Position Dilution Research Articles

Research on Design and Staged Deployment of LEO Navigation Constellation for MEO Navigation Satellite Failure

Low Earth orbit (LEO) satellites have unique advantages in navigation because of their high signal intensity and rapid geometric changes in a short period. In order to solve the problem of constellation performance degradation after a potential failure pertaining one or more medium Earth orbit (MEO) navigation satellites, this paper designs the LEO navigation constellation and considers the task requirements of different stages of constellation deployment. Firstly, the LEO navigation constellation is designed by a non-dominated sorting genetic algorithm II (NSGA-II). The average position dilution of precision (PDOP) is 1.676, which is an improvement compared to the average PDOP offered by the four traditional GNSS. Secondly, the staged deployment of constellation takes into account the degradation of constellation performance caused by the failure of MEO navigation satellites, and the Monte Carlo method is used to analyze the case of three simultaneous satellite failures. The results show that a single satellite failure within each orbital plane and adjacent satellites with close phase separation has a great impact on the performance of the MEO navigation constellation. On this basis, a staged deployment strategy was adopted in order to balance cost, risk, and performance. The three phases deploy 66, 156, and 288 satellites, respectively; as a make-up constellation under contingencies, a navigation enhancement constellation, and an independent navigation constellation, the deployment of the staged sub-constellations meets the mission requirements. The constellation design and staged deployment method proposed in this paper can provide reference for the future study of LEO navigation constellations.

LEO enhanced GNSS (LeGNSS) precise point positioning with emphasis on model comparison

With the rapid construction of the low-earth-orbit (LEO) constellation, LEO Enhanced Global Navigation Satellite System (LeGNSS) has become a hotspot in the research of GNSS applications and services, especially for fast convergence of precise point positioning (PPP). In this study, we analyze the impact of LEO satellites on the spatial geometry based on simulated LEO and real GNSS data, and evaluate the LeGNSS PPP performance with ionosphere-free (IF), undifferenced and uncombined (UDUC), and ionosphere-weighted (IW) models. Eight Multi-GNSS Experiment (MGEX) stations are selected for static and kinematic experiments. Results show that Position Dilution of Precision (PDOP) values of LeGNSS are about 0.5–1.2, which are improved by 38 % and 22 % compared with GPS-only and combined GPS, Galileo, and BDS (G\\E\\C) solutions. With LEO satellites, the positioning accuracy in east (E), north (N), and up (U) directions are improved by about 50 %, 30 %, and 50 % for the static mode, and about 35 %, 30 %, and 67 % for the kinematic mode. Moreover, the positioning accuracies of the IF, UDUC, and IW models are comparable. For convergence time, the static and kinematic results with LEO satellites are about 1.1 and 1.3 min, respectively, while those without LEO satellites are longer than 10.0 min. In addition, the model with inter-system bias (ISB) constraints can reduce the convergence time by within 1.0 min.

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.

Optimizing the Deployment of Ground Tracking Stations for Low Earth Orbit Satellite Constellations Based on Evolutionary Algorithms

Low Earth orbit (LEO) satellite constellations have emerged as an effective alternative for the provision of high-accuracy positioning, navigation and timing (PNT) solutions which are based on high-precision orbit and clock information. Determining an orbit with high precision is dependent on the number and distribution of ground tracking stations. Therefore, it is important to investigate methodologies that can ensure the adequate observing coverage of LEO navigation constellations. In this study, an evolutionary algorithm is applied to optimize the number and deployment of ground stations for tracking LEO constellations. According to the distribution area, two schemes of study are analyzed: (a) global deployment—the ground stations are deployed throughout the globe; (b) regional deployment—a selected region is used for deployment. For global deployment, the optimization objectives are focused on the ground station and observing rate for k-heavy observing coverage (HC), while the sole objective for the regional deployment scheme is the satellite position dilution of precision (SPDOP). It is shown that a deployment of 95 ground stations is optimal for achieving 3-HC with an observing rate of 97.37% and 4-HC with an observing rate of 92.01%. For regional distribution, 15, 20 and 25 ground stations are used for three optimal configurations of SPDOP at 2.058, 1.399 and 1.330, respectively. The results are significantly enhanced using intersatellite links for SPDOP evaluation, from 2.058, 1.399 and 1.330 to 0.439, 0.422 and 0.409, with 15, 20 and 25 ground stations, respectively.

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.

