KNOWLEDGE-BASED METHODS FOR OPTIMUM APPROXIMATION OF GEOMETRIC DILUTION OF PRECISION

Geometric Dilution of Precision (GDOP) represents the magnification positioning error in satellite navigation, smaller GDOP represents high positioning accuracy. The analytic results of relevant methods to derive the minimum of GDOP by geocentric coordinate system cannot be achieved in reality, because it does not think fully about the satellite visibility constrains. This article employs the elevation angle to express the satellite visibility, and on basis of the local Cartesian coordinates coordinate system, the essay derives the minimum of GDOP with constraint of four satellites visible. Based on the information track of Beidou satellite navigation system, the minimum of GDOP is verified by using the STK simulation software.

Code phase GNSS receivers convert the measured satellite pseudoranges into estimates of the position and clock offset of the receiver, typically via an iterative, linearized least squares method. Since the pseudoranges themselves are noisy, the resulting estimates of position and time are random variables. To describe the accuracy of this solution, it is common to describe it statistically via the error covariance matrix. Rather than considering the individual elements of this covariance matrix, users frequently reduce it to a scalar performance indicator; the most common of these is the Geometric Dilution of Precision (GDOP). It is well known that the GDOP is a function of the satellite geometry; with only a few visible satellites in poor locations, the GDOP can become quite large. However, for a future with multiple, fully occupied GNSS constellations it is expected that receivers would select those satellites to track so as to achieve the best possible performance. Hence, an understanding of both how small the GDOP can be as a function of the number of satellites visible and the characteristics of the constellations that meet that bound are of value. Further, once identified, a receiver could exploit those constellation characteristics in selecting a subset of satellites. Investigating the best possible GNSS satellite constellation with respect to the GDOP is not a new problem. Recently, these authors developed achievable lower bounds to the GDOP as a function of the number of satellites; the bounds were also extended to non-zero mask angle and to multiple GNSS constellations. Further, using actual GPS satellite ephemeris data, it was shown by example that good GDOP performance resulted from constellations similar to the “best” constellations resulting from the bounds. This paper examines augmentation of the GNSS pseudoragnes with data from non-GNSS sensors; specifically, ranges. While integration of GNSS and non-GNSS sensors is not novel, the perspective in the paper is how such external sensors impact potential receiver performance (i.e. minimum GDOP) and what role they play in satellite selection. Specifically, tight lower bounds to GDOP when the GNSS is augmented by this additional measurement (barometric altimeter or a DME slant range) are presented; achievability of the bounds is also examined.

UWB (Ultra Wideband) TOF (Time of Flight) location system is a high accuracy real time indoor location system. It includes many anchors and positioning tags. GDOP (geometric dilution of precision) is an index that used to measures the accuracy of GPS (Global positioning system). In this paper we will study GDOP from the GPS and use GDOP into indoor location system. Researching whether GDOP is a big impact to the accuracy of UWB indoor location system. At the end of the paper, there are two-dimensional positioning GDOP simulation based on MATLAB and several groups of experimental data which calculated by hyperbolic positioning algorithm.

The traditional approach to both earthquake and Global Positioning System (GPS) location problems in a homogeneous half-space produces a nonlinear relationship between a set of known positions, seismic stations or GPS satellites, and an unknown point, an earthquake hypocenter or GPS receiver. Linearization, followed by an iterative inversion, is typically used to solve both problems. Although sources and receivers are swapped in the earthquake and GPS location problems, the obser- vation equation is the same for both, due to the principle of reciprocity. Consequently, the mechanical part of the solution of the equations is the same and single-step closed- form solutions for the GPS location problem, such as the Bancroft algorithm, can also be used to solve for earthquake hypocenters in a homogeneous half-space. This article applies the Bancroft algorithm to synthetic and real data for the Charlevoix seismic zone and compares the location of ∼1200 events estimated with both the Bancroft algorithm and HYPOINVERSE. The Bancroft algorithm shows quantifiable improve- ments in accuracy compared with traditional methods. We also show how tools com- monly used by the GPS community, such as the geometric dilution of precision, can be used to better estimate the precision of the results obtained by a seismic network.

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.

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.

The number of visible satellites has significantly increased, which provides a possibility for high-precision positioning of global navigation satellite systems (GNSSs). However, GNSS receivers with higher computing power will be required owing to the usage of a large number of visible satellites, and selection of partial satellites with better spatial geometry is required for obtaining high positioning precision schemes for a variety of applications. The geometric dilution of precision (GDOP) is related to the geometrical arrangement of the user and the satellites and computationally intensive, involving matrix multiplication and inversion operations. Various intelligent algorithms for satellite selection have been suggested recently, such as genetic algorithms (GAs). the computation number of GDOP was reduced, owing to the adoption and optimization of these algorithms. However, the algorithms suffer from two issues: 1) the computation process is complex, and significant parametric tuning is required. 2) the algorithms may fall into local optima, instead of the global optimum, owing to the stochasticity of the optimization process. In the paper, we have proposed a novel algorithm for satellite selection, based on chaotic particle swarm optimization (CPSO), which has the advantages of faster convergence, a smaller number of adjustable parameters, and stronger adaptability, compared with the existing algorithms. Firstly, the visible satellites received by the GNSS receiver are continuously encoded and randomly grouped, form the initial population. Afterward, the positions of the particles are updated by the PSO’s velocitydisplacement model. Finally, the CPSO-based algorithm for selection of satellites is designed to replace poor-performing particles with particles in the initial population, which helps to effectively avoid sub-optimal solutions. The proposed algorithm was compared with the traversal method. The simulation results demonstrated that if more than five satellites are selected, the satellite selection time amounts to 37.5% of the time required by the traversal method, and the GDOP error is in the 0.7 range. The proposed algorithm was further validated on the BDS/GPS integrated navigation satellite selection, suggesting the effectiveness of the application in the multiple GNSSs integrated navigation.

