Search Results (19)

In the zenith-horizon placement for achieving minimum geometric dilution of precision (GDOP), one access node or sensor is positioned along the z-axis, while the remaining nodes are placed symmetrically on a three-dimensional (3D) cone. This configuration yields the minimum GDOP at the cone’s tip, which we term the designated min-GDOP point. However, in practical localization applications, the unknown node is not necessarily located at this designated min-GDOP point; instead, it may be situated anywhere within an area. As a result, evaluating localization accuracy across the entire area, rather than at a single point, is more relevant. Averaged horizontal dilution of precision (HDOP) and GDOP across the region provide more meaningful metrics for system-wide performance than values computed only at a specific location. Although many recent positioning applications leverage multiple unmanned aerial vehicles (UAVs), many established fixed sensor deployments predate the widespread adoption of UAVs. This paper proposes a novel approach with a single UAV working in conjunction with existing fixed access nodes for positioning. This approach offers improved adaptability for fixed infrastructure while circumventing the expense of establishing entirely new UAV systems, thus providing a valuable compromise. We investigate the criteria of average HDOP and GDOP over the given area. The objective is to determine optimal UAV positions along the flight path that minimize the average HDOP and/or GDOP across the area. Due to the analytical complexity, we employ numerical methods. Our simulation results demonstrate that minimizing average HDOP and GDOP often requires different UAV positions, depending on the number of access nodes and the size of the area. Consequently, achieving simultaneous minimization of both metrics with a single UAV trajectory is generally infeasible. When minimizing the average HDOP with a small number of access nodes, aligning the UAV’s XY-plane angle with those of the stationary nodes, offset by ${60}^{\circ }$, proves advantageous. This angular alignment becomes less critical as the number of access nodes increases. For scenarios where both HDOP and GDOP are important, UAV placement can be optimized by selecting appropriate trade-offs. Additionally, we quantify how increasing the number of access nodes improves the average HDOP and GDOP over the specified area. Full article

Horizontal dilution of precision (HDOP) is a widely used quality indicator of Global Navigation Satellite System (GNSS) positioning, considering only satellite geometry. In this study, HDOP was simulated using GNSS almanacs and high-resolution digital surface models (DSMs) along three European road sections: Oslo— Svinesund Bridge (Norway); Hamburg city center (Germany); and Rotterdam—Dutch–German border (Netherlands). This study was accomplished as part of the MODI project, which is a cross-border initiative to accelerate Cooperative, Connected, and Automated Mobility (CCAM). Our analysis revealed excellent or good overall GNSS performance in the study areas, particularly on highway sections with 99–100% of study points having a median HDOP that is categorized as excellent (HDOP < 2) or good (HDOP < 5). However, the road section in Hamburg’s city center presents challenges. When GPS is used alone, 8% of the study points experience weak or poor HDOP, and there are study points where the system is available (HDOP < 5) less than 50% of the time. Combining GNSS constellations significantly improved system availability, reaching 95% for 99% of the study points in Hamburg. To validate our simulations, we compared results with GNSS observations from a survey vehicle in Hamburg. Initial low correlation was attributed to the reception of signals from non-line-of-sight satellites. By excluding satellites with low signal-to-noise ratios, the correlation increased significantly, and reasonable agreement was obtained. We also examined the impact of using a 10 m DSM instead of a 1 m DSM in Hamburg. While the coarser spatial resolution offers computational benefits, it may miss critical details for accurate assessment of satellite visibility. Full article

The ultra-wideband (UWB) base station (BS) deployment pattern seriously affects mobile tag positioning accuracy, but the traditional classical deployment methods, such as rectangular and diamond deployment, cannot take into account the influence of non-line-of-sight (NLOS) occlusion, which leads to a blind area in positioning. In this paper, we propose a new UWB BS deployment optimization method that takes into account the influence of NLOS occlusion, determines the BS deployment range and occlusion by indoor map information, uses the locatable points coverage rate in the whole indoor positioning area as the fitness function, and proposes an improved particle swarm optimization algorithm based on the Levy flight strategy (LPSO) to solve the optimization problem. The simulation experiment results show that the locatable space coverage rate of rectangular and diamond deployment models gradually decreases and the blind positioning area gradually increases with the increase in NLOS occlusion. The locatable space coverage rate of the LPSO-optimized deployment is better than that of the standard PSO-optimized deployment model, while it is 19.0% and 22.6% better than the rectangular deployment and 3.0% and 6.5% better than the diamond deployment when the NLOS values are 3 and 5 for complex occlusion environments, respectively. The experimental results of the underground garage demonstrate that the optimal 13 BS layout scheme, obtained through LPSO, outperforms the 7 BS layout scheme by 34.9% while reducing the horizontal dilution of precision (HDOP) values by 81.7%. Therefore, the proposed UWB BS layout optimization scheme exhibits superior adaptability to large and complex indoor environments, effectively enhances signal coverage and positioning accuracy, and holds significant practical value. Full article

