scholarly journals Statistical Distribution Analysis of Navigation Positioning System Errors—Issue of the Empirical Sample Size

Sensors ◽  
2020 ◽  
Vol 20 (24) ◽  
pp. 7144 ◽  
Author(s):  
Mariusz Specht
Keyword(s):  
Random Walk ◽  
Normal Distribution ◽  
Global Positioning System ◽  
Empirical Distribution ◽  
Positioning System ◽  
Positioning Systems ◽  
Position Determination ◽  
The Real ◽  
Global Positioning ◽  
Measurement Session

Positioning systems are used to determine position coordinates in navigation (air, land, and marine). Statistical analysis of their accuracy assumes that the position errors (latitude—δφ and longitude—δλ) are random and that their distributions are consistent with the normal distribution. However, in practice, these errors do not appear in a random way, since the position determination in navigation systems is done with an iterative method. It causes so-called “Position Random Walk”, similar to the term “Random Walk” known from statistics. It results in the empirical distribution of δφ and δλ being inconsistent with the normal distribution, even for samples of up to several thousand measurements. This phenomenon results in a significant overestimation of the accuracy of position determination calculated from such a short series of measurements, causing these tests to lose their representativeness. This paper attempts to determine the length of a measurement session (number of measurements) that is representative of the positioning system. This will be a measurement session of such a length that the position error statistics (δφ and δλ) represented by the standard deviation values are close to the real values and the calculated mean values (φ¯ and λ¯) are also close to the real values. Special attention will also be paid to the selection of an appropriate (statistically reliable) number of measurements to be tested statistically to verify the hypothesis that the δφ and δλ distributions are consistent with the normal distribution. Empirical measurement data are taken from different positioning systems: Global Positioning System (GPS) (168′286 fixes), Differential Global Positioning System (DGPS) (864′000 fixes), European Geostationary Navigation Overlay Service (EGNOS) (928′492 fixes), and Decca Navigator system (4052 fixes). The analyses showed that all researched positioning systems (GPS, DGPS, EGNOS and Decca Navigator) are characterized by the Position Random Walk (PRW), which resulted in that the empirical distribution of δφ and δλ being inconsistent with the normal distribution. The size of the PRW depends on the nominal accuracy of position determination by the system. It was found that measurement sessions consisting of 1000 fixes (for the GPS system) overestimate the accuracy analysis results by 109.1% and cannot be considered representative. Furthermore, when analyzing the results of long measurement campaigns (GPS and DGPS), it was found that the representative length of the measurement session differs for each positioning system and should be determined for each of them individually.

Consistency analysis of global positioning system position errors with typical statistical distributions

2021 ◽  
pp. 1-18
Author(s):  
Mariusz Specht
Keyword(s):  
Normal Distribution ◽  
Global Positioning System ◽  
Position Error ◽  
Statistical Distribution ◽  
Positioning System ◽  
Statistical Distributions ◽  
Position Errors ◽  
Global Positioning ◽  
Gps System ◽  
Best Fit

Abstract Research into statistical distributions of φ, λ and two-dimensional (2D) position errors of the global positioning system (GPS) enables the evaluation of its accuracy. Based on this, the navigation applications in which the positioning system can be used are determined. However, studies of GPS accuracy indicate that the empirical φ and λ errors deviate from the typical normal distribution, significantly affecting the statistical distribution of 2D position errors. Therefore, determining the actual statistical distributions of position errors (1D and 2D) is decisive for the precision of calculating the actual accuracy of the GPS system. In this paper, based on two measurement sessions (900,000 and 237,000 fixes), the distributions of GPS position error statistics in both 1D and 2D space are analysed. Statistical distribution measures are determined using statistical tests, the hypothesis on the normal distribution of φ and λ errors is verified, and the consistency of GPS position errors with commonly used statistical distributions is assessed together with finding the best fit. Research has shown that φ and λ errors for the GPS system are normally distributed. It is proven that φ and λ errors are more concentrated around the central value than in a typical normal distribution (positive kurtosis) with a low value of asymmetry. Moreover, φ errors are clearly more concentrated than λ errors. This results in larger standard deviation values for φ errors than λ errors. The differences in both values were 25–39%. Regarding the 2D position error, it should be noted that the value of twice the distance root mean square (2DRMS) is about 10–14% greater than the value of R95. In addition, studies show that statistical distributions such as beta, gamma, lognormal and Weibull are the best fit for 2D position errors in the GPS system.

