Geometric Dilution Of Precision Research Articles

A Low SNR and Fast Passive Location Algorithm Based on Virtual Time Reversal

In order to achieve fast and accurate passive location of the target radiation source, this paper puts forward a Virtual Time Reversal Method Based on Uniform Linear Array (ULA-VTR) passive location algorithm. This framework employs the passive time reversal focusing theory, which does not to require the physical transmission of time reversal signals and does not require pre-estimation of the channel to realize passive direction finding. The above principle is utilized to perform the target radiation source signal through a uniform linear sensor array for detection. The article provides the signal model of linear time reversal array and the virtual retransmission process in the first place. Then utilizes ULA-VTR to establish a dual-station passive location framework and derives the coordinate transformation equation to find its observation angle, in addition, establishes the observation equation system for obtaining the site of the target radiation source. Ultimately, the paper analyses the computational complexity of the ULA-VTR algorithm and adopts Geometric Dilution of Precision(GDOP) to discuss the positioning performance. The experimental results indicate that the technique presented in this paper has higher positioning accuracy under the low SNR compared with other techniques.

Availability analysis of GNSS signals above GNSSs constellation

AbstractIn view of many problems associated with the availability of global navigation satellite system (GNSS) signals in high-altitude space, this paper presents a comprehensive and systematic analysis. First, the coverage and strength characteristics of GNSS signals in high-altitude space (i.e., space above the GNSS constellation) are presented, and the visibility of GNSS signals is evaluated by combining these two factors. Second, the geometric configuration and geometric dilution of precision (GDOP) of visible GNSS satellites are analysed. Then, the Doppler shift range of the GNSS signals is deduced based on the dynamic performance of high-altitude spacecraft. Finally, taking GaoFen-4 (GF-4) as the application object, the availability of GNSS signals is simulated and evaluated. GNSS signals in high-altitude space are generally weak, and the visible GNSS satellites are concentrated in the high-elevation range. The combination of main and side lobe signals and compatibility of multiple constellations can increase the number of visible satellites, improve the geometry configuration, reduce GDOP, and thus improve the availability of GNSS signals. The results of this research can provide technical support for the design and development of GNSS receivers suitable for high-altitude space.

Optimisation strategy of roadside units deployment towards VANET localisation with dead reckoning

In vehicle ad-hoc networks (VANETs), the full coverage of roadside units (RSUs) is not necessary with the assistance of dead reckoning (DR) for the RSU-based vehicle localisation. This study proposes an optimisation strategy of RSUs deployment, which seeks an optimal RSU layout ensuring the best localisation accuracy with a minimum number of RSUs. With the assistance of DR, first, the average geometric dilution of precision (GDOP) for a specific localisation region is derived through a non-linear recursive model. Then the RSUs deployment is formulated into an optimisation problem, and the objective is as a function of the average GDOP and deploying interval. Finally, the optimisation problem is solved by a centre particle swarm optimisation (CPSO) algorithm. The convergence and stability of CPSO are evaluated via simulations. Furthermore, simulations also show that the proposed strategy can optimise the localisation accuracy of RSUs deployment in the VANET scenario.

New Multi-Step Iterative Methods for Solving Systems of Nonlinear Equations and Their Application on GNSS Pseudorange Equations.

A two-step fifth and a multi-step order iterative method are derived, for finding the solution of system of nonlinear equations. The new two-step fifth order method requires two functions, two first order derivatives, and the multi-step methods needs a additional function per step. The performance of this method has been tested with finding solutions to several test problems then applied to solving pseudorange nonlinear equations on Global Navigation Satellite Signal (GNSS). To solve the problem, at least four satellite’s measurements are needed to locate the user position and receiver time offset. In this work, a number of satellites from 4 to 8 are considered such that the number of equations is more than the number of unknown variables to calculate the user position. Moreover, the Geometrical Dilution of Precision (GDOP) values are computed based on the satellite selection algorithm (fuzzy logic method) which could be able to bring the best suitable combination of satellites. We have restricted the number of satellites to 4 to 6 for solving the pseudorange equations to get better GDOP value even after increasing the number of satellites beyond six also yields a 0.4075 GDOP value. Actually, the conventional methods utilized in the position calculation module of the GNSS receiver typically converge with six iterations for finding the user position whereas the proposed method takes only three iterations which really decreases the computation time which provide quicker position calculation. A practical study was done to evaluate the computation efficiency index (CE) and efficiency index (IE) of the new model. From the simulation outcomes, it has been noted that the new method is more efficient and converges 33% faster than the conventional iterative methods with good accuracy of 92%.

