Vertical Dilution Of Precision Research Articles

Analysis of a HAPS-Aided GNSS in Urban Areas Using a RAIM Algorithm

The global averaged civilian positioning accuracy is still at meter level for all existing Global Navigation Satellite Systems (GNSSs), and the performance is even worse in urban areas. At lower altitudes than satellites, high altitude platform stations (HAPS) offer several benefits, such as lower latency, less pathloss, and likely smaller overall estimation error for the parameters associated in the pseudorange equation. HAPS can support GNSSs in many ways, and in this paper we treat the HAPS as another type of ranging source. In so doing, we examine the positioning performance of a HAPS-aided GPS system in an urban area using both a simulation and physical experiment. The HAPS measurements are unavailable today; therefore, they are modeled in a rather simple but logical manner in both the simulation and physical experiment. We show that the HAPS can improve the horizontal dilution of precision (HDOP), the vertical dilution of precision (VDOP), and the 3D positioning accuracy of GPS in both suburban and dense urban areas. We also demonstrate the applicability of a RAIM algorithm for the HAPS-aided GPS system, especially in the dense urban area.

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.

HDOP and VDOP Analysis in an Ideal Placement Environment for Dual GNSSs.

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.

Altimeter + INS/Giant LEO Constellation Dual-Satellite Integrated Navigation and Positioning Algorithm Based on Similar Ellipsoid Model and UKF

To solve the problem of location service interruption that is easily caused by incomplete visual satellite environments such as occlusion, urban blocks and mountains, we propose an altimeter + inertial navigation system (INS) + giant low earth orbit (LEO) dual-satellite (LEO2) switching integrated navigation algorithm based on a similar ellipsoid model and unscented Kalman filter (UKF). In addition to effectively improving the INS error, for the INS + LEO dual-satellite switching algorithm without altimeter assistance, our algorithm can also significantly suppress the problem of excessive navigation and positioning error caused by this algorithm in a long switching time, it does not require frequent switching of LEO satellites, and can ensure navigation and positioning functions without affecting LEO satellite communication services. In addition, the vertical dilution of precision (VDOP) value can be improved through the clock error elimination scheme, so, the vertical accuracy can be improved to a certain extent. For different altimeter deviations, we provide simulation experiments under different altimeter deviations; it can be found that after deducting the fixed height deviation, the algorithm can also achieve good accuracy. Compared with other typical algorithms, our proposed algorithm has higher accuracy, lower cost and stronger real-time performance, and is suitable for navigation and positioning scenarios in harsh environments.

Satellite Availability and Service Performance Evaluation for Next-Generation GNSS, RNSS and LEO Augmentation Constellation

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.

Extended Geometry and Probability Model for GNSS+ Constellation Performance Evaluation

We proposed an extended geometry and probability model (EGAPM) to analyze the performance of various kinds of (Global Navigation Satellite System) GNSS+ constellation design scenarios in terms of satellite visibility and dilution of precision (DOP) et al. on global and regional scales. Different from conventional methods, requiring real or simulated satellite ephemerides, this new model only uses some basic parameters of one satellite constellation. Verified by the reference values derived from precise satellite ephemerides, the accuracy of visible satellite visibility estimation using EGAPM gets an accuracy better than 0.11 on average. Applying the EGAPM to evaluate the geometry distribution quality of the hybrid GNSS+ constellation, where highly eccentric orbits (HEO), quasi-zenith orbit (QZO), inclined geosynchronous orbit (IGSO), geostationary earth orbit (GEO), medium earth orbit (MEO), and also low earth orbit (LEO) satellites included, we analyze the overall performance quantities of different constellation configurations. Results show that QZO satellites perform slightly better in the Northern Hemisphere than IGSO satellites. HEO satellites can significantly improve constellation geometry distribution quality in the high latitude regions. With 5 HEO satellites included in the third-generation BeiDou navigation satellite system (BDS-3), the average VDOP (vertical DOP) of the 30° N–90° N region can be decreased by 16.65%, meanwhile satellite visibility can be increased by 38.76%. What is more, the inclusion of the polar LEO constellation can significantly improve GNSS service performance. When including with 288 LEO satellites, the overall DOPs (GDOP (geometric DOP), HDOP (horizontal DOP), PDOP (position DOP), TDOP (time DOP), and VDOP) are decreased by about 40%, and the satellite visibility can be increased by 183.99% relative to the Global Positioning System (GPS) constellation.

