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 Consistency of the Empirical Distributions of Navigation Positioning System Errors with Theoretical Distributions—Comparative Analysis of the DGPS and EGNOS Systems in the Years 2006 and 2014

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 31
Author(s):  
Mariusz Specht
Keyword(s):  
Normal Distribution ◽  
Root Mean Square ◽  
Statistical Tests ◽  
Position Error ◽  
Positioning System ◽  
Navigation Systems ◽  
Mean Square ◽  
Positioning Systems ◽  
Position Errors ◽  
System Errors

Positioning systems are used to determine position coordinates in navigation (air, land and marine). The accuracy of an object’s position is described by the position error and a statistical analysis can determine its measures, which usually include: Root Mean Square (RMS), twice the Distance Root Mean Square (2DRMS), Circular Error Probable (CEP) and Spherical Probable Error (SEP). It is commonly assumed in navigation that position errors are random and that their distribution are consistent with the normal distribution. This assumption is based on the popularity of the Gauss distribution in science, the simplicity of calculating RMS values for 68% and 95% probabilities, as well as the intuitive perception of randomness in the statistics which this distribution reflects. It should be noted, however, that the necessary conditions for a random variable to be normally distributed include the independence of measurements and identical conditions of their realisation, which is not the case in the iterative method of determining successive positions, the filtration of coordinates or the dependence of the position error on meteorological conditions. In the preface to this publication, examples are provided which indicate that position errors in some navigation systems may not be consistent with the normal distribution. The subsequent section describes basic statistical tests for assessing the fit between the empirical and theoretical distributions (Anderson-Darling, chi-square and Kolmogorov-Smirnov). Next, statistical tests of the position error distributions of very long Differential Global Positioning System (DGPS) and European Geostationary Navigation Overlay Service (EGNOS) campaigns from different years (2006 and 2014) were performed with the number of measurements per session being 900’000 fixes. In addition, the paper discusses selected statistical distributions that fit the empirical measurement results better than the normal distribution. Research has shown that normal distribution is not the optimal statistical distribution to describe position errors of navigation systems. The distributions that describe navigation positioning system errors more accurately include: beta, gamma, logistic and lognormal distributions.

Validating GPS Based Measurements for Vehicle Control

2005 ◽  
Author(s):  
Kirstin L. Rock ◽  
Sven A. Beiker ◽  
Shad Laws ◽  
J. Christian Gerdes
Keyword(s):  
Excellent Agreement ◽  
Global Positioning System ◽  
Optical Sensor ◽  
State Observer ◽  
Vehicle Control ◽  
Positioning System ◽  
Sensor Systems ◽  
Global Positioning ◽  
Gps System

The increasingly widespread use of the Global Positioning System (GPS) in determining the location of vehicles raises the possibility of using the information provided by GPS for vehicle control purposes. The use of a multi-antenna GPS system provides the ability to measure not only position and velocity, but vehicle heading and sideslip as well. This paper presents a validation of a GPS based system with an automotive grade two-axis optical sensor. The results show excellent agreement between the two sensor systems, confirming the accuracy of the GPS based system even in highly dynamic situations. Although any GPS based system is subject to dropouts from driving under trees and bridges, cornering stiffness estimates obtained when GPS is available enable construction of a vehicle state observer for use in the absence of GPS.

Integrating Inertial Sensors With Global Positioning System (GPS) for Vehicle Dynamics Control

2004 ◽  
Vol 126 (2) ◽  
pp. 243-254 ◽  
Author(s):  
Jihan Ryu ◽  
J. Christian Gerdes
Keyword(s):  
Global Positioning System ◽  
Vehicle Dynamics ◽  
Inertial Sensors ◽  
Longitudinal Velocity ◽  
Positioning System ◽  
Sideslip Angle ◽  
Global Positioning ◽  
Reduce Measurement Error ◽  
Gps System ◽  
Vehicle Dynamics Control

This paper demonstrates a method of estimating several key vehicle states—sideslip angle, longitudinal velocity, roll and grade—by combining automotive grade inertial sensors with a Global Positioning System (GPS) receiver. Kinematic Kalman filters that are independent of uncertain vehicle parameters integrate the inertial sensors with GPS to provide high update estimates of the vehicle states and the sensor biases. Using a two-antenna GPS system, the effects of pitch and roll on the measurements can be quantified and are demonstrated to be quite significant in sideslip angle estimation. Employing the same GPS system as an input to the estimator, this paper develops a method that compensates for roll and pitch effects to improve the accuracy of the vehicle state and sensor bias estimates. In addition, calibration procedures for the sensitivity and cross-coupling of inertial sensors are provided to further reduce measurement error. The resulting state estimates compare well to the results from calibrated models and Kalman filter predictions and are clean enough to use in vehicle dynamics control systems without additional filtering.

