Positioning Error Distribution Research Articles

An evaluation of the BALROG and RoboBA algorithms for determining the position of Fermi/GBM GRBs

Abstract The Fermi/GBM instrument is a vital source of detections of gamma-ray bursts and has an increasingly important role to play in understanding gravitational-wave transients. In both cases, its impact is increased by accurate positions with reliable uncertainties. We evaluate the RoboBA and BALROG algorithms for determining the position of gamma-ray bursts detected by the Fermi/GBM instrument. We construct a sample of 54 bursts with detections both by Swift/BAT and by Fermi/GBM. We then compare the positions predicted by RoboBA and BALROG with the positions measured by BAT, which we can assume to be the true position. We find that RoboBA and BALROG are similarly precise for bright bursts whose uncertainties are dominated by systematic errors, but RoboBA performs better for faint bursts whose uncertainties are dominated by statistical noise. We further find that the uncertainties in the positions predicted by RoboBA are consistent with the distribution of position errors, whereas BALROG seems to be underestimating the uncertainties by a factor of about two. Additionally, we consider the implications of these results for the follow-up of the optical afterglows of Fermi/GBM bursts. In particular, for the DDOTI wide-field imager we conclude that a single pointing is best. Our sample would allow a similar study to be carried out for other telescopes.

High Accuracy Localization Scheme Using 1-Bit Side Information: Achievability from a GDoP Perspective

In this paper, we provide a novel methodology for high-precision positioning that utilizes 1-bit additional information, which applies to various positioning techniques. The proposed approach leverages binary information to indicate if a user is within a specified space of interest and refines the estimated location information outside this area. By matching the estimated locations outside the area of interest with the valid location information within, this methodology corrects the positional data obtained through any arbitrary positioning technique, aligning the estimated positions with the intended spatial boundaries. Performance analysis metrics, such as Average Positioning Error (APE) and Cumulative Distribution Function for positioning coverage, were employed to assess the effectiveness of the proposed methods. Numerical simulations demonstrate how the proposed method enhances the averaged positioning accuracy, significantly outperforming the conventional time of arrival method. Furthermore, the proposed positioning correction methodology demonstrates validated feasibility applicable to an arbitrary existing positioning method.

Error Modeling and Accuracy Analysis of Parallel Robots for Spacecraft Docking Motion Simulation System

Background:: A large number of on-orbit docking dynamics experiments are conducted in the spacecraft docking motion simulation system with the development of Chinese space science and technology, and therefore, the requirement for high-precision parallel robots has increased. The pose accuracy of parallel robots is one of the most important problems in this application. Objective:: In order to evaluate the pose accuracy of parallel robots in advance, a comprehensive pose accuracy analysis method considering major error sources is presented in this paper, and the influence of major error sources on the pose accuracy is also investigated to summarize the statistics and propagation characteristics of the pose error. Methods:: The first-order error model for the parallel robot is established based on a generalized error model for each hydraulic cylinder and a sensitivity analysis method. Using the error model, a statistical approach to the parallel robot pose accuracy analysis is presented, and the influence of different parameter errors and different poses on the pose accuracy of the parallel robot is investigated. Sensitivity analysis is applied to evaluate the contribution of each parameter error to the position and orientation error of the parallel robot. An automated pose accuracy analysis program that computes and graphically displays the position and orientation error distributions and the sensitivity analysis results is developed. Results: The statistical analysis results of the influence of different parameter errors and different poses on pose accuracy are obtained by using the automated pose accuracy analysis program. The means of the position and orientation errors are close to zero. The standard deviations in the x and y directions are larger than those in the z direction, and these standard deviations are amplified with the increase of the parameter errors. For the given elevation, sensitivity analysis to various parameter errors is performed. It is found that the length error sensitivities of the hydraulic cylinders are less than one, and position error sensitivities of the hook joints A4, A5, and A6 are much greater than those of hook joints A1, A2 and A3. Conclusion:: The elemental error sources belong to one of two groups, i.e., those affecting the hydraulic cylinder length and those affecting the hook joints. The distributions of the position and orientation errors are consistent with statistics theories. The parallel robot is more sensitive to the errors affecting the hook joints than those affecting the hydraulic cylinder length. These will help the designers and users of the parallel robot understand the statistics and propagation characteristics of the pose error. Some recent patents on error modeling and kinematic calibration of parallel robots are also discussed in this article.

