Geometric Dilution Of Precision Value Research Articles

Efficient near-field localization aided with reconfigurable intelligent surface using geometric dilution of precision

ABSTRACT Reconfigurable intelligent surfaces (RISs) are anticipated to constitute a critical component of forthcoming communication networks due to their ability to establish controllable wireless environments. Furthermore, RIS can be leveraged to solve infeasible localization problems. This paper presents a novel adoption of the geometric dilution of precision (GDoP) analysis in the design of non-line of sight (NLoS) single anchor millimetre wave (mmWave) large RIS-aided localization in the near-field. Considering downlink transmission, the time difference of arrival (TDoA) is used to estimate the positioning by extracting the signal contribution of each RIS tile. Considering the enriched time of arrival (ToA) measurements provided by RIS, the RIS tiles involved in TDoA-based estimation should be selected properly. Therefore, the GDoP adopted in this context is to select RIS tile combinations that achieve minimum GDoP values. It has been shown via numerical simulation that the proposed design of the RIS-aided localization outperforms other state-of-the-art techniques that adopt the signal-to-noise ratio (SNR) for the selection of the RIS tiles. It is demonstrated that the proposed scheme can provide sufficient localization accuracy involving only 10% of RIS tiles, whereas the SNR method requires about (70–80) % of the tiles to approximately achieve the same accuracy.

Pseudorange multipath at Zomba geodynamics Continuously Operating Reference Station (CORS) in Malawi

Multipath effects are mostly regarded as a nuisance in Global Navigation Satellite System (GNSS) receiver measurements and it is of utmost relevance to expose the magnitude this error has on observations. The impact of multipath is characterized in the context of a given environment and application. In Malawi, Zomba geodynamics Continuously Operating Reference Station (CORS) is in a multipath prone environment. The GNSS observations for this station have been used in geodynamics studies in Malawi without an understanding of multipath affecting the positioning accuracy. Taking this as an advantage, this paper evaluated pseudorange multipath (MP) and signal noise ratio (SNR) on both L1 (MP1 and SNR1) and L2 (MP2 and SNR2) for the station. This was specifically addressed by computing the elevation mask with minimum and maximum multipath effects. In addition, the number of satellite vehicles (SVs) and their associated Geometric Dilution of Precision (GDOP) are also determined to define their relationship with respect to elevation angles. One week GNSS observations spanning a twenty-four hour interval for DOY 001 to DOY 007 in January 2018 were analysed in Translation Editing and Quality Check (TEQC) software at four (10º, 15º, 20º and 25º) cut-off angles. Results indicate high multipath effects for both MP1 and MP2 at 10º elevation mask among the four elevation masks. The least MP1 and MP2 multipath effects were detected at an elevation angle of 25º. In addition, MP1 multipath was worse than MP2 all the angles. Moreover, statistical results demonstrated an increase in both SNR1 and SNR2 with respect to elevation angle. For these days, L2 signal was more affected by noise than L1. Further to this, an assessment of SVs and GDOP for the CORS show that at least ten (10) satellites were observed in each day at 10º and 15º elevation cut-off. The number of satellites dropped to five (5) at the elevation angle of 25º resulting into a larger GDOP value of 4.5 (a decrease by about 38% from 1.7 at 10º and 15º elevation cut-off angles). Therefore, to increase both the number of satellites and precision, Zomba CORS may be upgraded to a multi-constellation CORS by including other navigation systems such as GLONASS, Galileo and BeiDou. While it is possible to reject GNSS satellite observations below the horizon, it is recommended that post-processing of GNSS data for Zomba geodynamics CORS be done at elevation masks above 15º. Considering that multipath repeats itself every sidereal day, it is thus recommended to model or remove multipath affecting Zomba geodynamics CORS. In addition, the study also recommends that trees very close to Zomba CORS antenna be removed to reduce signal scattering.

A Multi-Target Passive Location Method Based on GDOP Value and Beam Resolution

In passive location systems on the ground, the judgment and location of multi-target is more challenging compared with the case of single target. In this paper, we propose a method for multi-target identification and location in an arbitrary structure with three base stations (BSs). First of all, we discuss the scene of multi-targets judgment based on geometric dilution of precision (GDOP) value. Secondly, we propose an algorithm that calculates the system coverage radius based on arbitrary three BS structures. The algorithm helps to identify the number of targets for unsupervised learning. Finally, we locate each target individually located again based on the linear constrained minimum variance (LCMV) beam former and time difference of arrival (TDOA) algorithm. In the simulations, we analyzed the location dispersion under different signal-to-noise ratio (SNR), then calculated the termination threshold of the k-means algorithm under different SNR. The simulation results show that, compared to the probability hypothesis density (PHD) filter and TDOA-angle-of-arrival (AOA) joint algorithm, the proposed method can increase more than 12.5% and 15.6% points. With the increase of the number of targets, the running time of our algorithm is controllable with better stability.

