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.

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.

An Overview of Positioning and Data Fusion Techniques Applied to Land Vehicle Navigation Systems

2010 ◽  
pp. 219-246 ◽  
Author(s):  
Denis Gingras
Keyword(s):  
Data Fusion ◽  
Mathematical Framework ◽  
Positioning System ◽  
Navigation Systems ◽  
Positioning Systems ◽  
Future Evolution ◽  
Land Vehicle Navigation ◽  
One Step ◽  
Definition Of ◽  
Position Estimate

In this chapter, the authors will review the problem of estimating in real-time the position of a vehicle for use in land navigation systems. After describing the application context and giving a definition of the problem, they will look at the mathematical framework and technologies involved to design positioning systems. The authors will compare the performance of some of the most popular data fusion approaches and provide some insights on their limitations and capabilities. They will then look at the case of robustness of the positioning system when one or some of the sensors are faulty and will describe how the positioning system can be made more robust and adaptive in order to take into account the occurrence of faulty or degraded sensors. Finally, they will go one step further and explore possible architectures for collaborative positioning systems, whereas many vehicles are interacting and exchanging data to improve their own position estimate. The chapter is concluded with some remarks on the future evolution of the field.

scholarly journals Adaptive Feedforward Control of a Pressure Compensated Differential Cylinder

2020 ◽  
Vol 10 (21) ◽  
pp. 7847
Author(s):  
Konrad Johan Jensen ◽  
Morten Kjeld Ebbesen ◽  
Michael Rygaard Hansen
Keyword(s):  
Control System ◽  
Root Mean Square ◽  
Motion Control ◽  
Experimental Verification ◽  
Feedforward Control ◽  
Position Error ◽  
Mean Square ◽  
Model Uncertainties ◽  
Feedforward Controller ◽  
Adaptive Feedforward

This paper presents the design, simulation and experimental verification of adaptive feedforward motion control for a hydraulic differential cylinder. The proposed solution is implemented on a hydraulic loader crane. Based on common adaptation methods, a typical electro-hydraulic motion control system has been extended with a novel adaptive feedforward controller that has two separate feedforward states, i.e, one for each direction of motion. Simulations show convergence of the feedforward states, as well as 23% reduction in root mean square (RMS) cylinder position error compared to a fixed gain feedforward controller. The experiments show an even more pronounced advantage of the proposed controller, with an 80% reduction in RMS cylinder position error, and that the separate feedforward states are able to adapt to model uncertainties in both directions of motion.

Evaluation Modeling and Optimal Adjustment of Position Error Based on Localization Sensitivity Analysis

2011 ◽  
Vol 697-698 ◽  
pp. 258-261
Author(s):  
G.Y. He ◽  
C.X. Hu ◽  
X. Liu
Keyword(s):  
Sensitivity Analysis ◽  
Evaluation Model ◽  
Geometric Error ◽  
Position Error ◽  
Position Errors ◽  
Surface Deviation ◽  
Optimal Adjustment ◽  
Fixture System ◽  
System Errors ◽  
The Relationship

Sensitivity analysis is to evaluate how sensitive the surface deviation of a workpiece is to a geometric error of locator. With this thinking, the relationship between geometric error of locators and the position error of holes group is presented. The fixture system errors model and evaluation model of position errors are established. Furthermore with both models, a method of optimizing the position errors by adjusting the locators’ position is presented, which can get to accuracy localization. At last, a simulation study is used to verify the method.

scholarly journals The Complexity Problem in Future Multisensor Navigation and Positioning Systems: A Modular Solution

2013 ◽  
Vol 67 (2) ◽  
pp. 311-326 ◽  
Author(s):  
Paul D. Groves
Keyword(s):  
Intellectual Property ◽  
Development Effort ◽  
Positioning System ◽  
Modular Approach ◽  
Navigation Systems ◽  
Integrated Navigation ◽  
Diverse Range ◽  
Positioning Systems ◽  
User Communities ◽  
Complexity Problem