Review of the Monothematic Series of Publications Concerning Research on Statistical Distributions of Navigation Positioning System Errors

This review presents the main results of the author’s study, obtained as part of the post-doctoral (habilitation) dissertation entitled “Research on Statistical Distributions of Navigation Positioning System Errors”, which constitutes a series of five thematically linked scientific publications. The main scientific aim of this series is to answer the question of what statistical distributions follow the position errors of navigation systems, such as Differential Global Positioning System (DGPS), European Geostationary Navigation Overlay Service (EGNOS), Global Positioning System (GPS), and others. All of the positioning systems under study (Decca Navigator, DGPS, EGNOS, and GPS) are characterised by the Position Random Walk (PRW), which means that latitude and longitude errors do not appear randomly, being a feature of the normal distribution. The research showed that the Gaussian distribution is not an optimal distribution for the modelling of navigation positioning system errors. A higher fit to the 1D and 2D position errors was exhibited by such distributions as beta, gamma, and lognormal. Moreover, it was proven that the Twice the Distance Root Mean Square (2DRMS(2D)) measure, which assumes a priori normal distribution of position errors in relation to latitude and latitude, was smaller by 10–14% than the position error value from which 95% fixes were smaller (it is known as the R95(2D) measure).

Motion error analysis of a shield machine tool-changing robot based on a screw-vector method

Industrial robots are widely used in various industrial fields, such as handling and welding, due to their good repeat positioning accuracy. The motion error determines the absolute accuracy. For robot design, dimensional parameter errors and drive parameter errors, a mathematical model of a kinematic exponential product with error screws was proposed. The influence of different rod lengths and transmission errors on the accuracy of the end motion was analysed. A composite analysis method based on screw theory and vector method is proposed for the spatial deflection error of robot rotating joints with clearance. By using screw theory, a mathematical error model of the axial movement and spatial deflection of the joint gap was established. A mathematical model of joint space radial movement was established by using the three-dimensional vector method. Through numerical simulation, the position distribution law of the random error of the robot terminal in the workspace and the distribution of the plane projection density were obtained. By solving the attitude matrix, the distribution of each Euler angle error was obtained. A simulation test was carried out to verify the model's correctness. The calculation showed that the method is simple and correct, and the obtained error distribution characteristics are of great significance to improving robotic kinematic calibration accuracy and optimising the spatial position error distribution.

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

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.

Determination of control network accuracy and coordinates of control points in facade surveying

The paper presents ways to determine the positions of control points with electronic total stations of varying accuracy from 1 to 5 seconds with and without reflectors at the sighting points, depending on the degree of vertical and horizontal positioning to the control points located at a distance of 50 m. It provides accuracy parameters of points in a high-order control network, containing root-mean-square positioning errors, the resultant error, the sizes and orientations of the semiaxes of the error ellipses and root-mean-square positioning error distributions. The paper considers an algorithm for performing facade surveying.

Data‐driven protection levels for camera and 3D map‐based safe urban localization

<h3>Abstract</h3> Reliably assessing the error in an estimated vehicle position is integral for ensuring the vehicle’s safety in urban environments. Many existing approaches use GNSS measurements to characterize protection levels (PLs) as probabilistic upper bounds on position error. However, GNSS signals might be reflected or blocked in urban environments, and thus additional sensor modalities need to be considered to determine PLs. In this paper, we propose an approach for computing PLs by matching camera image measurements to a LiDAR-based 3D map of the environment. We specify a Gaussian mixture model probability distribution of position error using deep neural-network-based data-driven models and statistical outlier weighting techniques. From the probability distribution, we compute PL by evaluating the position error bound using numerical line-search methods. Through experimental validation with real-world data, we demonstrate that the PLs computed from our method are reliable bounds on the position error in urban environments.

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

AbstractResearch into statistical distributions ofφ,λand 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 empiricalφandλerrors 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 ofφandλerrors 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 thatφandλerrors for the GPS system are normally distributed. It is proven thatφandλerrors are more concentrated around the central value than in a typical normal distribution (positive kurtosis) with a low value of asymmetry. Moreover,φerrors are clearly more concentrated thanλerrors. This results in larger standard deviation values forφerrors thanλerrors. 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.

Employing DIALux to relieve machine-learning training data collection when designing indoor positioning systems.

We propose and demonstrate using the DIALux software with our proposed linear-regression machine-learning (LRML) algorithm for designing a practical indoor visible light positioning (VLP) system. Experimental results reveal that the average position errors and error distributions of the model trained via the DIALux simulation and trained via the experimental data match with each other. This implies that the training data can be generated in DIALux if the room dimensions and LED luminary parameters are available. The proposed scheme could relieve the burden of training data collection in VLP systems.

Positioning accuracy reliability analysis of industrial robots based on differential kinematics and saddlepoint approximation

This paper proposes a new positioning accuracy reliability analysis method based on the differential kinematics and saddlepoint approximation to evaluate the influence of kinematic parameter uncertainties on the robotic motion. Firstly, considering the reliability analysis instability caused by complex nonlinear limit state function, the reliability model of positioning accuracy is established based on the differential kinematics and error propagation. Subsequently, the parameters of the position error distribution are deduced analytically to combine with the eigen-decomposition to complete the modeling of the cumulant generating function, thereby the kinematic reliability is yielded according to the saddlepoint approximation method. Finally, the comparative analysis of a six degrees of freedom serial industrial robot is conducted and the results of which demonstrate that the proposed method provides a better performance than the existing methods in terms of accuracy and efficiency for kinematic reliability analysis.

