0.86 to 1.94 cm versus LC-LC setup of 1.19 to 2.28 cm. For the continuity criterion, the average fixed solutions percentage for the LC-LC setup: RTK=91.43%, PPK=92.92%, whereas for the SG-LC: RTK=95.51%, PPK=98.39%. On availability, the number of valid satellites (NSat) and position dilution of precision (PDOP) of RTK and PPK solutions for each setup are LC-LC: RTK=11, PPK=23, PDOP=1.0 and SG-LC: RTK=11, PPK=24, PDOP=1.9. Lastly, in terms of costing, LC-LC costs Php 58,340 while SG-LC costs Php 1,279,645. Overall, the parity of LC-LC with SG-LC in terms of the five criteria suggests viability of using LC-LC for accurate real-time water level monitoring.

Online Self-Calibration of Cable-Driven Parallel Robots Using Covariance-Based Data Quality Assessment Metrics

Abstract This paper presents an algorithm to perform self-calibration of cable-driven parallel robots (CDPRs), where the CDPR's end-effector pose is estimated in conjunction with the calibration of biases in the CDPR's measurements. Two new metrics, known as the position dilution of precision (PDOP) and orientation dilution of precision (ODOP) are introduced as a means to quantify the quality of data collected with regards to self-calibration. These metrics are based on a covariance matrix that is computed online as part of the proposed self-calibration algorithm, which results in the PDOP and ODOP directly corresponding to the standard deviation of the position and orientation errors, respectively. These metrics are used to intuitively select which data points contribute to improved calibration, resulting in a computationally-efficient algorithm requiring few data points to maintain accurate calibration. Additionally, the PDOP and ODOP provide a means to assess when sufficient calibration data has been collected. Numerical results involving an inverse kinematic simulation with rigid cables and a dynamic simulation with flexible cables indicate that the proposed algorithm is capable of performing self-calibration in a computationally-efficient manner. Moreover, the simulation results indicate that the proposed PDOP and ODOP metrics result in smaller position and orientation errors when used to prune the data set compared to the observability indices found in the literature. Accuracy of the proposed algorithm is also confirmed through experiments when compared to ground-truth pose data.

Improving the underwater navigation performance of an IMU with acoustic long baseline calibration

Underwater acoustic Long-Baseline System (LBL) is an important technique for submarine positioning and navigation. However, the high cost of the seafloor equipment and complex construction of a seafloor network restrict the distribution of the LBL within a small area, making an underwater vehicle difficult for long-distance and high-precision acoustic-based or inertial-based navigation. We therefore propose an acoustic LBL-based Inertial Measurement Unit (IMU) calibration algorithm. When the underwater vehicle can receive the acoustic signal from a seafloor beacon, the IMU is precisely calibrated to reduce the cumulative error of Strapdown Inertial Navigation System (SINS). In this way, the IMU is expected to maintain a certain degree of accuracy by relying solely on SINS when the vehicle reaches out the range of the LBL network and cannot receive the acoustic signal. We present the acoustic LBL-based IMU online calibration model and analyze the factors that affect the accuracy of IMU calibration. The results fulfill the expectation that the gyroscope bias and accelerometer bias are the main error sources that affect the divergence of SINS position errors, and the track line of the underwater vehicle directly affects the accuracy of the calibration results. In addition, we deduce that an optimal calibration trajectory needs to consider the effects of the three-dimensional observability and position dilution of precision. In the experiment, we compare the effects of seven calibration trajectories: straight and diamond-shaped with and without the change of depth, and three sets of curves with the change of depth: circular, S-shaped, and figure-eight. Among them, we find that the figure-eight is the optimal trajectory for acoustic LBL-based IMU online calibration. We take the maintenance period during which the accumulated SINS Three Dimensional (3D) position errors are below 1 km to evaluate the calibration performance. The filed experimental results show that for the Micro-electromechanical Systems-grade IMU sensor, the maintenance period for the IMU calibrated with the proposed algorithm can be increased by 121% and 38.9% compared to the IMU without calibration and with the laboratory default parameter calibration, indicating the effectiveness of the proposed calibration algorithm.