Dilution of Precision in Three Dimensional Angle-of-Arrival Positioning Systems

Dilution of precision (DOP) for time-of-arrival (TOA) or time-difference-of-arrival (TDOA) positioning systems has been thoroughly investigated. This is not the case for angle-of-arrival (AOA) positioning systems, especially three dimensional AOA systems. However, the recent increase in deployment of antenna arrays and multipath mitigation techniques make AOA systems more attractive. In this paper, the DOPs for position systems using range measurements are reviewed and an expression for 3D AOA DOP is derived. The average values of DOPs for different deployments of base station geometries are examined. It is found that for a 3D AOA system, unlike TOA or TDOA systems, vertical DOP (VDOP) is generally smaller than horizontal DOP (HDOP), and the best VDOP can be achieved when the base stations are at the same height as the user. Moving the base stations away from the plane of the user may decrease the HDOP and Geometric DOP (GDOP) slightly, but it also increases the VDOP. For applications that the height of the user changes frequently, the base stations should be deployed with height close to half the height of the area of interest.

Optimal Sensor Placement for Dilution of Precision Minimization Via Quadratically Constrained Fractional Programming

An approach to find the global optimal solution of the dilution of precision (DOP) problem is presented. The DOP optimization problem considered assumes an environment comprising multiple randomly predeployed sensors (or navigation sources) and an additional sensor is to be introduced at the location that minimizes variations of the DOP problem (e.g., weighted geometric DOP, horizontal DOP, vertical DOP, etc.). It is shown that the DOP problem can be formulated as a quadratically constrained fractional quadratic program. An algorithm for solving this program is presented and Monte Carlo simulation results are given demonstrating convergence of the proposed approach to the global optimal solution. Additionally, Monte Carlo simulation results are presented, demonstrating the efficacy of the proposed algorithm to solving the DOP minimization problem versus using nonlinear numerical optimization solvers, which often converge to local optima. Also, the superiority of the proposed approach is demonstrated against other approaches that approximate the DOP minimization problem.

Outdoor Localisation for Navigation Tracking using Differential Global Positioning System Estimation (DGPS) : Positioning Errors Analysis


 
 
 
 Global Positioning System (GPS) is a very popular outdoor positioning system. Due to the satellites’ errors signal, the Global Positioning System (GPS) receivers determine the accuracy of a current location with about 100 meters in latitude and 156 meters in longitude. In this few years, the technology on autonomous vehicles is rising. Autonomous vehicles need to navigate with high positioning accuracy for preventing any potential danger to road user. So in this paper, Differential Global Positioning System (DGPS) experiment will be introduced for improve the positioning accuracy. Differential Global Positioning System (DGPS) operations compose of Reference Station and Rover Station. Both of the station will use the GPS receiver for receiving the positioning data from GPS satellites and the positioning data collected from Reference Station will be used to calculate the positioning errors and the errors correction will then be transferred to Rover Station to improve the positioning accuracy. The results obtained will be discussed based on the average and range of errors in both latitude and longitude, number of satellites detected, Horizontal Dilution of Precision (HDOP), Vertical Dilution of Precision (VDOP) and the improvement on Differential Global Positioning System (DGPS) at the same time in different day. In four days’ results, it can be seen that the number of satellites detected will be affected by the Horizontal Dilution of Precision (HDOP) and Vertical Dilution of Precision (VDOP) which cause the positioning errors in latitude and longtitude. The average of positioning errors range between -4.165m and 2.925m in latitude and -0.618m and 1.998m in longitude.
 
 
 

Autonomous “Figure-8” Flights of a Quadcopter: Experimental Datasets

This article describes the data acquired from multiple flights of a custom-built quadcopter. The Quadcopter was programmed to fly a pre-defined “Figure-8” flight path, at a constant altitude. The data set includes flights with a varying number of waypoints (10 and 15 waypoints in each lobe of the “Figure-8”) and at two different velocities (1.5 and 2.5 m/s). The data also contains information on the output of the flight controller in terms of the Pulse Width Modulation (PWM) signals to each of the four Electronic Speed Controllers (ESC) driving the motors, the recorded outputs of the Inertial Measurement Unit (linear accelerations ax, ay, az and angular velocities p, q, r), GPS data (Latitude, Longitude, altitude, Horizontal Dilution of Precision (HDOP) and Vertical Dilution of Precision (VDOP). The data are included as Supplemental Material.