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.

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.

Characterizing Positioning Errors When Using the Second-Generation Australian Satellite-Based Augmentation System

Abstract Fault detection and exclusion (FDE) is the main task for pre-processing of global navigation satellite system (GNSS) positions and is a fundamental process in integrity monitoring that is needed to achieve reliable positioning for applications such as in intelligent transport systems. A widely used method is the solution separation (SS) algorithm. The FDE in SS traditionally builds the models assuming positioning errors are normally distributed. However, in urban environments, this traditional assumption may no longer be valid. The objective of this study is to investigate this and further examine the performance of alternative distributions, which can be useful for FDE modelling and thus improved navigation. In particular, it investigates characterization of positioning errors using GNSS when the Australian satellite-based augmentation system (SBAS) test bed is used, which comprised different positioning modes, including single-point positioning (SPP) using the L1 global positioning system (GPS) legacy SBAS, the second-generation dual-frequency multi-constellation (DFMC) SBAS service for GPS and Galileo, and, finally, precise point positioning (PPP) using GPS and Galileo observations. Statistical analyses are carried out to study the position error distributions over different possible operational environments, including open sky, low-density urban environment, and high-density urban environment. Significant autocorrelation values are also found over all areas. This, however, is more evident for PPP solution. Furthermore, the applied distribution analyses applied suggest that in addition to the normal distribution, logistic, Weibull, and gamma distribution functions can fit the error data in various cases. This information can be used in building more representative FDE models according to the work environment.

Adapted Error Map Based Mobile Robot UWB Indoor Positioning

Ultrawideband (UWB) has gained a lot of attention in indoor positioning due to its high time resolution, whereas its accuracy could be easily affected by the indoor environment. A UWB error map could represent the distribution of the positioning errors in a static indoor space and help to improve the accuracy of indoor positioning. However, the building of the error map needs much work. In this article, we propose a UWB error map building method, which adapts the distribution of positioning error measurement points to a rough positioning error distribution. An adapted error map based particle filter (AEMBPF), which adopts the error map in the initialization and weight update of the particle set, is then proposed to improve the accuracy of UWB positioning. The experimental results have shown a nearly 50% reduction in the number of measurement points and better positioning accuracy with faster convergence speed.

Introducing operator characteristic curves to define appropriate frequency of quality control tests: A case study involving whole breast radiotherapy image guidance

Background and purposeSampling theory and operator characteristic curves are methods that can determine an optimal schedule for quality control tests. We apply this method to positional data for whole breast radiotherapy since several surveys report inconsistent image guidance practice for this technique. Materials and methodsPositional errors were defined, for 55 consecutive breast cancer patients, by comparing the central lung distance measured on portal images with that obtained from the corresponding digitally reconstructed radiograph. From the distribution of positional errors, the probability of a setup error >5 mm in the direction of the mediastinum was established. Using operator characteristic curves, we compared the effectiveness of various image-guidance schedules in dealing with such errors. We also calculated the dosimetric impact of undetected errors. ResultsSetup errors >5 mm towards the mediastinum for this cohort were unlikely, at 2.7%. Imaging half of the fractions protects most patients against three or more undetected errors. Undetected, such an error increases, on average, the maximum dose to 10 cm3 of the heart by 50 cGy, the mean heart dose by 4 cGy, and the left lung V20Gy by 0.2%; therefore, the clinical impact is minute. Given that detected positional errors outside of tolerance are corrected, their residual likelihood decreases with the ratio of fractions being imaged. ConclusionsFor most tangential breast radiotherapy patients, setup errors >5 mm towards the mediastinum are unlikely, and their dosimetric impact is remote. Imaging half of the fractions of a course of whole breast radiotherapy prevents these errors to occur more than twice.

Development of a subject-specific guide system for Low-Intensity Focused Ultrasound (LIFU) brain stimulation

Low-Intensity Focused Ultrasound (LIFU) has recently been considered as a promising neuromodulation technique because it can noninvasively stimulate the brain with a high spatial resolution. As spatial resolution is improved, there is a growing demand for developing more accurate and convenient guide systems. Therefore, in the present study, we have developed and prototyped a 3D printed wearable subject-specific helmet for LIFU stimulation that is guaranteed to be accurate. The spatial relationship between the target position and the full-width at half-maximum (FWHM) of acoustic pressure of the transducer, i.e. focal volume, was compared using the conventional image-guided navigation system. According to the distribution of positional errors, the target position was located well within the focal volume.