scholarly journals New Global Referencing Approach in a Camera-LCD Micro Positioning System

Sensors ◽  
2020 ◽  
Vol 20 (7) ◽  
pp. 2118
Author(s):  
Óscar de Francisco Ortiz ◽  
Irene Ortiz ◽  
Antonio Bueno
Keyword(s):  
Global Positioning System ◽  
New Technology ◽  
Positioning System ◽  
New Approach ◽  
Positioning Systems ◽  
System A ◽  
Quality Product ◽  
Global Positioning ◽  
Accuracy And Repeatability ◽  
Current Systems

In any precision manufacturing process, positioning systems play a very important role in achieving a quality product. As a new approach to current systems, camera-LCD positioning systems are a new technology that can provide substantial improvements enabling better accuracy and repeatability. However, in order to provide stability to the system a global positioning system is required. This paper presents an improvement of a positioning system based on the treatment of images on an LCD in which a new algorithm with absolute reference has been implemented. The method is based on basic geometry and linear algebra applied to computer vision. The algorithm determines the spiral center using an image taken at any point. Consequently, the system constantly knows its position and does not lose its reference. Several modifications of the algorithm are proposed and compared. The simulation and test of the algorithm provide an important improvement in the reliability and stability of the positioning system providing errors of microns for the calculation of the global position used by the algorithm.

Evaluating the Ability of Global Positioning System Receivers to Measure a Real-World Operating Mode for Emissions Research

2005 ◽  
Vol 1941 (1) ◽  
pp. 43-50 ◽  
Author(s):  
Eric Jackson ◽  
Lisa Aultman-Hall ◽  
Britt A. Holmén ◽  
Jianhe Du
Keyword(s):  
Global Positioning System ◽  
Real World ◽  
Vehicle Emissions ◽  
Transportation Network ◽  
Operating Mode ◽  
Positioning System ◽  
Gps Receivers ◽  
The Real ◽  
Acceleration Data ◽  
Global Positioning

This paper evaluates the ability of Global Positioning System (GPS) receivers to determine accurately the second-by-second operating mode of a vehicle in the real-world transportation network. GPS offers the ability to obtain second-by-second velocity directly and to obtain acceleration data indirectly from a vehicle traveling in the real-world traffic network. Although GPS has been used successfully in travel behavior and route choice surveys, the uncertainty in accuracy of velocity and acceleration data obtained from the GPS warrants further investigation to gain a better understanding of the range and spatial distribution of vehicle emissions. In this study, data from two GPS receivers and a ScanTool were collected over five repetitions of a 65-mi route. The results indicate that GPS receivers perform as well as the ScanTool when measuring velocity. Furthermore, the GPS receivers determined the 1-s operating mode of the vehicle successfully when measured against the ScanTool. These results will aid in the future development of vehicle emissions models and allow for an analysis of real-world emissions based on real-world operating mode data.

Urban Fleet Monitoring with GPS and GLONASS

1998 ◽  
Vol 51 (3) ◽  
pp. 382-393 ◽  
Author(s):  
M. Tsakiri ◽  
M. Stewart ◽  
T. Forward ◽  
D. Sandison ◽  
J. Walker
Keyword(s):  
Global Positioning System ◽  
Public Transport ◽  
Urban Areas ◽  
Dead Reckoning ◽  
Satellite System ◽  
Basic Function ◽  
Positioning System ◽  
Positioning Systems ◽  
Global Positioning ◽  
Global Navigation Satellite

The increasing volume of traffic in urban areas has resulted in steady growth of the mean driving time on fixed routes. Longer driving times lead to significantly higher transportation costs, particularly for vehicle fleets, where efficiency in the distribution of their transport tasks is important in staying competitive in the market. For bus fleets, the optimal control and command of the vehicles is, as well as the economic requirements, a basic function of their general mission. The Global Positioning System (GPS) allows reliable and accurate positioning of public transport vehicles except within the physical limitations imposed by built-up city ‘urban canyons’. With a view to the next generation of satellite positioning systems for public transport fleet management, this paper highlights the limitations imposed on current GPS systems operating in the urban canyon. The capabilities of a future positioning system operating in this type of environment are discussed. It is suggested that such a system could comprise receivers capable of integrating the Global Positioning System (GPS) and the Russian equivalent, the Global Navigation Satellite System (GLONASS), and relatively cheap dead-reckoning sensors.