In indoor positioning scenarios, the deployment of base stations plays a crucial role in the accuracy of positioning information. In recent years, how to reasonably deploy base stations to reduce HDOP (horizontal dilution of precision) has become a hot topic in the field of indoor positioning research. Currently, most research focuses only on HDOP in a specific indoor scenario and is often limited to simulation experiments, leaving room for further investigation. This paper conducts research on HDOP in multiple scenarios based on measured data. Firstly, the theoretical minimum value of HDOP is calculated for different numbers of base stations. Then, the relationship among the number of base stations, deployment methods, and HDOP is studied. Finally, an experimental platform is set up to analyze the relationship between HDOP and positioning errors based on measured data. The experimental results are as follows: (1) in simulated experiments in circular scenarios, the optimal deployment method entails evenly distributing the base stations around the circumference, with the deployment of an additional base station possibly reducing the average HDOP by about 10%, (2) in rectangular scenarios, the optimal deployment method entails evenly deploying the base stations along the two long sides. Measured data show that positioning errors are roughly proportional to the HDOP, but there are exceptions, and the reasons are analyzed. This research provides reference and support for the deployment of base stations in multi-scene indoor positioning systems. Full article

The centimetre-level accuracy of Ultra-wideband (UWB) has attracted significant attention in indoor positioning. However, the precision of UWB positioning is severely compromised by non-line-of-sight (NLOS) conditions that arise from complex indoor environments. On the other hand, odometry is widely applicable to wheeled robots due to its reliable short-term accuracy and high sampling frequency, but it suffers from long-term drift. This paper proposes a tightly coupled fusion method with a Dynamic Unscented Kalman Filter (DUKF), which utilises odometry to identify and mitigate NLOS effects on UWB measurements. Horizontal Dilution of Precision (HDOP) was introduced to assess the impact of geometric distribution between robots and UWB anchors on UWB positioning accuracy. By dynamically adjusting UKF parameters based on NLOS condition, HDOP values, and robot motion status, the proposed method achieves excellent UWB positioning results in a severe NLOS environment, which enables UWB positioning even when only one line-of-sight (LOS) UWB anchor is available. Experimental results under severe NLOS conditions demonstrate that the proposed system achieves a Root Mean Square Error (RMSE) of approximately 7.5 cm. Full article

Seafloor geodetic network (SGN) is the foundation for building an underwater positioning, navigation and timing (PNT) system. Traditional network deployment mainly focuses on the deployment of underwater sensor network nodes. However, for SGN, there is no surface buoy node and submarine buoy node, and the number of anchors is limited because it is quite expensive to fully cover large scale areas. To achieve wide coverage and good positioning service of each set of underwater base stations, we focus on the network design of a single set of reference stations in this paper. We propose several deployment plans for a local SGN and then analyze their service quality indicators by considering the stratification effect caused by non-uniformly distributed sound speed. To evaluate the performance of each topology of SGN, we compare their coverage range, horizontal dilution precision (HDOP) and accuracy performance of positioning tests. Based on the overall performance in our simulation, we believe that the star five-node topology is a good topology design under sufficient economic conditions. Full article

This paper addresses cooperative navigation using range radios to enable absolute positioning of low-flying UAS (LF) while operating in GNSS-denied environments. High-flying UAS (HF) are positioned above the denied area and broadcast position reports. These reports, in combination with range measurements from the LF to the HF, enable absolute positioning of the LF. (1) Methods: As the navigation performance is directly influenced by the geometry of both LF and HF’s relative positions, HF positions shall be optimized such that the Dilution of Precision (DOP) becomes minimal. The authors derive optimal azimuth angle combinations, which guarantee a minimal Horizontal Dilution of Precision (HDOP), and show the error characteristic for sub-optimal configurations, which enables the formulation of multi-vehicle-constrained optimization problems for specific combinations of numbers of HF and LF. (2) Results: An optimization problem is derived and solved for two HF aiding three LF as an example application for the derived rules. (3) Conclusions: The resulting geometry has yielded promising HDOP values, improving navigation performance in GNSS-denied environments. Full article