Application of the SBAS/EGNOS positioning method to determine UAV coordinates

Abstract: The article presents the results of research on determining the UAV (Unmanned Aerial Vehicle) position using the SBAS (Satellite Based Augmentation System) positioning method for the EGNOS (European Geostationary Navigation Overlay Service) support system. The experiment used a single-frequency AsteRx-m2 UAS receiver, which recorded GPS (Global Positioning System) satellite observations and EGNOS corrections. The test flight was performed in 2020 near Warsaw. Navigational calculations for determining the position of the UAV during the flight were made in the gLAB v.5.5.1 software. Based on the performed calculations, the following were determined: BSP coordinates in the ellipsoidal system BLh, mean errors of BSP coordinates, and values of DOP (Dilution of Precision) geometric coefficients. In addition, during the calculations, it was found that the mean error values of the determined BSP coordinates do not exceed 3.6 m, and the maximum value of the geometric coefficient GDOP (Geometric DOP) is less than 3.5. Keywords: SBAS, EGNOS, BSP, mean errors, DOP

A satellite selection algorithm based on adaptive simulated annealing particle swarm optimization for the BeiDou Navigation Satellite System/Global Positioning System receiver

In this article, we propose a new particle swarm optimization–based satellite selection algorithm for BeiDou Navigation Satellite System/Global Positioning System receiver, which aims to reduce the computational complexity of receivers under the multi-constellation Global Navigation Satellite System. The influences of the key parameters of the algorithm—such as the inertia weighting factor, acceleration coefficient, and population size—on the performance of the particle swarm optimization satellite selection algorithm are discussed herein. In addition, the algorithm is improved using the adaptive simulated annealing particle swarm optimization (ASAPSO) approach to prevent converging to a local minimum. The new approach takes advantage of the adaptive adjustment of the evolutionary parameters and particle velocity; thus, it improves the ability of the approach to escape local extrema. The theoretical derivations are discussed. The experiments are validated using 3-h real Global Navigation Satellite System observation data. The results show that in terms of the accuracy of the geometric dilution of precision error of the algorithm, the ASAPSO satellite selection algorithm is about 86% smaller than the greedy satellite selection algorithm, and about 80% is less than the geometric dilution of precision error of the particle swarm optimization satellite selection algorithm. In addition, the speed of selecting the minimum geometric dilution of precision value of satellites based on the ASAPSO algorithm is better than that of the traditional traversal algorithm and particle swarm optimization algorithm. Therefore, the proposed ASAPSO algorithm reduces the satellite selection time and improves the geometric dilution of precision using the selected satellite algorithm.

Base Station Selection for Hybrid TDOA/RTT/DOA Positioning in Mixed LOS/NLOS Environment.

The fifth generation (5G) cellular communication system is designed to support Time Difference of Arrival (TDOA), Round-Trip Time (RTT), and Direction of Arrival (DOA) measurements for indoor positioning. To mitigate the positioning error caused by non-line-of-sight (NLOS), existing base station selection methods identify channel conditions and only use line-of-sight (LOS) signals for positioning. However, different selected base station combination would lead to a different geometric dilution of precision (GDOP), base station selection based only on channel condition is not fully applicable for the hybrid positioning. This paper derives the GDOP for the hybrid TDOA, RTT, and DOA positioning, and proposes a GDOP-assisted base station selection method, which is based on both channel conditions and GDOP value changes. The simulation shows that using the proposed base station selection method could lead to higher positioning accuracy than base station selection based only on channel condition. In the simulation, in the side region of the scenario, where the change of selected base station combination causes a notable increment in GDOP value, the positioning accuracy improvement caused by the proposed method is greater than that in the center region.