Application of the Real-Time Kinematic Global Positioning System in Bridge Safety Monitoring

2005 ◽  
Vol 10 (2) ◽  
pp. 163-168 ◽  
Author(s):  
Jinjun Guo ◽  
Liang Xu ◽  
Lianjun Dai ◽  
Mike McDonald ◽  
Jianping Wu ◽  
...  
Keyword(s):  
Real Time ◽  
Global Positioning System ◽  
Safety Monitoring ◽  
Positioning System ◽  
The Real ◽  
Bridge Safety ◽  
Real Time Kinematic ◽  
Global Positioning

On-Board car diagnostics

2021 ◽  
pp. 09-16
Author(s):  
Keyword(s):  
Augmented Reality ◽  
Control Systems ◽  
Global Positioning System ◽  
Technical Condition ◽  
Positioning System ◽  
Global Positioning Systems ◽  
Positioning Systems ◽  
Global Positioning ◽  
History Of ◽  
Augmented Reality Technology

The article deals with the history of the development of automotive on-Board control systems since the late 60s of the last century to the present time, the assessment of their effectiveness. The perspective directions of development of onboard systems of control of a technical condition with use of global positioning systems GLONASS and GPS, the technology of "augmented reality" are described. Keywords diagnostics, OBD, KAN Protocol, global positioning system GLONASS and GPS, "augmented reality" technology

scholarly journals Determination of Navigation System Positioning Accuracy Using the Reliability Method Based on Real Measurements

2021 ◽  
Vol 13 (21) ◽  
pp. 4424
Author(s):  
Mariusz Specht
Keyword(s):  
Global Positioning System ◽  
Navigation System ◽  
Classical Method ◽  
Positioning System ◽  
Positioning Accuracy ◽  
Positioning Systems ◽  
Position Errors ◽  
Accuracy Measure ◽  
Reliability Method ◽  
Global Positioning

In navigation, the Twice the Distance Root Mean Square (2DRMS) is commonly used as a position accuracy measure. Its determination, based on statistical methods, assumes that the position errors are normally distributed and are often not reflected in actual measurements. As a result of the widespread adoption of this measure, the positioning accuracy of navigation systems is overestimated by 10–15%. In this paper, a new method is presented for determining the navigation system positioning accuracy based on a reliability model where the system’s operation and failure statistics are referred to as life and failure times. Based on real measurements, the method proposed in this article will be compared with the classical method (based on the 2DRMS measure). Real (empirical) measurements made by the principal modern navigation positioning systems were used in the analyses: Global Positioning System (GPS) (168’286 fixes), Differential Global Positioning System (DGPS) (900’000 fixes) and European Geostationary Navigation Overlay Service (EGNOS) (900’000 fixes). Research performed on real data, many of which can be considered representative, have shown that the reliability method provides a better (compared to the 2DRMS measure) estimate of navigation system positioning accuracy. Thanks to its application, it is possible to determine the position error distribution of the navigation system more precisely when compared to the classical method, as well as to indicate those applications that can be used by this system, ensuring the safety of the navigation process.

scholarly journals Augmenting GPS with Geolocated Fiducials to Improve Accuracy for Mobile Robot Applications

2019 ◽  
Vol 10 (1) ◽  
pp. 146 ◽  
Author(s):  
Robert Ross ◽  
Rahinul Hoque
Keyword(s):  
Global Positioning System ◽  
Field Testing ◽  
Small Time ◽  
Positioning System ◽  
Fiducial Markers ◽  
Positioning Systems ◽  
Time Period ◽  
Global Positioning ◽  
Improve Accuracy ◽  
Gps Accuracy

In recent decades Global Positioning Systems (GPS) have become a ubiquitous tool to support navigation. Traditional GPS has an error in the order of 10–15 m, which is adequate for many applications (e.g., vehicle navigation) but for many robotics applications lacks required accuracy. In this paper we describe a technique, FAGPS (Fiducial Augmented Global Positioning System) to periodically use fiducial markers to lower the GPS drift, and hence for a small time-period have a more accurate GPS determination. We describe results from simulations and from field testing in open-sky environments where horizontal GPS accuracy was improved from a twice the distance root mean square (2DRMS) error of 5.5 m to 2.99 m for a period of up-to 30 min.

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