Analysis and Application of Geometric Dilution of Precision Based on Altitude-Assisted INS/SAR Integrated Navigation

The inertial navigation system/synthetic aperture radar (INS/SAR) integrated navigation system can provide all-weather navigation information both day and night. Altitude is often used as independent information to assist the navigation system in reducing vertical channel errors. In this study, GPS geometric dilution of precision (GDOP) analysis method is introduced into the INS/SAR integrated navigation. By comparing the effects of the presence or absence of altitude assistance and different distributions of SAR measurement ground points on the observability and navigation accuracy, the analysis results based on the GDOP analysis method are provided. The simulation results show that an altitude-assisted navigation system with SAR measurement ground points on two sides achieves the best observability. In addition, there is a positive correlation between the observability and elevation angle. The flight experiment results verify the effectiveness of the proposed method and are consistent with the simulation results.

3-D Deformation Measurement Based on Three GB-MIMO Radar Systems: Experimental Verification and Accuracy Analysis

An experiment which involves the simultaneous deployment of three ground-based multiple-input multiple-output (GB-MIMO) radar systems to measure 3-D deformation of a displaceable corner reflector (DCR) is outlined in this letter. The DCR successively displaces in three mutually orthogonal directions and each radar measures 1-D deformation independently. Since the displacement directions of the DCR cannot be measured, they are estimated by solving a nonlinear equation set based on the rotation relationship between two 3-D coordinate systems, whose effectiveness is verified by simulation. Considering that the measurement accuracies of the DCR’s displacements along three axial directions of a 3-D coordinate system, that is, 3-D deformation, are related with how the coordinate system is built, the geometric dilution of precision (GDOP) is then utilized to take accuracy analysis. The measured and theoretical GDOP are rather close, which validates the feasibility of 3-D deformation measurement with three radar systems.

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.

High-Accuracy Positioning Based on Pseudo-Ranges: Integrated Difference and Performance Analysis of the Loran System.

The Long Range Navigation (Loran) system as a backup of the Global Navigation Satellite System (GNSS) is a good choice. The dominant deterioration factors of position accuracy are the pseudo-range measurement errors and the geometric dilution of precision (GDOP). This paper focuses on the algorithm integrated difference with pseudo-ranges to improve the position accuracy. Firstly, the theoretical prediction of propagation delay and raw measurement are compared. The results show that the measured pseudo-range consists of a constant term and a temporal term, which reflect the propagation situation along the true path. Secondly, a position solution algorithm based on a pseudo-range and difference is presented, exceeding the limit of a single chain. Finally, some simulation tests are implemented utilizing the new proposed position algorithm to verify the differential performance. This method can reduce the GDOP conveniently through increasing the number of transmitters. In view of the amplitude and characteristics of errors in measurement, systematic error and random noise are distinguished and discussed. The absolute accuracy responds to the pseudo-range bias that is different from geometric distance and repeatable accuracy is mainly influenced by random noise. The difference method can improve the absolute accuracy via the correction degree without changing the geometry of the transmitters.

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.

Optimal Walker Constellation Design of LEO-Based Global Navigation and Augmentation System

Low Earth orbit (LEO) satellites located at altitudes of 500 km~1500 km can carry much stronger signals and move faster than medium Earth orbit (MEO) satellites at about a 20,000 km altitude. Taking advantage of these features, LEO satellites promise to make contributions to navigation and positioning where global navigation satellite system (GNSS) signals are blocked as well as the rapid convergence of precise point positioning (PPP). In this paper, LEO-based optimal global navigation and augmentation constellations are designed by a non-dominated sorting genetic algorithm III (NSGA-III) and genetic algorithm (GA), respectively. Additionally, a LEO augmentation constellation with GNSS satellites included is designed using the NSGA-III. For global navigation constellations, the results demonstrate that the optimal constellations with a near-polar Walker configuration need 264, 240, 210, 210, 200, 190 and 180 satellites with altitudes of 900, 1000, 1100, 1200, 1300, 1400 and 1500 km, respectively. For global augmentation constellations at an altitude of 900 km, for instance, 72, 91, and 108 satellites are required in order to achieve a global average of four, five and six visible satellites for an elevation angle above 7 degrees with one Walker constellation. To achieve a more even coverage, a hybrid constellation with two Walker constellations is also presented. On this basis, the GDOPs (geometric dilution of precision) of the GNSS with and without an LEO constellation are compared. In addition, we prove that the computation efficiency of the constellation design can be considerably improved by using master–slave parallel computing.