A navigation satellite selection algorithm for optimized positioning based on Gibbs sampler

In various applications of satellite navigation and positioning, it is a key topic to select suitable satellites for positioning solutions to reduce the computational burden of the receiver in satellite selection system. Moreover, in order to reduce the processing burden of receivers, the satellite selection algorithm based on Gibbs sampler is proposed. First, the visible satellites are randomly sampled and divided into a group. The group is regarded as an initial combination selection scheme. Then, the geometric dilution of precision is chosen as an objective function to evaluate the scheme’s quality. In addition, the scheme is updated by the conditional probability distribution model of the Gibbs sampler algorithm, and it gradually approaches the global optimal solution of the satellite combination with better geometric distribution of the space satellite. Furthermore, an “adaptive perturbation” strategy is introduced to improve the global searching ability of the algorithm. Finally, the extensive experimental results demonstrate that when the number of selected satellite is more than 6, the time that the proposed algorithm with the improvement of “adaptive perturbation” takes to select satellite once is 43.7% of the time that the primitive Gibbs sampler algorithm takes. And its solutions are always 0.1 smaller than the related algorithms in geometric dilution of precision value. Therefore, the proposed algorithm can be considered as a promising candidate for satellite navigation application systems.

Improving the navigation spacecraft radio visibility with signal processing algorithms usage

The article deals with topical issues of spacecraft external design for the global navigation satellite system (GLONASS). The development and analysis of data processing algorithms are considered a part of the external design phase. Data for processing algorithms was obtained from real orbital grouping spacecraft. Mathematical modelling was performed based on real data to analyse navigation signals propagation conditions from GLONASS satellites. Implementation of mathematical modelling approach included such aspects as finding the optimal antenna pattern and filtering radio frequency signals. Theoretically optimal antenna directivity patterns were implemented taking into account available data about satellite orbital parameters. Bessel, Butterworth, Chebyshev and elliptic filters were used as standard filtering methods. Modified low-pass filtering algorithm was considered as an improved filtering algorithm. Application of the modified filtering method allowed to reduce geometric dilution of precision value in the consumer positioning case. Obtained results are applicable to design possible options for improving the existing GLONASS orbital group.

Satellite selection with an end-to-end deep learning network

Benefiting from multi-constellation Global Navigation Satellite Systems (GNSS), more and more visible satellites can be used to improve user positioning performance. However, due to limited tracking receiver channels and power consumption, and other issues, it may be not possible, or desirable, to use all satellites in view for positioning. The optimal subset is generally selected from all possible satellite combinations to minimize either Geometric Dilution of Precision (GDOP) or weighted GDOP (WGDOP). However, this brute force approach is difficult to implement in real-time applications due to the time- and power-consuming calculation of the DOP values. As an alternative to a brute force satellite selection procedure, the authors propose an end-to-end deep learning network for satellite selection based on the PointNet and VoxelNet networks. The satellite selection is converted to a satellite segmentation problem, with specified input channel for each satellite and two class labels, one for selected satellites and the other for those not selected. The aim of the satellite segmentation is that a fixed number of satellites with the minimum GDOP/WGDOP value can be segmented from any feeding order of input satellites. To validate the proposed satellite segmentation network, training and test data from 220 IGS stations tracking GPS and GLONASS satellites were used. The segmentation performance using different architectures and representations of input channels, including receiver-to-satellite unit vector and elevation and azimuth, were compared. It was found that the input channel with elevation and azimuth can achieve better performance than using the receiver-to-satellite unit vector, and an architecture with stacked feature encoding (FE) layers has better satellite segmentation performance than one without stacked FE layers. In addition, the models with GDOP and WGDOP criteria for selecting 9 and 12 satellites were trained. It was demonstrated that the satellite segmentation network was about 90 times faster than using the brute force approach. Furthermore, all the trained models can effectively select the satellites making the most contribution to the desired GDOP/WGDOP value. Approximately 99% of the tests had GDOP and WGDOP value differences smaller than 0.03 and 0.2, respectively, between the predicted subset and the optimal subset.

GDOP Analysis with Optimal Satellites Using GA for Southern Region of Indian Subcontinent

The emergence of Global Positioning System (GPS) has reformed the application areas of navigation, predominantly in aviation sector. Satellite geometry plays crucial role, which indicates the geometric positions of the satellites as perceived by the GPS receiver. But, many factors affect the position accuracy of GPS. The position accuracy sustained by satellite geometry. Effect of geometry can be restrained by Geometric Dilution Of Precision (GDOP). Stronger the geometry, finer the GDOP value. In general the GDOP ranges from 2 to 6. In a GPS system, minimum of four satellites are involved while computing the user position. From the set of more visible satellites, optimal subsets with minimum number of satellites need to be selected to reduce the superfluity. This paper gives a new hybrid method for estimation of GDOP using optimum number of satellites to improve position accuracy using popular optimization technique i.e., Genetic Algorithm (GA).