Analysis of the precision of determination of aircraft coordinates using EGNOS+SDCM solution

This paper presents an algorithm for determining the precision parameter for aircraft position coordinates based on a combined GPS/EGNOS and GPS/SDCM solution. The proposed algorithm uses a weighted average model that com-bines a single GPS/EGNOS and GPS/SDCM position navigation solution to determine the resulting aircraft coordi-nates. The weighted mean model include the linear coefficients as a function of: the inverse of the number of tracked GPS satellites for which EGNOS and SDCM corrections have been generated, and the inverse of the geometric coeffi-cient of the PDOP (Position Dilution of Precision). The corrections between the single GPS/EGNOS and GPS/SDCM solution to the aircraft's resultant coordinates are then calculated on this basis. Finally, the standard deviation for the aircraft resultant BLh (B-Latitude, L-Longitude, h- ellipsoidal height) coordinates is calculated as a measure of preci-sion. The research experiment used recorded on-board GPS+SBAS data from two GNSS receivers mounted on a Dia-mond DA 20-C1 aircraft. The test flight was carried out on the Olsztyn-Suwaki-Olsztyn route. The calculations of aircraft position based on GPS/EGNOS and GPS/SDCM solution were performed in the RTKLIB v.2.4.3 program in the RTKPOST module. Next, aircraft resultant coordinates and standard deviations were computed in Scilab v.6.0.0 soft-ware package. Based on the tests performed, it was found that for the Trimble Alloy receiver, the standard deviation values for the ellipsoidal coordinates BLh of the aircraft do not exceed 1.77 m. However, for the Septentrio AsterRx2i receiver, the values of standard deviations for the aircraft's ellipsoidal BLh coordinates do not exceed 5.04 m. The use of linear coefficients as the inverse of the number of tracked GPS satellites with SBAS corrections in the GPS/EGNOS+GPS/SDCM positioning model resulted in a reduction in standard deviations of approximately 50-51% relative to the solution with linear coefficients calculated as the inverse of the PDOP parameter. In paper, the standard deviation was also obtained using arithmetic mean model. However the values of standard deviation from weighted mean model are lower than arithmetic mean model.

An Efficient BDS-3 Long-Range Undifferenced Network RTK Positioning Algorithm

In 2020, the BeiDou-3 global navigation satellite system (BDS-3) was officially completed and put into service. Currently, network real-time kinematic (RTK) technology is considered the main means through which to improve the positioning accuracy of the BeiDou navigation satellite system (BDS). This paper proposes a long-range undifferenced network RTK (URTK) algorithm, based on multi-frequency observation data of the BDS. First, the multi-frequency phase integer ambiguity resolution (AR) model considering atmospheric error parameters is designed, and the multi-frequency phase integer ambiguity of the long-range BDS reference station is determined. Then, the undifferenced integer ambiguity of each reference station is obtained, using linear variation based on the accurately determined phase integer ambiguity between reference stations, and the undifferenced observation error of each reference station is calculated. Considering the weakening spatial correlation of the observation errors between long-range stations, undifferenced classification error corrections of a reference station network are separated, according to different error characteristics. Finally, the inverse distance weighting method is employed to calculate the classification undifferenced error correction of the rover station. The rover station corrects the observation error through applying the undifferenced error correction to achieve high-precision positioning. The measured data of a long-range continuous operation reference station (CORS) network are selected for an experiment. The results show that the proposed algorithm can quickly and accurately realize the resolution of the BDS integer ambiguity of a reference station network and establish an undifferenced area error correction model in order to achieve accurate classification of undifferenced error correction values for a rover station. In China, the BDS-3 is superior to the global positioning system (GPS) in terms of the satellite number, position dilution of precision (PDOP) value, AR success rate, stability, and convergence time. The results show that the AR success rate, stability, and convergence time increase with the operational frequency, and the BDS-3 can achieve centimeter-level positioning of single-system rover stations without relying on the GPS.