A refined metric for multi-GNSS constellation availability assessment in polar regions

Human activity in the polar regions is increasing, and as a result of this, the positioning performance of global navigation satellite systems (GNSSs) in these regions is attracting more attention. Since the constellation design of GNSS systems (such as GPS, GLONASS, Galileo, and BDS) only provides superior coverage for human activity in the middle and low latitudes, the elevation angles of GNSS satellites are lower in the polar regions. In this study, the authors first analyzed the availability of GPS, GLONASS, Galileo, and BDS in the polar regions using the classic geometric dilution of precision (GDOP) metric. It was discovered that if only a stand-alone navigation system is employed, satellite visibility in the Arctic and Antarctic regions is excellent, but the GDOP is much higher than in the middle and low latitudes areas. Another interesting phenomenon is that a single navigation system other than GPS (i.e., GLONASS, Galileo, or BDS) will have some areas that cannot be located in the middle and low latitudes and will not appear in the polar regions. A simple solution of this problem is to combine multiple navigation systems to attain better GDOP. In reality, there are currently few achievable or practical solutions for the weight ratio of different satellites in the actual multi-system combined GDOP algorithm. Based on the signal-in-space analysis of different GNSS satellites, the authors propose a NEW WDOP metric for the spatial constellation configuration of multi-GNSSs, including detailed mathematical models and algorithms. The NEW WDOP metric was then used to assess the availability of multi-GNSSs in the polar regions with dual-system, three-system, and four-system combinations. This study thus draws some conclusions using the NEW WDOP model and measured data. In particular, when navigating and positioning in polar regions with a stand-alone GNSS, the mean of the NEW WDOP values is approximately 2.5, and there are many outlier values. Meanwhile, the mean of the NEW WDOP values with the dual GNSS combinations is <1.5, but the value of the NEW WDOP for some combinations in the polar regions is still extremely large and contains some outliers. However, the mean of the NEW WDOP with the three-system or four-system combinations in the polar regions is approximately 1, and the number of outliers is very small; in particular, the four-system combination has no outliers. The results of this study contribute some useful information for the GNSS application of multi-system combinations and satellite selection in the polar regions.

Modeling and Improving the Energy Performance of GPS Receivers for Location Services

Integrated GPS receivers have become a basic module in today’s mobile devices. While serving as the cornerstone for location based services, GPS modules have a serious battery drain problem due to high computation load. This paper aims to reveal the impact of key software parameters on GPS energy consumption, by establishing an energy model for a standard GPS receiver architecture as found in both academic and industrial designs. In particular, our measurements show that the receiver’s energy consumption is in large part linear with the number of tracked satellites as well as the length of the raw GPS signal. This leads to an energy efficient design of selective tracking algorithm with large satellite Geometric Dilution of Precision (GDOP) weight, well spatial distribution, and large signal intensity. Real experimental results on three typical scenarios show that our selective tracking algorithm provides better tradeoff between positioning accuracy and energy consumption than standard GPS receivers.

The Positioning Accuracy and Performance Simulation Analysis of BeiDou-3 in Cote d’Ivoire

BeiDou Navigation Satellite System will operate world widely in 2020. Therefore, it is very important to master the accuracy and positioning performance of BeiDou-3 in West Africa. The number of visible satellite, the navigation accuracy and Geometric Dilution of Precision (GDOP) of BeiDou-3 (3 GEO-3IGSO-24MEO) are simulated using STK software in Cote d’Ivoire. Using data of five stations in Cote d’Ivoire, the simulation results are compared for BeiDou-3 and GPS. Thus, the results are allowed to possess a database about the positioning performance of BeiDou-3 not only for Cote d’Ivoire but also benefit for surrounding Regions of the Gulf of Guinea.