Study of network topology effect on measurement accuracy for a distributed rotary-laser measurement system

The workshop Measurement Positioning System (wMPS) is a large-scale measurement system that better copes with the current challenges of dimensional metrology. However, as a distributed measuring system with multiple transmitters forming a spatial measurement network, the network topology of transmitters relative to the receiver exerts a significant influence on the measurement accuracy albeit one that is difficult to quantify. An evaluation metric, termed the geometric dilution of precision (GDOP), is introduced to quantify the quality of the network topology of the wMPS. The GDOP is derived from the measurement error model of wMPS and its mathematical derivation is expounded. Two significant factors (density and layout of the transmitter) affecting the network topology are analyzed by simulations and experiments. The experimental results show that GDOP is approximately proportional to the measurement error. More transmitters, and a relatively good layout thereof, can decrease the value of GDOP and the measurement error.

GDOP minimum in multi-GNSS positioning

In positioning, navigation and timing (PNT) applications with the Global Navigation Satellite System (GNSS), the geometric dilution of precision (GDOP) offers an important index for selecting satellites from all tracked satellites for positioning calculation. In general, the lower the GDOP values are, the more accurate the PNT solution is. Therefore, the GDOP minimum should be pursued. In this paper, we mainly focused on the GDOP minimum when the single-point positioning is based on the integration of three GNSSs. The GDOP minimum for any number of tracked satellites is theoretically derived in this paper. In addition, when the number of the satellites is equal to that of the unknown parameters, the correctness of GDOP minimum obtained has also been validated from two different perspectives.

On the relation between GDOP and the volume described by the user-to-satellite unit vectors for GNSS positioning

The geometric dilution of precision (GDOP) is related to the satellite geometry. Thus far, research has focused on minimizing the GDOP by selecting a set of satellites that maximizes the volume spanned by the user-to-satellite unit vectors. However, this relation has been only analyzed when four satellites are used for computing the three-dimensional position, for which the relation is nearly direct. The analysis applicable to any number of satellites is presented here. Results show that the relation between GDOP and volume spanned by the user-to-satellite unit vectors does not ensure that the optimal GDOP value is achieved by means of the volume maximization. Satellite distribution should also be considered in such a way that the selection of geometries that are closer to a regular polytope is favored.

Mathematical minimum of Geometric Dilution of Precision (GDOP) for dual-GNSS constellations

Selecting optimal satellites for positioning calculation is a basic problem for the positioning, navigation and timing (PNT) applications with Global Navigation Satellite System (GNSS), and the Geometric Dilution of Precision (GDOP) is a key index to handle this problem. In general, the lower the GDOP values are, the more accurate the PNT solution is. Therefore, the minimum value of GDOP should be pursued. In this paper, we focused on the five-satellite as at least five satellites are required for dual-GNSS constellations. Utilizing the characteristics of matrix partial orders, the mathematical minimum of GDOP in the five-satellite case together with the optimal distribution of the five satellites has been theoretically derived. Furthermore, from a theoretical point of view, the detailed expressions of the impact of different constellational combinations of these satellites on the GDOP have been obtained. The results demonstrated that, for dual-GNSS, even if the geometric distribution of the five satellites is fixed, different constellational combinations of these satellites lead to different values of GDOP. This is different from the single-GNSS case.

Minimum of Geometric Dilution of Precision (GDOP) for five satellites with dual-GNSS constellations

The Geometric Dilution of Precision (GDOP) is a term to specify multiplicative effect of the satellite geometry on positioning and timing precision. For positioning, navigation and timing (PNT) applications with multi-GNSS constellations, the lower the GDOP values are, the more accurate the PNT solution is, and thus, the minimum value of GDOP should be discussed. Firstly, this paper analyses the traditional method for calculating the minimum of GDOP for dual-GNSS constellations. Then, from the point of the practical constraints of a GNSS receiver on the earth surface, a new formula for the specific minimum of GDOP together with the design matrix is derived. The minimum of GDOP is expressed as a function with two satellite elevation angles as variables. The numerical experiments have demonstrated the validation of the new formula for the minimum of GDOP.

Target Positioning with GDOP Assisted Nodes Selection Algorithm in Wireless Sensor Networks

In wireless sensor networks (WSN), the geometric distribution of anchor nodes has a significant influence on the positioning accuracy. Geometric dilution of precision (GDOP) can be used to measure the positioning precision of the localization system. In order to select the optimal node combination, traditional algorithms based on GDOP need to spend much time on calculating every possible combination of nodes. This paper proposes GDOP assisted nodes selection (GANS) algorithm to calculate GDOP value of the current geometric distribution. Sensor node's contribution to the overall GDOP value is adopted as the evaluation criteria. The nodes whose contribution value is greater than the threshold will be selected. The anchor nodes subset, which participates in the positioning, will be real-time determined. Simulation results show that the GANS algorithm can effectively reduce the energy consumption of the system, while the positioning accuracy has no obvious loss. Meanwhile, computational complexity is also obviously decreased.