Multi-orbit lunar GNSS constellation design with distant retrograde orbit and Halo orbit combination

The Moon is the closest natural satellite to mankind, with valuable resources on it, and is an important base station for mankind to enter deep space. How to establish a reasonable lunar Global Navigation Satellite System (GNSS) to provide real-time positioning, navigation, and timing (PNT) services for Moon exploration and development has become a hot topic for many international scholars. Based on the special spatial configuration characteristics of Libration point orbits (LPOs), the coverage capability of Halo orbits and Distant Retrograde Orbit (DRO) in LPOs is discussed and analyzed in detail. It is concluded that the Halo orbit with a period of 8 days has a better coverage effect on the lunar polar regions and the DRO has a more stable coverage effect on the lunar equatorial regions, and the multi-orbital lunar GNSS constellation with the optimized combination of DRO and Halo orbits is proposed by combining the advantages of both. This multi-orbital constellation can make up for the fact that a single type of orbit requires a larger number of satellites to fully cover the Moon, using a smaller number of satellites for the purpose of providing PNT services to the entire lunar surface. We designed simulation experiments to test whether the multi-orbital constellations meet the full lunar surface positioning requirements, and compare the coverage, positioning, and occultation effects of the four constellation designs that pass the test, and finally obtain a set of well-performing lunar GNSS constellations. The results indicate that the multi-orbital lunar GNSS constellation combining DRO and Halo orbits can cover 100% of the Moon surface, provides there are more than 4 visible satellites at any time on the Moon surface, which meets the navigation and positioning requirements, and the Position Dilution of Precision (PDOP) value is stable within 2.0, which can meet the demand for higher precision Moon surface navigation and positioning.

BDS/GPS/Galileo Precise Point Positioning Performance Analysis of Android Smartphones Based on Real-Time Stream Data

Smartphones with the Android operating system can acquire Global Navigation Satellite System (GNSS) raw pseudorange and carrier phase observations, which can provide a new way for the general public to obtain precise position information. However, only postprocessing precise orbit and clock offset products in some older smart devices are applied in current studies. The performances of precise point positioning (PPP) with the smartphone using real-time products and newly smartphones are still unrevealed, which is more valuable for real-time applications. This study investigates the observation data quality and multi-GNSS real-time PPP performance using recent smartphones. Firstly, the observed carrier-to-noise density ratio (C/N0), number of satellites and position dilution of precision (PDOP) of GNSS observations are evaluated. The results demonstrate that the C/N0 received by Huawei Mate40 is better than that of the Huawei P40 for GPS, BDS, QZSS and Galileo systems, while the GLONASS is poorer, and the PDOP of the Huawei P40 is slightly better than that of Mate40. Additionally, a comprehensive analysis of real-time precise orbit and clock offset products performance is conducted. The experiment result expresses that the orbit and clock offset performance of GPS and Galileo is better than that of BDS-3 and GLONASS, and BDS-2 is the worst. Finally, single- and dual-frequency multi-GNSS combined PPP experiments using observations received from smartphones and real-time products are conducted; the results indicate that the real-time static PPP using a smartphone can achieve decimeter-level positioning accuracy, and kinematic PPP can achieve meter-level positioning accuracy after convergence.

Positioning with GNSS and 5G: Analysis of Geometric Accuracy in Urban Scenarios.

GNSS positioning in urban scenarios suffers for the scarce visibility of satellites. Integration with 5G services for positioning could improve this situation. In this paper, the digital surface models (DSMs) relevant to different urban scenarios, namely residential streets and urban canyons, are simulated around one observer in northern Italy (Milano) for one day of the year chosen as an example. The time series of the number of in-view GNSS satellites, their geometry and the derived quality indexes (position dilution of precision (PDOP)) are computed and analyzed. As expected, in urban canyons, a significant number of epochs does not provide four satellites within view, and many more epochs present really mediocre PDOPs. In residential streets, the situation is always quite fair. Different geometric configurations of 5G base stations are simulated around the observer. The availability of 5G times of arrival (ToAs) and their differences (TDoAs) is hypothesized, and the integration of these observations with GNSS pseudoranges is analyzed, again in terms of the PDOPs. In residential streets, 5G availability improves the positioning. In urban canyons, the optimal configuration of 5G base stations (five base stations around the observer) completely solves the positioning problem for all the epochs of the day. Less favorable configurations (four and three base stations) improve epochs with poor PDOPs in a GNSS-only configuration. They allow the positioning of epochs with few satellites but cannot completely replace the GNSS.