A Numeric-Symbolic Solution of GNSS Phase Ambiguity

Solution of the Global Navigation Satellite Systems (GNSS) phase ambiguity is considered as a global quadratic mixed integer programming task, which can be transformed into a pure integer problem with a given digit of accuracy. In this paper, three alter-native algorithms are suggested. Two of them are based on local and global linearization via McCormic Envelopes, respectively. These algorithms can be effective in case of simple configuration and relatively modest number of satellites. The third method is a locally nonlinear, iterative algorithm handling the problem as {-1, 0, 1} programming and also lets compute the next best integer solution easily. However, it should keep in mind that the algorithm is a heuristic one, which does not guarantee to find the global integer optimum always exactly. The procedure is very powerful utilizing the ability of the numeric-symbolic abilities of a computer algebraic system, like Wolfram Mathematica and it is properly fast for minimum 4 satellites with normal configuration, which means the Geometric Dilution of Precision (GDOP) should be between 1 and 8. Wolfram Alpha and Wolfram Clouds Apps give possibility to run the suggested code even via cell phones. All of these algorithms are illustrated with numerical examples. The result of the third one was successfully compared with the LAMBDA method, in case of ten satellites sending signals on two carrier frequencies (L1 and L2) with weighting matrix used to weight the GNSS observation and computed as the inverse of the corresponding covariance matrix.

Temporal Analysis of GDOP to Quantify the Benefits of GPS and GLONASS Combination on Satellite Geometry

Global Navigation Satellite Systems (GNSS) have developed rapidly over the last few years. At present, there are GNSS receivers that combine satellites from two or more different constellations. The geometry of the satellites in relation to the receiver location, i.e. how nearly or distantly they are disposed in the sky, impacts on the quality of the survey, which is essential to achieve the highest level of position accuracy. A dimensionless number identified as Geometric Dilution of Precision (GDOP) is used to represent the efficiency of the satellite distribution and can be easy calculated for each location and time using satellite ephemeris. This paper quantifies the influence of multi-GNSS constellation, in particular GPS (Global Positioning System) and GLONASS (Globalnaya Navigazionnaya Sputnikovaya Sistema) combination, on satellite geometry considering a precise period. A new index named Temporal Variability of Geometric Dilution of Precision (TVGDOP) is proposed and analyzed in different scenarios (different cut-off angles as well as real obstacles such as terrain morphology and buildings). The new index is calculated for each of the two satellite systems (GPS and GLONASS) as well as for their integration. The TVGDOP values enable the three cases to be compared and permit to quantify the benefits of GNSS integration on satellite geometry. The results confirm the efficiency of the proposed index to highlight the better performance of combination GPS+GLONASS especially in presence of obstacles.

Identification and Exclusion Multiple Outliers in GNC Microsystem

Monitoring the positioning reliability is of great importance for modern Global Navigation Satellite System (GNSS), especially for receivers which are on duty in multi-constellation Guidance Navigation and Control (GNC). Integrity and relevant techniques are gaining popularity among which many researches focus on receiver autonomous integrity monitoring (RAIM) referring to independent integrity without any external assistance. Therefore, the performances of RAIM have to be lucubrated in order to assure the positioning quality. An innovative method has been proposed for failure identification and exclusion in GNSS among GNC microsystem. This method is established on the evaluation of subsets precheck and residual vector adjustment to conduct RAIM. It is applicable to multi-constellation receivers carrying on FDE. Concerning on abundant visible satellites, we consider Geometric Dilution Precision (GDOP) for optimized satellite spatial geometry and manage to avoid matrix inverse operation by Newton efficient equivalence solution, which saves large quantity computational complexity in GNC microsystem. The main purpose is to improve the ability of GNSS receiver accuracy, availability, continuity and integrity. The multiple outlier hypothesis has also been evaluated to ensure the integrity by the statistical global and local tests of least squares residual. Simulation consequences imply that we are able to obtain fairly good behaviors when processing single and two outliers.

Ultrasound TDoA Positioning Using the Best Linear Unbiased Estimator and Efficient Anchor Placement

In this article, positioning based on ultrasound time-difference-of-arrival (TDoA) measurements is investigated. The best linear unbiased estimator (BLUE) algorithm is proposed, compared to a least-squares estimator (LSE), and validated using numerical simulations. Optimal placement of anchor nodes is also investigated by evaluating and minimizing the geometrical dilution of precision (GDOP) with some geometrical constraints. The comparison was carried out by assuming the multipath channel affecting line-of-sight (LoS) propagation. It is shown that the accuracy and the processing time of the proposed BLUE approach are similar to that of the LSE while providing a simpler implementation. It is also shown that anchors' constellations that minimize the GDOP can lead to increased robustness to multipath and that the BLUE provides a more robust performance than LSE when multipath is introduced in a LoS environment.