A Practical Method of Observer Velocity Optimization with Airborne ESM Sensor

In bearings-only target motion analysis, the observer trajectory has an important effect on the accuracy of target localization and tracking. This paper presented a practical method of observer velocity optimization based on Monte-Carlo run for airborne ESM measurement system. For verifying the validity of our method, the geometric dilution of precision (GDOP) is taken as the performance index. Finally, three scenarios are given and the GDOP values of the ESM measurement system in scenarios are calculated to illustrate the observer velocity optimization strategy.

Calculation of Weighted Geometric Dilution of Precision

To achieve high accuracy in wireless positioning systems, both accurate measurements and good geometric relationship between the mobile device and the measurement units are required. Geometric dilution of precision (GDOP) is widely used as a criterion for selecting measurement units, since it represents the geometric effect on the relationship between measurement error and positioning determination error. In the calculation of GDOP value, the maximum volume method does not necessarily guarantee the selection of the optimal four measurement units with minimum GDOP. The conventional matrix inversion method for GDOP calculation demands a large amount of operation and causes high power consumption. To select the subset of the most appropriate location measurement units which give the minimum positioning error, we need to consider not only the GDOP effect but also the error statistics property. In this paper, we employ the weighted GDOP (WGDOP), instead of GDOP, to select measurement units so as to improve the accuracy of location. The handheld global positioning system (GPS) devices and mobile phones with GPS chips can merely provide limited calculation ability and power capacity. Therefore, it is very imperative to obtain WGDOP accurately and efficiently. This paper proposed two formations of WGDOP with less computation when four measurements are available for location purposes. The proposed formulae can reduce the computational complexity required for computing the matrix inversion. The simpler WGDOP formulae for both the 2D and the 3D location estimation, without inverting a matrix, can be applied not only to GPS but also to wireless sensor networks (WSN) and cellular communication systems. Furthermore, the proposed formulae are able to provide precise solution of WGDOP calculation without incurring any approximation error.

Classifying the Geometric Dilution of Precision of GPS satellites utilizing Bayesian decision theory

The errors resulting from satellite configuration geometry can be determined by Geometric Dilution of Precision (GDOP). Considering optimal satellite subset selection, lower GDOP value usually causes better accuracy in GPS positioning. However, GDOP computation based on complicated transformation and inversion of measurement matrices is a time consuming procedure. This paper deals with classification of GPS GDOP utilizing Parzen estimation based Bayesian decision theory. The conditional probability of each class is estimated by Parzen algorithm. Then based on Bayesian decision theory, the class with maximum posterior probability is selected. The experiments on measured dataset demonstrate that the proposed algorithm lead, in mean classification improvement, to 4.08% in comparison with Support Vector Machine (SVM) and 9.83% in comparison with K-Nearest Neighbour (KNN) classifier. Extra work on feature extraction has been performed based on Principle Component Analysis (PCA). The results demonstrate that the feature extraction approach has best performance respect to all classifiers.

The application research of global navigation constellation for HEO (high earth orbit) satellites and deep-space satellites

It has been widely studied that GNSS(global navigation satellite system) offers navigation for Ground-Based users and LEO(low earth orbit.) users. At present, it mainly depends on Ground-Based measurement and control system that HEO satellites and deep-space satellites determine their orbits and attitude, and synchronize their time. The Ground-Based measurement and control system which has complex equipment and high investment can’t support abundant aerocrafts at the same time, and can’t operate autonomously. This article studied the possibility of orbit determination, attitude determination, and time synchronization with global navigation constellation for HEO satellites and deep-space satellites, and consequently achieved the extended applications of global navigation constellation. It found out a high efficient way for global navigation constellation to operating as time and space reference for constellation networks, in order that constellation networks autonomously operate and navigate. And it also putted forward a solution to realize passive navigation for HEO satellites and deep-space satellites by skillfully designing the links between satellites, without increasing equipment on satellites. The research focused on the number of visible satellites and GDOP(geometric dilution of precision) value. The precision of positioning and time determination was also analyzed in order to provide new ideas for the construction of global navigation constellation.