ASSESSING EFFICIENCY OF GPS EPHEMERIDES IN DIFFERENT REGION USING PRECISE POINT POSITIONING

Abstract. Precise Point Positioning (PPP) is a technique that process Global Positioning System (GPS) observation that can achieve sub-decimetre accuracy. Precise ephemerides that contain satellite clock and position plays a vital role in minimising orbital and clock error in PPP. This study hypothesize that the efficiency of ephemerides varies across region, influenced by the density of stations involved in generating the ephemerides. GPS observations from stations in five different regions were processed using PPP technique by using RTKLIB. Four types of ephemerides were used namely broadcast, ultra-rapid, rapid, and final ephemerides during the processing of each station. Root-mean-squared error (RMSE) of 3D error of the PPP solution for the stations in each region is quantified. Among the five regions selected, Europe has the lowest RMSE of 155.67 cm, 27.93 cm, 27.38 cm and 27.06 cm for broadcast, ultra-rapid, rapid, and final ephemeris respectively. This high accuracy can be attributed to the density of International GNSS Service (IGS) stations in Europe that are available for the generation of ephemerides. Position Dilution of Precision (PDOP) was also found to contribute to the accuracy of PPP solution in a region, whereby a low PDOP often promises higher positioning accuracy. More regional stations are suggested to be involved in the generation of ephemerides to improve the efficiency of ephemerides in that region.

Methodology for optimizing a Constellation of a Lunar Global Navigation System with a multi-objective optimization algorithm

Global Navigation Satellite Systems (GNSS) are not only used in terrestrial applications, but also in Low-Earth orbit satellites and in higher altitude missions. NASA’s Magnetospheric Multiscale (MMS) mission has demonstrated the capabilities of existing GNSS systems to provide positioning, navigation, and timing (PNT) services in the Cis-lunar space.The resurgence in plans by national space agencies for Lunar exploration presents a need for accurate, precise, and reliable navigation systems to ensure the safety and success of future missions.Moreover, the increased amount of Moon missions over recent years, shows the requirement of navigation capabilities for Low Lunar orbiters, Moon landers, Moon rovers, and manned missions.The success of Global Navigation Satellite Systems (GNSS) on Earth, presents an opportunity for the study of a potential design requirements and expected performance of a Lunar GNSS constellation.We have approached this problem through the methodology of multi-objective optimization; numerically simulating the orbits, and using the Position Dilution of Precision (PDoP) as the figure of merit to optimize a set of 200 constellation designs and improving them gradually over 1864 generations. Over 12,000 unique constellation designs were generated with the best 10 constellations presented in this paper for consideration and further study. Compared to the literature, these 10 constellations achieved a 44% improvement in PDoP (2.73) using the same number of satellites in each constellation, and meeting the performance requirements of planned Lunar missions.

Deployment of Ultra Dense Network Devices in Space. Part 2. Search Using Geometric Factor