Research on distribution of aperture position error in multi-beam coherent imaging and its impact on image quality

Research on distribution of aperture position error in multi-beam coherent imaging and its impact on image quality

The Performance of Global Models in TC Track Forecasting Over the Western North Pacific from 2010 to 2012

ABSTRACT Forecasts of tropical cyclone (TC) tracks from six global models during 2010 and 2012 were assessed to study the current capability of track forecast guidance over the western North Pacific. To measure the performance of the global model forecasts, a series of statistical evaluations of track forecasts up to 120 h were carried out, including the mean, median, percentile distribution, regional distribution, relative position, correlation analysis, and binned analysis. Results showed that certain improvements have been made for the six global models in their prediction accuracy and stability in the past three years. Remarkably, stepped decreases in the values of each quantile were found at all lead time levels from 2010 to 2012 for NCEP-GFS. an analysis of the regional distribution of position errors showed that a high-latitude region, low-latitude region (which covers mostly the TC genesis region) and the South China Sea are the three main areas within which large errors tend to concentrate. The majority of the models show their own respective characteristics of systematic bias at each lead time, as established through the relative position analysis results. Only the results of NCEP-GFS and CMA-T639 did not show any obvious systematic bias in the three-year study period. Binned analyses indicated that the prediction accuracy and stability of most of the models were better for strong TCs than for weak TCs at short lead time levels. It was also found that the models tend to perform better for initially large TCs, or for those with weak vertical wind shear at lead times shorter than 48 h. The results demonstrate the heavy reliance of forecast errors upon the initial characteristics of a TC or its environmental conditions.

144. Metric for assessment of mechanical reproducibility of leaves positions during VMAT treatment

Purpose To assess mechanical reproducibility of Multi Leaf Collimator (MLC) leaves positions during VMAT delivery and to formulate a suitable metric for daily quality assurance (QA) measurements. Methods A plan consisting of 2 dynamic arcs (CW and CCW) has been delivered on a Varian linac for 12 months (444 total arcs) as daily QA to assess MLC Long Term Reproducibility (LTR) and 10 times consecutively (20 total arcs) for Short Term Reproducibility (STR). Dynalog files were generated from the linac and analyzed in MatLAB environment. The distribution of the positioning errors of MLC weighted for leaves aperture was calculated for every delivery. An Index Error (IE) was calculated as the percentiles of these distributions that minimize the CV among the sampled data (Fig. 1): average values ( X m ) and standard deviations (SD) were calculated in order to define the thresholds for 95% of statistic confidence of the sample (TH = X m + 2SD). IE is calculated with daily frequency and the percentage of events out of TH is evaluated including a window data of 1 month. The Attention Level (AL) is reached when the number of the events (Fig. 2) out of threshold is the 5% of the sample. The events out of the statistic confidence are related to mechanical mismatch of MLC during delivery. Results The minimization CV value is obtained for the 49th percentile of MLC weighted positioning error distribution. The trends of average, SD and CV for the LTR and STR (Table) samples are similar this means the absence of perturbative boundary conditions. During monitoring of MLC performance the method highlighted the beginning of the malfunction (blue-line in Fig. 2) and the subsequent return into the limits following the maintenance service. Conclusions The IE calculated as 49th percentile of MLC positioning error distributions can be used to define an AL for MLC performance monitoring for VMAT delivery and daily QA. The proposed metric provides a strong method for monitoring mechanical errors during VMAT plans. Furthermore, a mechanical equivalence between linacs could be assessed to ensure a safe machine switching when service is occurring.

Action and perception in literacy: A common-code for spelling and reading.

There is strong evidence that reading and spelling in alphabetical scripts depend on a shared representation (common-coding). However, computational models usually treat the two skills separately, producing a wide variety of proposals as to how the identity and position of letters is represented. This article treats reading and spelling in terms of the common-coding hypothesis for perception-action coupling. Empirical evidence for common representations in spelling-reading is reviewed. A novel version of the Start-End Competitive Queuing (SE-CQ) spelling model is introduced, and tested against the distribution of positional errors in Letter Position Dysgraphia, data from intralist intrusion errors in spelling to dictation, and dysgraphia because of nonperipheral neglect. It is argued that no other current model is equally capable of explaining this range of data. To pursue the common-coding hypothesis, the representation used in SE-CQ is applied, without modification, to the coding of letter identity and position for reading and lexical access, and a lexical matching rule for the representation is proposed (Start End Position Code model, SE-PC). Simulations show the model's compatibility with benchmark findings from form priming, its ability to account for positional effects in letter identification priming and the positional distribution of perseverative intrusion errors. The model supports the view that spelling and reading use a common orthographic description, providing a well-defined account of the major features of this representation. (PsycINFO Database Record