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. Full article

This study evaluated the positioning accuracy of moving forest harvesters using global navigation satellite system (GNSS) signals under a forest canopy, and developed approaches for forecasting accuracy under a mature spruce canopy cover. Real-time kinematic positioning with a Trimble R12 receiver on top of a harvester achieved high positioning accuracy, with 86% of observations meeting a maximum precision of 8 mm. However, the presence of a canopy cover hampered the GNSS’s performance as there were fewer satellites available, leading to an increased number of inaccurate positions and larger values of the dilution of precision in geometry (GDOP), position (PDOP), vertical (VDOP) and horizontal directions (HDOP). The canopy cover estimated from the viewshed analysis of the digital surface model (DSM) was found to be a significant predictor of the dilution of precision and maximum deviation from the true position. These findings suggest that viewshed analysis provides more precise results than a mere canopy cover percentage for evaluating the impact of canopy cover on the GNSS’s positioning of a harvester, despite its computational demands. Developing intelligent algorithms for precise positioning under the canopy can facilitate autonomous harvesting and forwarding, allowing for the implementation of digitalization in forest operations. Full article

The Differential Global Positioning System (DGPS) is a marine navigation system operating at frequencies of 283.5–325 kHz, which is now the primary method for locating vessels in coastal shipping, as well as hydrography and mapping systems worldwide. Its positioning accuracy is determined by the following: the pseudorange error to Global Positioning System (GPS) satellites, the age of pseudorange corrections, and the value of the Horizontal Dilution of Precision (HDOP), which, in terms of accuracy, is crucial in positioning using GPS satellites. In 2020, the International Hydrographic Organization (IHO) introduced a new (the highest) order of hydrographic surveys, i.e., the Exclusive Order, which requires a positioning system to provide an accuracy of 1 m (p = 0.95). The aim of this article is to provide an answer to the question as to whether the maritime DGPS system, whose positioning accuracy is constantly increasing with that of the GPS system, fulfils the requirements for the hydrographic surveys of harbours. To this end, an extensive experimental study on the maritime DGPS system, involving a total of nearly 3.5 million fixes, was conducted. Statistical analyses showed that when ensuring the HDOP values range from 0.8 to 1.4, the DGPS system can be used in hydrographic surveys of harbours. Full article

Satellite positioning lies within the very core of numerous Intelligent Transportation Systems (ITS) and Future Internet applications. With the emergence of connected vehicles, the performance requirements of Global Navigation Satellite Systems (GNSS) are constantly pushed to their limits. To this end, Cooperative Positioning (CP) solutions have attracted attention in order to enhance the accuracy and reliability of low-cost GNSS receivers, especially in complex propagation environments. In this paper, the problem of efficient and robust CP employing low-cost GNSS receivers is investigated over critical ITS scenarios. By adopting a Cooperative-Differential GNSS (C-DGNSS) framework, the target’s vehicle receiver can obtain Position–Velocity–Time (PVT) corrections from a neighboring vehicle and update its own position in real-time. A ranking module based on multi-attribute decision-making (MADM) algorithms is proposed for the neighboring vehicle rating and optimal selection. The considered MADM techniques are simulated with various weightings, normalization techniques, and criteria associated with positioning accuracy and reliability. The obtained criteria values are experimental GNSS measurements from several low-cost receivers. A comparative and sensitivity analysis are provided by evaluating the MADM algorithms in terms of ranking performance and robustness. The positioning data time series and the numerical results are then presented, and comments are made. Scoring-based and distance-based MADM methods perform better, while L1 RMS, HDOP, and Hz std are the most critical criteria. The multi-purpose applicability of the proposed scheme, not only for land vehicles, is also discussed. Full article