This work is a continuation of the study devoted to mathematical and simulation modeling of methods for searching for locations of gNB base station devices in space according to the criterion of the geometric factor of reducing the positioning accuracy of the user device UE. The task in this formulation is relevant and in demand for ultra-dense networks of the millimeter (30–300 GHz) and submillimeter or terahertz band (0.3–3 THz) of the fifth and subsequent generations, respectively. As a criterion for the spatial placement of the infrastructure of fixed network devices acting as a base station, access point and / or repeater / router, the geometric factor of reducing the positioning accuracy of the DOP (Dilution of Precision) of the user device is used. Based on the algorithmic, methodological and software, formalized in the previous work for searching for gNB placements in space according to the criterion of geometric factors for reducing positioning accuracy in the horizontal plane HDOP (Horizontal DOP), the vertical plane VDOP (Vertical DOP) and by location in the PDOP (Position DOP) space, this study removes the restriction on the fixed placement of UEs in space, and also provides for an increase in the number of gNBs more than five, for which placements are searched. Subject of study. The article is devoted to mathematical and simulation modeling of methods for searching for locations of base station devices in space according to the criterion of a geometric factor for reducing the positioning accuracy of a user device. Method. Iterative enumeration of all possible locations of stationary base stations and mobile user devices with a given step in space to minimize the geometric factor of reducing positioning accuracy in the selected service area. Main results. The result of this work is the formalization of algorithmic, methodological and software to obtain the final configuration of locations for a given number of stationary base stations in the selected service area. Practical significance. The results obtained make it possible to search for and justify the locations of base stations and/or routers in scenarios of ultra-dense placement of user devices in a space saturated with biomass.

Deployment of Ultra Dense Network Devices in Space. Part 1. Models and Methods of Geometric Factor

The use of the millimeter band (30 GHz–300 GHz) in fifth generation networks and the submillimeter or terahertz band (0.3–3 THz) in sixth generation networks, due to the physical characteristics of radio wave propagation, inevitably leads to a reduction in the radio communication range and the use of predominantly lineof-sight radio links. From the point of view of the network architecture, this circumstance entails an increase in the density of the spatial arrangement of devices, which, in turn, leads to the emergence of new tasks for the network organization at the physical, channel and network levels of the open systems inter-action model. One of the approaches to the spatial arrangement of the infrastructure of stationary network devices acting as a base station, access point and / or repeater / router can be the geometric factor of DOP (Dilution of Precision) in positioning accuracy known in classical radar and radio navigation. To date, from the analysis of open foreign sources, it can be argued that this approach has already become widespread in the tasks of finding and justifying the locations of base stations of fifth generation communication networks. This is due to the new role of positioning not only as a service of communication net-works, but also as an auxiliary means of solving the problems of net-work organization at the three lower levels of the data transmission medium. In connection with the ongoing convergence of infocommunication and positioning services provided by the infrastructure of communication networks of the fifth and subsequent generations, there is every reason to believe that the approach of placing network devices based on DOP deserves attention and can be used for communication networks of the sixth-generation of terahertz band, where the density of transceivers will already exceed 1 device per square meter. Subject of study. The article is devoted to mathematical and simulation modeling of methods for searching for locations of base station devices in space according to the criterion of the geometric factor of the dilution of precision for positioning accuracy of the user device. Method. Calculation of geometric factors for the dilution of precision of positioning accuracy in the horizontal plane HDOP (Horizontal DOP), in the vertical plane VDOP (Vertical DOP) and by location in space PDOP (Position DOP). Main results. The result of this work is the formalization of algorithmic, methodological and software for DOP calculations and search for locations of base station devices in space based on geometric factors of the DOP for the positioning accuracy of user devices. Practical significance. The results obtained make it possible to search for the locations of the base stations of an ultra-dense network in space under the condition of a fixed location of the user device, as well as to perform a quantitative and qualitative assessment of the obtained placements according to the DOP criteria.

Optimization design of two-layer Walker constellation for LEO navigation augmentation using a dynamic multi-objective differential evolutionary algorithm based on elite guidance.

The online version contains supplementary material available at 10.1007/s10291-022-01366-5.