Navigation and positioning system users are demanding greater accuracy and reliability in ever more challenging environments. This is driving a wave of rapid innovation, with the result that multisensor integrated navigation systems will become much more complex. This introduces a number of problems, including how to find the necessary expertise to integrate a diverse range of technologies, how to combine technologies from different organisations that wish to protect their intellectual property, and how to incorporate new navigation technologies and methods without having to redesign the whole system. It also makes it desirable to share development effort over a range of different applications. To address this, the feasibility of a modular approach to the design and development of multisensor integrated navigation and positioning systems is analysed. Assessments of the requirements of different user communities and the adaptability of the different navigation and positioning technologies to different contexts and requirements are presented. Based on this, the adoption of an open interface standard for modular integration is recommended and the issues to be resolved in developing that standard are outlined.

scholarly journals Application of areal interpolation methods when determining zones of potential fertility of soils of agricultural lands

2021 ◽  
Vol 27 (4) ◽  
pp. 120-134
Author(s):  
Nikolay Klebanovich ◽  
Arkady Kindeev ◽  
Vitalina Kizeeva
Keyword(s):  
Soil Fertility ◽  
Normal Distribution ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Humus Content ◽  
Mean Square ◽  
Areal Interpolation ◽  
Advantages And Disadvantages ◽  
Verification Methods ◽  
Mean Square Errors

The article presents one of the possible options for improving the methodology for identifying zones of potential soil fertility. The necessity of using areal interpolation as the only method of geostatistical analysis that takes into account the area of input objects is proved. To check the data for a Gaussian normal distribution, it is necessary to use several verification methods, since when evaluating only statistical parameters, significant (in the case of phosphorus, abnormal) deviations were found, however, when evaluating histograms and quartile-quartile plots, it is necessary to bring the data to a normal distribution was relevant only for humus and phosphorus. The main advantages and disadvantages of the areal interpolation method are shown. With a significant deviation from the normal distribution, in the absence of built-in functions for automated reduction of data to the Gaussian distribution, one of the few ways can be the logarithm of the data. After zoning, it is necessary to perform a reverse translation to the original values for a representative visualization of the results. As a result of the selection of theoretical semivariograms-deconvolutions, the degrees of spatial dependence and optimal distances for the studied properties are determined. It is clear that the lag of acidity and potassium content is 1000 m and 1050 m, respectively. For phosphorus, it is 1300 m. For the humus content, the lag is much lower—440 m. The maximum autocorrelation distance is typical for potassium and humus—2330 and 1528 m; the minimum for phosphorus is 637. The reliability of the cartograms of agrochemical properties is confirmed by the calculated root-mean-square errors. The deviations of pH values are in the range of up to 0.15 units. The highest mean square error of interpolation is observed in weakly acidic soils. The error in the interpolated values of humus from the initial data is inherent in anthropogenically transformed soils. The root-mean-square error of phosphorus values can be estimated as insignificant. The largest errors in K2O—in isolated cases, they reach 120 mg/ha in the central and eastern parts of the region. The resulting map of potential soil fertility was used to determine the relationship with the granulometric composition of soils. A low level is observed on sandy and sandy loam soils, a high level—on loams. Also, the productivity is affected by the relief of the territory—in the dissected areas, productivity is lower than on the plains.

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 Performance Evaluation of Precise Point Positioning Using Dual Frequency Multi-GNSS Observations

2020 ◽  
Vol 55 (4) ◽  
pp. 150-170
Author(s):  
Jabir Shabbir Malik
Keyword(s):  
Root Mean Square ◽  
Precise Point Positioning ◽  
Convergence Time ◽  
Observation Data ◽  
Three Dimension ◽  
Mean Square ◽  
Positioning Accuracy ◽  
Position Accuracy ◽  
Position Errors ◽  
Point Positioning