Increasing the number of satellites in a global navigation satellite system (GNSS) improves the positioning accuracy and increases availability. However, it reduces the positioning accuracy improvement rate and increases the calculation loads, which can cause battery usage problems in mobile devices using a GNSS. An appropriate satellite selection method is required. One current method entails the use of ideal satellite placement with respect to the minimum geometric dilution of precision (GDOP). In this study, the described ideal satellite placement with the minimum GDOP were divided in terms of the horizontal dilution of precision (HDOP) and vertical dilution of precision (VDOP). HDOP and VDOP were mathematically derived and analyzed. The derived formula was verified using simulations. The analysis was performed with actual dual GNSS satellite data. The satellites adjacent to the ideal placement were selected and the DOP was calculated. Simply selecting satellites closest to the ideal placement afforded large values for HDOP and VDOP. This issue was addressed using a satellite changing algorithm considering the dual GNSS, resulting in reduced values of the HDOP and VDOP. Full article

Positioning accuracy is affected by the combined effect of user range errors and the geometric distribution of satellites. Dilution of precision (DOP) is defined as the geometric strength of visible satellites. DOP is calculated based on the satellite broadcast or precise ephemerides. However, because the modernization program of next-generation navigation satellite systems is still under construction, there is a lack of real ephemerides to assess the performance of next-generation constellations. Without requiring real ephemerides, we describe a method to estimate satellite visibility and DOP. The improvement of four next-generation Global Navigation Satellite Systems (four-GNSS-NG), compared to the navigation constellations that are currently in operation (four-GNSS), is statistically analyzed. The augmentation of the full constellation the Quasi-Zenith Satellite System (7-QZSS) and the Navigation with Indian Constellation (11-NavIC) for regional users and the low Earth orbit (LEO) constellation enhancing four-GNSS performance are also analyzed based on this method. The results indicate that the average number visible satellites of the four-GNSS-NG will reach 44.86, and the average geometry DOP (GDOP) will be 1.19, which is an improvement of 17.3% and 7.8%, respectively. With the augmentation of the 120-satellite mixed-orbit LEO constellation, the multi-GNSS visible satellites will increase by 5 to 8 at all latitudes, while the GDOP will be reduced by 6.2% on average. Adding 7-QZSS and 11-NavIC to the four-GNSS-NG, 37.51 to 71.58 satellites are available on global scales. The average position DOP (PDOP), horizontal DOP (HDOP), vertical DOP (VDOP), and time DOP (TDOP) are reduced to 0.82, 0.46, 0.67 and 0.44, respectively. Full article

The positioning accuracy of a ground-based system in an indoor environment is closely related to the geometric configuration of pseudolites. This paper presents a simple closed-form equation for computing the weighted horizontal dilution of precision (WHDOP) with four eigenvalues, which can reduce the amount of calculation. By comparing the result of WHDOP with traditional matrix inversion operation, the effectiveness of WHDOP of the proposed simple calculation method is analyzed. The proposed WHDOP has a linear relationship with the actual static positioning result error in an indoor environment proved by the Pearson analysis method. Twenty positioning points are randomly selected, and the positioning variance and WHDOP of each positioning point have been calculated. The correlation coefficient of WHDOP and the positioning variance is calculated to be 0.82. A pseudolite system layout method based on a simulated annealing algorithm is proposed by using WHDOP, instead of Geometric dilution of precision (GDOP). In this paper, the constraints of time synchronization are discussed. In wireless connection system, the distance between master station and slave station should be kept within a certain range. Specifically, for a given indoor scene, many positioning target points are randomly generated in this area by using the Monte Carlo method. The mean WHDOP value of all positioning points corresponding to the synchronous pseudolite layout is used as the objective function. The results of brute force search are compared with the method, which proves the accuracy of the new algorithm. Full article

Pseudolite deployment is the premise of ground-based pseudolite system networking, which affects the coverage and positioning accuracy of ground-based pseudolite systems. Optimal deployment algorithms can help to achieve a higher signal coverage and lower mean horizontal precision factor (HDOP) with a limited number of pseudolites. In this paper, we proposed a multi-objective particle swarm optimization (MOPSO) algorithm for the deployment of a ground-based pseudolite system. The new algorithm combines Digital Elevation Model (DEM) data and uses the mean HDOP of the DEM grid to measure the geometry of the pseudolite system. The signal coverage of the pseudolite system was calculated based on the visual area analysis with respect to reference planes, which effectively avoids the repeated calculation of the intersection and improves the calculation efficiency. A selected area covering 10 km×10 km in the Jiuzhaigou area of China was used to verify the new algorithm. The results showed that both the coverage and HDOP achieved were optimal using the new algorithm, where the coverage area can be up to approximately 50% and 30% more than using the existing particle swarm optimization (PSO) and convex polyhedron volume optimization (CPVO) algorithms, respectively. Full article