GNSS RTK/UWB/DBA Fusion Positioning Method and Its Performance Evaluation

As a significant space–time infrastructure, the Global Navigation Satellite System (GNSS) provides high-precision positioning, navigation, and timing (PNT) information to users all over the world. However, GNSS real-time kinematic (RTK) mobile receiver signal attenuation is obvious in complex environments such as under trees, urban canyons, and indoors, among others, and it is incapable of meeting the demand of multi-level mass users for indoor and outdoor seamless positioning applications. The goal of this study was to address the limitations and vulnerabilities of the GNSS RTK positioning above-mentioned. First, we propose a GNSS RTK/UWB/DBA fusion positioning model and provide detailed algorithm steps for various types of observations. The performance of the GNSS RTK/UWB/DBA fusion positioning under various occlusion environments is then thoroughly evaluated using static and dynamic cart experiments. The experiment results show that as the elevation mask angle increases, the number of available GNSS satellites decreases and the ambiguity resolution success rate decreases; in comparison to GNSS RTK, the proposed GNSS RTK/UWB/DBA fusion positioning model can significantly improve the spatial geometry distribution of observations, reduce the position dilution of precision (PDOP) value, and improve the ambiguity resolution success rate. At an elevation mask angle of 50 degrees, GNSS RTK/UWB/DBA combination positioning can improve the ambiguity resolution success rate by 20% to 60%, and a positioning error less than 5 cm by 20% to 50%. It also indicates that the GNSS RTK/UWB/DBA fusion positioning model has higher positioning accuracy and can effectively improve the availability and reliability of GNSS RTK in a local harsh environment.

Control Extension Using Global Navigation Satellite System Receivers in Auchi, Nigeria

Auchi is the headquarters of Etsako West Local Government Area of Edo State, which is opening up with many developments and diverse construction activities taking place. It was observed that there are limited numbers of reliable survey controls to check these activities; hence the study focuses on second order control (Class 1) extension along the New Auchi- Igarra road to the Polytechnic (Up Iyekhei) road through the Water Board. The controls serve as references for engineering, topographic, cadastral, and route survey projects in and around the project location. An in-situ check using point positioning technique revealed that they were in good condition for use (FGP/EDY072, FGP/EDY089, and FGP/EDY090) were used for extension, and an in-situ check using point positioning technique revealed that they were in good condition for A total of 15 points (AME 001 to AME 015) were observed in static mode with Hi Target GNSS dual frequency receivers and were post processed based on the Clark 1880 spheroid while the total length was 8.503km (8503m). The interval of the new controls ranged between 58.30m and 1569.76m; which is aimed at providing users within these routes a good proximity to at least three of the controls for effective usage. Not less than fifteen satellites were acquired by the GNSS receivers for every observation, and a time range of not less than 60 minutes (1 hour) was used for data acquisition at every station, with a Positional Dilution of Precision (PDOP) value that ranged between 1.1 and 1.5. The study was intended for horizontal control only, but the vertical control values were obtained as well. For easy future location of the new extended controls, a proper description of the controls was carried and recorded in appropriate field sheets. The entire survey was carried out according to specification and is fit to be used for subsequent lower order surveys within the project area.

Analysis of the Determination of the Accuracy Parameter for Dual Receivers Based on EGNOS Solution in Aerial Navigation

Abstract The paper presents the results of research on the determination of the accuracy parameter for European Geostationary Navigation Overlay System (EGNOS) positioning for a dual set of on-board global navigation satellite system (GNSS) receivers. The study focusses in particular on presenting a modified algorithm to determine the accuracy of EGNOS positioning for a mixed model with measurement weights. The mathematical algorithm considers the measurement weights as a function of the squared inverse and the inverse of the position dilution of precision (PDOP) geometrical coefficient. The research uses actual EGNOS measurement data recorded by two on-board GNSS receivers installed in a Diamond DA 20-C airplane. The calculations determined the accuracy of EGNOS positioning separately for each receiver and the resultant value for the set of two GNSS receivers. Based on the conducted tests, it was determined that the mixed model with measurement weights in the form of a function of the inverse square of the PDOP geometrical coefficient was the most efficient and that it improved the accuracy of EGNOS positioning by 37%–63% compared to the results of position errors calculated separately for each GNSS receiver.