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 Designing of Jamming-Resistant Global Positioning System Receiver

2019 ◽  
Vol 9 (1) ◽  
pp. 2497-2501
Keyword(s):  
Convergence Rate ◽  
Global Positioning System ◽  
Experimental Results ◽  
Online Version ◽  
Positioning System ◽  
Output Capacity ◽  
Global Positioning ◽  
Period Data ◽  
Gps System

The Global Positioning System (GPS) that guarantees the perfect location and period data has mostly used steering appliance for several applications. In this paper, Designing of Jamming-resistant GPS system receiver is propose to achieve impartial developments and the parameters are utilized to correctly compute the narrowband signals in the online version. The proposed algorithm can improve the faster convergence rate and improved inference correctness. The experimental results prove that the proposed method employs a good performance compared to the related methods in terms of Mean output capacity.

Marine Navigation with NAVSTAR/Global Positioning System (GPS) Today and in the Future

1982 ◽  
Vol 36 (1) ◽  
pp. 9-28 ◽  
Author(s):  
David E. Wells ◽  
Demitris Delikaraoglou ◽  
Petr Vaníč
Keyword(s):  
Global Positioning System ◽  
Navigation System ◽  
Positioning System ◽  
Eastern Canada ◽  
Satellite Navigation System ◽  
Satellite Constellation ◽  
Global Positioning ◽  
The Future ◽  
Gps System ◽  
Marine Navigation

The principles of operation of the NAVSTAR/GPS system are described within the context of the more familiar shore-based radionavigation systems, and of the Transit satellite navigation system. The present GPS satellite constellation of up to six prototype satellites, and the eventual constellation of up to 18 operational satellites are described. Some details of GPS signal structure, receiver operation, and error models are given. Results of our simulations of 1980 GPS marine navigation performance off eastern Canada are presented. These indicate GPS is presently capable of providing 150 m or better real-time positioning for about 11 hours a day in this region. GPS performance in the future is discussed.

scholarly journals Purwarupa Portable Global Positioning System

2015 ◽  
Vol 3 (1) ◽  
pp. 105
Author(s):  
Haniah . ◽  
Agfianto Eko Putra
Keyword(s):  
Global Positioning System ◽  
Positioning System ◽  
Gps Receiver ◽  
Average Deviation ◽  
Global Positioning ◽  
Lcd Display ◽  
Position Data ◽  
Gps System ◽  
To Receive ◽  
Static Point

AbstrakTelah dibuat sebuah sistem GPS portable menggunakan receiver GPS serta tampilan LCD 128X64. Sistem ini dapat membantu pengguna untuk mengetahui posisi mereka berada agar tidak tersesat. Sistem ini menampilkan data latitude, longitude, kecepatan dan waktu yang ditampilkan pada LCD 128X64. Sehingga pengguna bisa mengetahui posisi mereka dengan melihat posisi garis lintang dan garis bujur. Sistem ini dibuat dengan menggunakan mikrokontroler ATmega32 sebagai pemroses, GPS receiver Polstar PMB-688 untuk menerima data posisi dari satelit dan LCD 128X64 sebagai penampil. Sistem yang dibuat telah mampu menampilkan posisi garis lintang, garis bujur dan kecepatan secara akurat. Deviasi rata-rata untuk GPS portabel dibanding dengan GPS garmin adalah 1,753449 m ± 0,113532 m sedangkan deviasi rata-rata untuk kecepatan adalah 0,441 km/j ± 0,247 km/j.   Kata kunci— GPS, Posisi, Polstar PMB-688, Atmega32, Mikrokontroler.  Abstract Has created a portable GPS system uses a GPS receiver as well as an LCD display 128X64. This system can help users to identify where they are located so as not to get lost. This system displays the latitude, longitude, speed and time are displayed on the LCD 128X64. So users can know their position by looking at the position of latitude and longitude. This system using microcontroller ATmega32 as processor, GPS receiver Polstar PMB-688 to receive position data from satellites and LCD 128X64 as a viewer. The system is already capable of showing the position of the latitude, longitude and speed accurately. Average deviation for GPS portable than static point is 1.753449 m ± 0.113532 m while the average deviation for speed is 0.441000 kmh ± 0.247000 kmh. Keywords— GPS, Position, Polstar PMB-688, Atmega32, Mikrocontroller.