A Closed-Form Localization Algorithm and GDOP Analysis for Multiple TDOAs and Single TOA Based Hybrid Positioning

Cellular communication systems support mobile phones positioning function for Enhanced-911 (E-911) location requirements, but the positioning accuracy is poor. The fifth-generation (5G) cellular communication system can use indoor distribution systems to provide accurate multiple time-difference-of-arrival (TDOA) and single time-of-arrival (TOA) measurements, which could significantly improve the indoor positioning ability. Unlike iterative localization algorithms for TDOA or TOA, the existing closed-form algorithms, such as the Chan-Ho algorithm, do not have convergence problems, but can only estimate position based on one kind of measurement. This paper proposes a closed-form localization algorithm for multiple TDOAs and single TOA measurements. The proposed algorithm estimates the final position result using three-step weighted least squares (WLSs). The first WLS provides an initial position for the last two steps. Then the algorithm uses two WLSs to estimate position based on heteroscedastic TDOA and TOA measurements. In addition, the geometric dilution of precision (GDOP) of the proposed hybrid TDOA and TOA positioning has been derived. The analysis of GDOP shows that the proposed hybrid positioning has lower GDOP than TDOA-only positioning, which means the proposed hybrid positioning has a higher accuracy limitation than TDOA-only positioning. The simulation shows that the proposed localization algorithm could have better performance than closed-form TDOA-only positioning methods, and the positioning accuracy could approximate Cramer-Rao lower bound (CRLB) when the TDOA measurement errors are small.

Analysis of signal strength, satellite visibility, position accuracy and ionospheric TEC estimation of IRNSS

The Indian Regional Navigation Satellite System (IRNSS) is an indigenously developed satellite navigation system to meet practical needs. The system, comprising a constellation of seven satellites in GEO orbit, has been fully operational since 2018. It is essential to evaluate the performance of the IRNSS continuously for various applications. As a part of ISRO field trial and data collection program an IRNSS Standard Positioning Service User Receiver (UR) placed at ACS College of Engineering (ACSCE), Bangalore, for independent field trial and data collection. The receiver is operational on a $24\times 7$ basis. A MATLAB Graphical User Interface has been developed to analyze and plot the data variation of signal strength, elevation angle, visibility of satellites, user position, position error, geometric dilution of precision (GDOP) and find the availability of the number of satellites plotted for every second based on the received data. From the results, it is observed that the signal strength (C/No) is good, i.e. above 40 dBHz, visibility of satellites at receiver location is good. The mean position at user location is found to be $X=1349700~\mbox{m}$, $Y = 6070902~\mbox{m}$, $Z = 1413860~\mbox{m}$ and latitude of 12.8914 degree, longitude of 77.465 degree and altitude of 739 m. The mean position from IRNSS is compared with Google map results showing a good match. The geometry distance of receiver location with respect to Earth center is estimated and observed. The RMS of position error for L1, L5 and dual frequency (L5+S) at ACSCE, Bangalore, is 9.7444 m, 6.6873 m and 5.6667 m, respectively. Hence, as expected the dual-frequency (L5+S) receiver gives an accurate position rather than the single-frequency signals. The IRNSS TEC is measured using Ionospheric group delay and the pseudo-range of L5 and S band which is collected from ACSCE receiver. A third order Savitzky-Golay-Filtered technique is used for TEC smoothing. RMSE between IRNSS TEC from pseudo-range and GPS TEC is 0.6482 TECU and the correlation coefficient is 0.9981. RMSE between IRNSS TEC from ionospheric delay of L5/S and GPS TEC is 1.971 TECU and the correlation coefficient is 0.9966. Finally, smoothed TEC values derived from pseudo-range measurements give a good result and can be used to generate daily TEC maps. In order to analyze the performance of IRNSS over the Indian region, we have chosen three other receiver stations located at Osmania University (Hyderabad), University of Burdwan (Bardhaman, West Bengal) and Shri Mata Vaishno Devi University (Katra, Jammu and Kashmir). Based on the results, we conclude that the IRNSS constellation is performing well and providing good signals for accurate user position determination and ionospheric data analysis.

TDOA‐based adaptive observer trajectory optimisation algorithm for tracking in passive coherent location system

In the passive coherent location system with fixed observers, the target tracking performance is limited by the inappropriate localisation geometry. This study proposes an adaptive observer trajectory optimisation (AOTO) algorithm in terms of minimising the geometric dilution of precision (GDOP) based on the time difference of arrival (TDOA) measurements gained from multiple emitters. The target states are estimated by the extended Kalman filter (EKF) algorithm. Simulation results demonstrate that the AOTO algorithm can effectively improve the tracking accuracy compared with the corresponding tracking approaches with fixed observers.