Algorithm for Topology Search Using Dilution of Precision Criterion in Ultra-Dense Network Positioning Service Area

User equipment (UE) location estimation in emerging 5G/B5G/6G Ultra-Dense Networks (UDNs) is a breakthrough technology in future wireless info-communication ecosystems. Apart from communication aspects, network infrastructure densification promises significant improvement in UE positioning accuracy. Unlike networks of previous generations, an increased number of gNodeBs (gNBs) per unit area and/or volume in UDNs allows to perform measurements for UE positioning only with those base stations whose topologies are most suitable from the geometric point of view. Quantitative measurements of gNB topology suitability include horizontal (HDOP), vertical (VDOP), and position (PDOP) dilution of the precision (DOP) criteria on the plane, in height, and in space, respectively. In the current work, we formalize a set of methods for gNB topology search using time of arrival (TOA), time difference of arrival (TDOA), angle of arrival (AOA), and combined TOA–AOA and TDOA-AOA measurements. The background of the topology search using DOP criteria is a significantly increased number of gNBs per unit volume in UDNs. Based on a simulation, we propose a novel approach for a topology search in a positioning service area, resulting in a PDOP less than one for the Gazprom Arena with only five gNBs. The contribution of the current research includes algorithm and software for an iterative search of all possible gNB and UE locations in space, minimizing UE geometric DOP. The practical application of the algorithm is the gNB topology substantiation for the given positioning scenarios in 5G/B5G/6G UDNs.

Instantaneous velocity determination and positioning using Doppler shift from a LEO constellation

To provide backup and supplementation for the Global Navigation Satellite System (GNSS), Doppler shift from Low Earth Orbit (LEO) satellites can be used as signals of opportunity to provide positioning, navigation, and timing service. In this contribution, we first investigate the model and performance of instantaneous velocity determination and positioning with LEO satellites. Given a LEO constellation with 288 satellites, we simulate Doppler shift observations at nine multi-GNSS experiment stations. Owing to the lower orbit, the performance of LEO velocity determination is much more sensitive to the initial receiver position error than that of GNSS. Statistical results show that with the initial receiver position error increased from 0.1 to 10 m, the Root Mean Square Errors (RMSEs) increase from 0.73 to 2.65 cm/s, 0.68 to 2.96 cm/s, and 1.67 to 4.15 cm/s in the east, north, and up directions, respectively. The performances with GPS are compared with GPS + LEO, and it is found that LEO Doppler shift observations contribute to GPS velocity determination. As for LEO Doppler positioning, even if more than 30 visible LEO satellites are available, the position dilution of precision values can reach several hundreds. Assuming that the error of LEO Doppler measurements is 0.01 m/s, the instantaneous Doppler positioning accuracy can achieve about a few meters, which is comparable to that of GNSS pseudorange positioning. A constant velocity model is adopted for state transition. Static LEO Doppler positioning results show that an accuracy at centimeter to decimeter level can be achieved after solution convergence. For a static simulated kinematic positioning test, the RMSEs range from a few decimeters to several meters in different regions by giving different constraints. For a dynamic positioning test, the RMSEs are about 2–3 m in high latitude region.

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.

UWB Anchor Node Optimization Deployment Using MGWO for the Coal Mine Working Face End

Appropriate deployment of anchor nodes (ANs) is an essential prerequisite for achieving high-precision positioning. To ameliorate the comprehensive positioning performance, the weight position dilution of precision (WPDOP), that is utilized to evaluate the appropriateness of the ANs placement geometry is proposed by taking into account the different error variances for each AN. A simple closed-form calculation WPDOP method is theoretically derived for UWB positioning system by utilizing elementary symmetric polynomials and Newton’s identity, which is applied to evaluate the Ultra-wideband (UWB) deployment at the end of coal mine working face (CMWF). Several basic ANs layout strategies, based on the projection shape in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x-y</i> plane, are designed for the end of CMWF, and the modified grey wolf optimizer (MGWO) algorithm is executed to optimize the ANs deployment scheme in order to attain the better configuration and higher positioning accuracy. Simulation and experiments verification are simultaneously performed via the UWB positioning system. The experimental results sufficiently demonstrate that MGWO deployment scheme offers lower average WPDOP values than the obtained ones when applying random placement, and the lowest average improvement percentage was approximately equal to 37.6%. Furthermore, after implementing the MGWO algorithm, the V-shape deployment configuration is capable to provide the lowest average WPDOP values and outperforms the other arrangements, keeping the lowest localization error. This is regarded as the best deployment and it gives significant guidance for the ANs sensor deployment at the end of CMWF.

GPS CONTINUOUSLY OPERATING REFERENCE STATION (CORS) SELECTION TOWARDS REGIONAL GPS ORBIT DETERMINATION: A SIMULATED STUDY USING TRILATERATION TECHNIQUE

Global Positioning System (GPS) orbital error can be minimized using precise satellite orbit. These precise satellite orbits are calculated using GPS measurements from ground CORS. The distribution of the CORS involved in GPS satellite orbit determination is important, especially in the case of regional GPS orbit determination. A regional GPS orbit is an orbital product generated using locally distributed CORS network and is expected to improve the GPS measurement in the region. Satellite Position Dilution of Precision (SPDOP) is proposed as an indicator to measure the geometry of the CORS with respect to the GPS satellite. GPS measurements are simulated by calculating the range from GPS satellites to the CORS. The simulated measurement is then used to calculate the position of GPS satellite using trilateration algorithm. Results shows the SPDOP has a linear relationship with orbit determination accuracy. This study shows that SPDOP can be used as an indicator for a better CORS selection in GPS orbit determination.

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.