scholarly journals USE OF GLOBAL POSITIONING SYSTEM (GPS) FOR BASIC SURVEY ON STUDENTS

2019 ◽  
Vol 7 (1) ◽  
pp. 22-33
Author(s):  
Petrisly Perkasa
Keyword(s):  
Global Positioning System ◽  
Modern Technology ◽  
Base Station ◽  
Positioning System ◽  
Gps Receiver ◽  
The Us ◽  
Global Positioning ◽  
Gps System ◽  
In Transit ◽  
To Receive

As been coming ages, modern technology integrates into every life aspect including in field survey. Nowadays, one of the modern technology namely Global Positioning System (GPS). The GPS system was first developed by the US Department of Defense used for both military and civilian purposes. This system is designed to provide threedimensional position, speed, and information about world which is not affected by time and weather. Presently, GPS has been widely used by people all over the world who is need information about position, speed or time. To determine the coordinates of points on earth, the receiver requires at least 4 satellites to capture the signal correctly with the coordinates obtained referring to the global datum such World Geodetic System 1984 (WGS'84). GPS is divided into 3 types: Type of navigation or handheld, generally used in battle field or navigation purposes. Some vehicles have been equipped with GPS for navigation aids by adding a map to guide the rider thus rider know which pathway should be chosen to arrived at the destination. GPS mapping is a GPS tool used to calculate an area or create an important route in transit. Type Mapping has an accuracy level between 1-3 meters and mapping types require a base station serving to receive satellite signals and transmit them to a GPS receiver. Geodetic type is the most meticulous and most sophisticated type than navigation or mapping because it has a level of accuracy below 1 meter. The price of geodetic type is most expensive.

scholarly journals Circularly polarized microstrip patch antenna array for GPS application

2019 ◽  
Vol 15 (2) ◽  
pp. 920
Author(s):  
Taher Khalifa ◽  
N. M. Sahar ◽  
N. Ramli ◽  
M. T. Islam
Keyword(s):  
Antenna Array ◽  
Global Positioning System ◽  
Wireless Systems ◽  
High Gain ◽  
Positioning System ◽  
Circularly Polarized ◽  
Feed Line ◽  
Microstrip Patch ◽  
Global Positioning ◽  
Gps System

<span>The 12 elements antenna array for GPS system having high gain with circular polarization is presented in this paper. The circularly polarized antenna is very suitable for the use of various wireless systems such as Global Positioning System with operating frequency is 1.27 GHz with AR is less than 3 dB between 82˚ and 140˚.The antenna consists of twelve main radiation patches connected in parallel. The antennas array are designed on the Rogers RT5880 substrate with a dielectric constant (εr) of 2.2 and thickness is 0.787 mm. The antenna is excited with an inset feed line and it operates in L-band with a resonant frequency of 1.27 GHz.</span>

scholarly journals Modified WiFi-RSS Fingerprint Technique to locate Indoors-Smartphones: FENG building at Koya University as a case study

2017 ◽  
Vol 2 (3) ◽  
pp. 212-217 ◽  
Author(s):  
Halgurd S. Maghdid ◽  
Ladeh Sardar Abdulrahman ◽  
Mohammed H. Ahmed ◽  
Azhin Tahir Sabir
Keyword(s):  
Global Positioning System ◽  
High Performance ◽  
Low Cost ◽  
Satellite System ◽  
Positioning System ◽  
Global Positioning ◽  
Accurate Position ◽  
Global Navigation Satellite ◽  
Gps System

Positioning system used for different purposes and different services, many researches are going on to find a more accurate position with low error within high performance. There are many localization solutions with different architectures, configurations, accuracies and reliabilities for both outdoors and indoors. For example, Global Navigation Satellite System (GNSS) technology has been used for outdoors.  Global Positioning System (GPS) is one of the most common outdoors tracking solutions in the world, for outdoors, however, when indoors; it could not be accurately tracked users by using a GPS system. This is because, when users enters into indoors the GPS signals will no longer available due to blocked by the roof of buildings and it is no longer considered as a viable option.  WiFi Positioning System (WPS) can be used as an alternative solution to define users’ position, especially when GPS signal is not available. Further, WPS is a low cost solution, because there is no need to deploying WiFi Access Points (WAPs) in the vicinity, as they are installed to access the Internet. In this paper, specifically, WiFi-RSS Fingerprinting technique is used to locate smartphones using WAPs signals with a modified calculation. The new modified calculation is to dynamic weighting of the WAPs RSS values based on the real-live indoors structure. The achieved positioning accuracy, based on several trial experiments, is up to 6 meters via the implemented algorithm in the MALTAB.

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