Base-Station Random Placement Effect on the Accuracy of Ultrawideband Body-Centric Localization Applications

This letter presents an investigation on the effect of random placement of base stations on three-dimensional body-centric localization in the ultrawideband frequency range. Different base station configurations are studied (varied in xyz -axis, xy -axis, and z -axis direction), keeping the same range estimation error values as obtained from the body-centric localization experimental data in order to keep the main focus on the influence of the base-station configurations. It is observed that random positions of the base stations in the z- axis lead to higher localization error (3–8 cm) as the target nodes are spread out more in the z -axis direction. The localization error is analyzed in terms of geometric, horizontal, vertical dilution of precision (DOP), which is a measure of effectiveness of the placement of the base stations. For the DOP values (5–15), 1–3 cm error reduction is observed, and for higher DOP (>20) values, the error increases by 3–5 cm for short-range communication. Further analysis is carried out by varying the range estimation error in terms of mean value and standard deviation for evaluating the random base-station configurations, which also plays an important role in the accuracy of estimating the location of the target.

Analysis of Wide Area Multilateration Localization Accuracy Under Different Stations Layout ond Aircraft Height

Layout of stations and height of aircraft are very important to localization accuracy of wide area multilateration (WAM) system, and the error produced by layout of stations and height of aircraft may influence WAM system’s localization accuracy. To find the approach to reduce the error, this paper firstly calculates relationship between localization accuracy and height error according to hyperbolic algorithm and least square method, and obtains the change law of horizontal dilution of precision (HDOP) and vertical dilution of precision (VDOP) with height. Secondly, the system localization precision of levels of the same height and levels of different aircraft heights after giving consideration to the various circumstances of wide area stations layout are simulated and analyzed. Thirdly, the impact of different station layouts and baseline length of the levels of the same height on localization precision are discussed. Simulation and discussion results show that the aircraft height has a large impact on the WAM system’s localization precision. In particular, the vertical localization precision reduces obviously when the height is low. When the height is unchanged, a proper station layout and baseline length can improve the system’s localization precision.

Research on Geometric Layout of Pseudo-Satellite in the Small Airport

Because complex terrain conditions, the small airport satellite navigation signal being blocked, while reducing the positioning accuracy of the approach and landing segment, but also increase the operating costs of the small airport. This paper through independent pseudo-satellite network, from PDOP (Position Dilution of Precision) and VDOP (Vertical Dilution of Precision) studied several layout of airport pseudo-satellites. Through simulation show that the geometric layout of the pseudo-satellite can improve positioning accuracy of approach and landing segment in the small airport and reduce the DOPs, ​​provide reference for practical engineering applications.

Testing of GPS Accuracy for Precision Forestry Applications

The use of existing geospatial technologies such as GIS and global positioning systems (GPS) to precision forestry is booming. The objective of this study was to examine the applicability of GPS and radio beacon differential global positioning system (RBN DGPS) for forestry machinery positioning. This would be an important step toward the realization of site-specific chemical application in China. A Trimble AG132 GPS receiver was mounted on a moveable platform and real-time differential GPS signals were obtained from the Yangtze River Beacon Station. The experiments were conducted on campus of Nanjing Forestry University, China. GPS data were collected and downloaded into a laptop computer via a RS-232 serial port and customer-developed data-acquisition software. Two tests were conducted: (1) a stationary test (where the mobile platform was maintained at a fixed location) in an open sky and forest condition to examine the precision (repeatability) of GPS signals, and (2) a mobile test (where the platform was moving) to examine the dynamic conformity degree. Analysis of variance was used to clarify the effects of positioning mode and stand area on the precision of GPS. In the stationary test, the variability of X and Y coordinates is smaller in RBN DGPS mode than that in the non-differential mode; and the performance of GPS in terms of position dilution of precision, horizontal dilution of precision, vertical dilution of precision, time dilution of precision values, effective positioning rate and the number of visible satellites was superior when used in RBN DGPS mode. In the mobile test, the desired traces of the moveable platform (circles) were much better followed by the GPS locations recorded in the RBN DGPS mode. Compared with non-differential mode, RBN DGPS is more suitable for precision forestry positioning requirements. RBN DGPS improves accuracy both in open sky and forest condition, and the service is available to end users in China with no additional costs.