Positioning of User Equipment (UE) in 5G Ultra-Dense Networks (UDN) promises significant improvement in location accuracy estimation due to densification of Access Points (AP) infrastructure. For range and bearing primary measurements network geometry plays a significant role in the resultant positioning accuracy, regardless of time (TOA) and angle (AOA) of arrival secondary processing technique. Existing approaches for positioning system topology search in terrestrial cellular networks utilize geometric dilution of precision (GDOP) minimization under certain conditions, satisfying application requirements. Drawback of existing approaches, yielding tractable analytical results, is that they predominantly have assumption of 2-dimensional (2D) AP distribution according to regular hexagonal grid, square lattice or Poisson point process (PPP). If for previous 2G-4G cellular networks it is justified, for 5G UDN these assumptions do not retain. According to latest 3GPP specifications, enhanced positioning service area should provide sub-meter 3D UE location estimation in horizontal and vertical planes. The contribution of current research is a simulation model for 5G UDN positioning system topology search using well known in Global Navigation Satellite Systems (GNSS) horizontal (HDOP), vertical (VDOP) and position (PDOP) dilution of precision (DOP) criterion. Simulation results reveal, that fixed AP number topology, achieving DOP criterion in horizontal plane, does not provide satisfying DOP in vertical one.

This paper presents a model to predict the GDOP value (Geometric Dilution of Precision) and the probability of its occurrence at a point in space and time using airborne LiDAR (Light Detection and Ranging) data and the ultra-rapid product (URP) available from the International GPS Service. LiDAR data help to classify the terrain around a GPS (Global Positioning System) receiver into categories such as ground, opaque objects, translucent objects and transparent regions as per their response to the transmission of GPS signal. Through field experiments it is established that URP can be used satisfactorily to determine GDOP. Further experiments have shown that the translucent objects (mainly trees here) lower the GDOP quality as they obstruct the GPS signal. LiDAR data density on trees is used as a measure of the translucency of trees to the GPS signal. Through GPS observations taken in field a relationship has been established between LiDAR data density on trees and the probability that a satellite which is behind the tree is visible at the GPS receiver. A model is presented which, for all possible combinations of visible satellites, computes the GDOP value along with the probability of occurrence of this GDOP. A few results are presented to show the performance of the model developed and its possible application in location based queries.

Lockheed Martin Mission Systems is developing a high fidelity simulator for the Air Force's Global Positioning System (GPS) satellite command and control operations. To accomplish this goal, each spacecraft subsystem was broken down into a series of algorithms that describes the subsystem dynamic behavior. The measurable effects produced by these algorithms were compared to actual GPS satellite data for algorithm validation. Several subsystems that posed particular difficulty include orbit determination, thermal control, and reaction control. The primary algorithms used to simulate these subsystems are included herein as well as a discussion pertaining to issues surrounding the development of these algorithms. Finally, some of the required anomalies are discussed along with their relation to the derived algorithms.

The challenges of optical wireless positioning are addressed in this paper by a thorough investigation of angle of arrival (AOA) positioning characteristics. The overall positioning precision for AOA positioning is studied in terms of two contributing factors—being angular precision and geometric dilution of precision (DOP). Angular precision is characterized for an optical wireless receiver having an especially wide angular field-of-view (FOV). Geometric DOP is characterized for optical beacons deployed in the form of triangle, square, and hexagon cell geometries. The mean and standard deviation of the positioning errors are extracted from the positioning error distributions for each of the three cell geometries. It is found that the overarching goal to establish low and uniform positioning error distributions can be met by implementing an optical wireless receiver with a wide angular FOV and by implementing the optical beacon geometry with a correspondingly small height-to-side-length ratio. The prospects of these findings are discussed for future optical wireless positioning systems.

The GPS (Global Positioning System) receiving antenna installation angle on a quasi-inertial orientation of the exploration-satellite is studied. Firstly, according to the mission requirements, the satellite attitude requirements are analyzed. Secondly, theoretical analysis and simulation were conducted according to the attitude requirements of posture on the installation of the GPS receiver antenna installation angle, preferably by the GDOP (Geometric Dilution of Precision) values. Finally, conclusion is drawn based on the simulation results that the GPS receiving antenna axial is near to the ± <em>y</em> axis of body reference frame, viz. the orbital plane normal or negative normal direction.

We present a simple model of the signals transmitted by global positioning system (GPS) satellites and of the reception of these signals by a GPS receiver, neglecting atmospheric effects. The model idealizes the receiver and transmitter as electric dipole antennas. We derive the open-circuit voltage induced in the antenna of the receiver as a function of time, position, velocity, and orientation of the respective antenna. As an application of this model, we show that by using a single dipole antenna, a user of the GPS can compute his position, time, and two angles of attitude, by tracking the phases of the open-circuit antenna voltages for six GPS satellites.

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.

The navigation performance of Iridium satellite is simulated and analyzed based on STK from two aspects—the number of visible satellites and geometric dilution of precision (GDOP). Meanwhile we compare it with GPS and GALILEO system to demonstrate its performance. Experiment shows that the Iridium satellite system has a good coverage merit at two poles, which is even better than that of GPS and GALILEO. However, its global coverage is unstable and GDOP changes sharply from high latitude area to low latitude area which means Iridium satellite cannot orientate or navigate around the equator well. Then we explore the application fields of the Iridium satellite system.