AbstractIn addition to GPS and GLONASS constellation, the number of (Global Navigation Satellite System) GNSS satellites are increasing, it is now possible to evaluate and analyze the position accuracy with multi GNSS constellation. In this paper, statistical assessment of static Precise Point Positioning (PPP) using GPS, GLONASS, dual system GPS/GLONASS, three system GPS/GLONASS/Galileo, GPS/GLONASS/BeiDou and multi system GPS/GLONASS/Galileo/BeiDou PPP combinations is evaluated. Observation data of seven whole days from seven IGS multi GNSS experiment (MGEX) stations is used for analysis. Position accuracy and convergence time is analyzed. Results show that the GPS/GLONASS positioning accuracy increases over GPS PPP. Standard deviations (STDs) of position errors for GPS PPP are 4.63, 3.00 and 6.96 cm in east, north and up components while STDs for GPS/GLONASS PPP are 4.10, 3.42 and 6.50 cm respectively. Root mean square for three dimension (RMS3D) for GPS/GLONASS PPP solution is 8.96 cm. With the addition of Galileo and BeiDou to the combined GPS/GLONASS further enhances the positioning accuracy. Root mean square for horizontal component reach to 5.35 cm of GPS/GLONASS/Galileo/BeiDou PPP solutions. Results analysis of GPS/GLONASS/Galileo PPP solutions show an improvement of convergence time by only 3.81% to achieve accuracy level of 3.0 cm over GPS/GLONASS/BeiDou PPP mode. Results also demonstrate that position accuracy improvement after adding BeiDou observations to the GPS/GLONASS PPP mode is not significant.

scholarly journals DESIGN AND FABRICATION OF RUNNING CHEETAH MECHANICAL TOY USING FOUR-BAR LINKAGE

2020 ◽  
Vol 5 (4) ◽  
pp. 53-60
Author(s):  
Adimas Wicaksana
Keyword(s):  
Root Mean Square ◽  
Closed Loop ◽  
Design Method ◽  
Position Error ◽  
Prototype Model ◽  
Mean Square ◽  
Four Bar Linkage ◽  
Novel Design

Four-bar is the simplest planar 1-DOF closed loop linkage. It has been studied for centuries for its versatility and simplicity. In this paper a novel design method to obtain a four-bar linkage given a path and its endpoints will be presented. This method will then be applied to a case study of making a model that produces a specified movement based on reference animation. The mechanism obtained had an average root-mean-square of position error of roughly 14.3 pixels for front leg and 25.9 pixels for hind leg. This number is quite small compared to the perimeter of the traced path, which are 530 pixels and 617 pixels for front leg and hind leg respectively. A prototype model of the designed mechanism was fabricated to verify its manufacturing viability and to confirm the correctness of the path generated.

scholarly journals Trueness of digital implant impressions based on implant angulation and scan body materials

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jae-Hyun Lee ◽  
Jae-Hwi Bae ◽  
Su Young Lee
Keyword(s):  
Root Mean Square ◽  
Statistical Tests ◽  
In Vitro Study ◽  
Mean Square ◽  
Second Molar ◽  
Impression Accuracy ◽  
Scan Data ◽  
The Right ◽  
Nonparametric Statistical

AbstractEffects of implant angulation on digital implant impression accuracy remain controversial. Therefore, this in vitro study aimed to compare the digital implant impression trueness among models with different implant angulations and scan body materials. Six partially edentulous mandibular models with dental implants on the right second premolar and second molar areas were categorized according to the implant angulation of the distal implant (parallel, or 15° mesially or lingually tilted compared to the mesial implant) and scan body materials (polyetheretherketone or titanium). After scanning each model with intraoral scanners, the root mean square and within-tolerance values were calculated with respect to the reference, and nonparametric statistical tests were performed (α = .05). Scan data from models with the mesially tilted distal implant showed better trueness than the corresponding parallel and lingually tilted groups in terms of root mean square values (p < .017). The root mean square value in the titanium scan body group was lower than that in the polyetheretherketone scan body group (p < .001). However, the percentage within a tolerance of ± .1 mm was higher in the polyetheretherketone scan body group than in the titanium scan body group (p = .001). Intraoral scan data of models where the terminal implant was mesially tilted showed better trueness.

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