Non-Gaussian Error Modeling for GBAS Integrity Assessment

Four basic error sources exist for residual pseudo-range errors in a single frequency differential GPS system for ground based augmentation (GBAS): signal multipath, increased receiver noise (carrier-to-noise density ratios ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> )) due to interference, residual differential troposphere error, and the error induced by ionosphere gradients. Without restricting ourselves to classical Gaussian overbounding, we combine their probability density functions (pdfs) to a total pseudo-range error distribution. This distribution is propagated through the GBAS Hatch filter and then mapped into the position domain using a worst case (selected by maximum vertical dilution of precision (VDOP)) of a full 31 satellite constellation with the two most critical satellites failed observed at Braunschweig Airport, Germany. Our calculations yield a significant reduction amounting to 46% of the position domain error at the 1.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup> integrity risk level when compared with the classical Gaussian overbounding approach.

Analysis of a clock-aided global navigation satellite system (GNSS)

This paper presents a dilution of precision (DOP) analysis of a clock-aided global navigation satellite system (GNSS). Firstly, the analysis shows that a best linear unbiased estimator should be used in the clock-aided GNSS to get the best improvements in accuracy. Secondly, the influence of the clock on vertical DOP (VDOP) and horizontal DOP (HDOP) is analysed by using the clock characteristics as a weighting matrix. The analysis highlights quantitative improvements in the VDOP and HDOP and explains why improvements in the VDOP are superior to those of the HDOP in the clock-aided GNSS. Finally, the paper analyses how incorrectly known a priori clock variances degrade the level of accuracy and offers guidelines for determining a weighting matrix in the cases where the clock characteristics are not clearly known.

The use of immersive real-time 3D computer graphics for visualisation of dilution of precision in virtual environments

Dilution of precision (DOP) is a fundamental concept in satellite navigation and surveying. A deeper understanding of this concept can be achieved through the means of 3D immersive visualisation. In this article, we present a method for visualising and exploring the spatial variation of DOP and discuss its presentation within an immersive virtual environment. The work demonstrates a real-time simulation of global positioning system (GPS) satellite geometry, modelled and visualised within a virtual representation of the university campus. The number of satellites visible to the receiver is modelled in real time as a user walks through the university campus. During this process, the changing satellite geometry is visualised in both 3D and aerial views. Various DOP values update to the screen against a pseudo-realistic building backdrop as the user travels. Both the aerial views and the changing volumes of the tetrahedra drawn in 3D provide an effective way of interpreting why exceptionally large or small horizontal DOP and vertical DOP values can occur in an urban context. Because the factors affecting DOPs are inherently 3D, communicating the spatial uncertainty of global positioning system coordinates within an immersive stereo environment has been viewed as a particularly powerful communication tool by both undergraduate and postgraduate students studying GI Science.

Global Availability and Reliability Assessment of the GPS and Galileo Global Navigation Satellite Systems

The performance of a Global Navigation Satellite System can be quantified by availability, accuracy, and reliability. The deployment of Galileo by the European Union will provide double the number of navigation satellites currently available to users and offer improvements in accuracy and reliability. This paper briefly describes the design of the proposed Galileo system in comparison with the existing Global Positioning System (GPS). Availability and accuracy are then defined and statistical reliability theory is reviewed. Worldwide availability, accuracy, and reliability estimates for GPS, Galileo, and the combined GPS/Galileo system are obtained by software simulation. The simulation results are presented using Horizontal and Vertical Dilution of Precision as measures of availability and accuracy and maximum Horizontal Position Error due to one undetected blunder as a measure of reliability. The validity of these quantities as measures of accuracy and reliability is discussed and compared with other me...

Efficient DOP Calculation for GPS with and without Altimeter Aiding

Geometric Dilution Of Precision (GDOP) is a factor that describes the effect of geometry on the relationship between measurement error and position determination error. It is used to provide an indication of the quality of the solution. Conventional closed-form GDOP calculation formula applied to all possible combinations of visible satellites is rather time consuming, especially as the number of satellites grows. Approximations, such as the maximum volume method, are faster but optimum selection is not guaranteed. In this paper, a more concise but efficient solution for the calculation of GDOP value in the case of four Global Positioning System (GPS) satellites is firstly reviewed and then extended to cover the other forms of dilution of precision (DOP) values, including vertical DOP (VDOP) and horizontal DOP (HDOP). Secondly, a review and extension of the conventional solution is performed in the case of three GPS satellites aided by an altimeter. Based on the ideas gained from these two approaches, a simpler closed-form DOP formula for three GPS satellites aided by an altimeter is derived. The advantage of the proposed formulation is that it is simpler and thus reduces the computational load in comparison to the conventional one.