AN OPTIMAL DEPLOYMENT METHOD OF UWB POSITIONING BASE-STATION

Abstract. Aiming at the prominent problem of high deployment cost of UWB (Ultra Wideband) positioning system and the waste of resources caused by repeated coverage of UWB base-station signals, the optimal deployment of the location and number of UWB positioning base stations is studied. Using Genetic Optimization Algorithm to optimize the objective function with Position Dilution of Precision (PDOP) and base-station Sharing-Value. The simulation and experimental results show that for the optimization of the location of UWB base stations, the three-dimensional average positioning error of the optimized layout method can be reduced by at least 0.3m compared with other typical layout methods; for the optimization of the number of base stations, the number by the optimized layout method is significantly lower than the typical layout method and decreases more as the actual base station deployment area increases. Therefore, the performance of the proposed method for optimal deployment of UWB positioning base stations is fully verified, which provides a reference for the optimal deployment of UWB positioning base stations in practical applications.

A New Optimal Subset Selection Method of Partial Ambiguity Resolution for Precise Point Positioning

Rapid and accurate ambiguity resolution is the core of high-precision precise point positioning (PPP) data processing. However, the ambiguity parameters in PPP observation models are easily affected by atmospheric residual and gross errors, which lead to the probability of successfully fixing decreases and computational burden increases in full ambiguity resolution. Therefore, an increasing number of partial ambiguity resolution (PAR) strategies have been proposed. The selection of the optimal subset of PAR is crucial in this method. The traditional optimal subset selection method of PAR commonly leads to a single judgment criterion and weakened geometric configuration strength because the satellites with low elevation angles are often easily eliminated during the optimal subset selection. In this paper, a multi-factor constrained optimal subset selection method for PAR was proposed, which incorporates the ambiguity variance, the ambiguity dilution of precision (ADOP), satellite position dilution of precision (PDOP) and ratio test values. In order to verify the feasibility of the proposed optimal subset selection method, PAR tests under two schemes were performed for GPS/Galileo based on the static observation data of 15 Multi-GNSS Experiment (MGEX) tracking stations. The results show that, compared with the ambiguity variance sorting method, the proposed subset selection method can further improve the accuracy of the coordinate solution and the strength of geometric figure positioning. The average root mean square of the coordinate residuals is found to decrease by about 12.90%, 6.83% and 9.39% in the eastern, northern and vertical directions, respectively. The increase in the fixed epoch rate ranged from 0.87% to 33.33%, with an average of about 8.71%.

GNSS Real–Time Precise Point Positioning in Arctic Northeast Passage

Human activities in the Arctic regions have been increasing in recent years due to the impacts of climate change, such as Arctic Sea ice decline. For example, there has been an increase in Arctic shipping routes. A robust navigation system with a high positioning accuracy is required when traversing the extremely challenging Arctic environment to ensure the safety of human activities. However, the high–precision GNSS navigation and the positioning method, e.g., real–time kinematic (RTK), is not available in the polar regions due to the accessibility issues of the required infrastructures. On the other hand, the International GNSS Service (IGS) enables real–time applications; additionally, quick and convenient satellite communication systems are also available. This offers the possibility of real–time precise point positioning (RT–PPP) with multi–GNSS for high-precision navigation in the Arctic. In our paper, we analyzed the performance of multi–GNSS RT–PPP in the Arctic Northeast Passage (NEP), highlighting the following contributions: First, a GNSS device is installed on the M/V TIANHUI, which passed through the NEP from 10 September to 20 September 2019; Second, we quantitatively evaluated the collected GNSS signals in terms of the maximum satellite elevations, number of visible satellites (NSAT), position dilution of precision (PDOP) values, signal–to–noise ratio (SNR), and multipath errors. Third, we evaluated the accuracy of the CLK93 real–time products compared with the Deutsches GeoForschungsZentrum (GFZ) final products GBM. Finally, we carried out experiments for both single– (SF) and dual–frequency (DF) RT–PPP in the NEP during the 11–day testing period. Our experimental results show that meter–level positioning accuracy can be achieved with SF RT–PPP, while the DF RT–PPP model reaches sub–decimeter values and even centimeter–level accuracy. In addition, using the multi–GNSS method, we showed that the average RMS values of DF RT–PPP in the horizontal and vertical directions are 0.080 m and 0.057 m, respectively, demonstrating an improvement of approximately 70% over single–GPS solutions.

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.