Circular Error Research Articles

Study on Mathematical Model of Radial Runout Error

According to the standard definition of radial circular error, set up any space surface radial runout errors of least squares mathematics model. The coordinate origin of the model can be freely selected, nor equal angle interval among discrete sampling points. Analysis by computer simulation, results show that the model developed is right and pratical. On the basis of mathematical models, using four direct algorithm for unconstrained optimization, radial runout errors can be evaluated in accordance with the minimum conditions. Mathematical models can be used for three-coordinate measuring machine and also available for other intelligent instrument for measuring parts of the radial runout errors.

어선원 인명피해 최소화를 위한 구명동의용 위성자동위치발신기의 특성

The efficiency tests of automatic positioning transmitter (APT) using satellite on life jacket were carried out to minimize casualties of fishermen and to make system optimization for effective SAR (Search and Rescue) operation. As the result of the tests, average position was equaled on the comparison between SPOT using low earth orbit satellite and DGPS (Differential Global Positining System), but standard deviation of DGPS for latitude and longitude were 66.4% and 46.3% smaller than those of SPOT. The position precision of SPOT was almost two times lower than LGT using geostationary satellite to compare 95% circular error probability. However, the success rate of receiver for SPOT was revealed as 86.5~94.1% on the experiments in the South Sea and the West Sea and it was 4.5 times higher than LGT. Therefore, SPOT is expected to contribute greatly to the rapid rescue of victim.

GENERATION OF THE AUSTRALIAN GEOGRAPHIC REFERENCE IMAGE THROUGH LONG-STRIP ALOS PRISM ORIENTATION

Abstract. The Australian Geographic Reference Image (AGRI) is a national satellite image mosaic that covers the vast Australian continent. Formed from 9560 ALOS PRISM images, AGRI provides a spatially correct reference image at 2.5 m resolution, with 1-pixel accuracy. The production of AGRI was made feasible by the development and implementation of a long-strip adjustment technique that facilitated a refinement in the georeferencing process of orbit and attitude parameters for orbital segments comprising 50 or more images. The strip of images is effectively treated as a single image. The ground control requirements for such full-pass georeferencing, which does not require the measurement of tie or pass points, amount to only 4–8 GCPs for the complete strip rather than 4 or more per image within the strip. Once the adjusted orbit parameters are obtained, the georeferencing and orthorectification process can revert to a fully automatic image-by-image computation. This paper first overviews AGRI and then describes the longstrip adjustment technique that made its production possible. Testing and validation are then discussed via the example of the georeferencing of a 1527 km single strip of 55 PRISM images. The testing phase verified that 1-pixel accuracy georeferencing could be achieved with the long-strip adjustment approach, and in the production of AGRI accuracy checks against 2460 checkpoints yielded an RMS discrepancy of close to 2.5 m and a 90% Circular Error (CEP90) of 5.5 m.

Investigation of Flexure Effect on Transfer Alignment Performance

Transfer Alignment (TA) is the initialisation process of the Inertial Navigation System (INS) of an air-launched weapon before its release by using the data from the aircraft INS. The aim of this paper is to improve the TA performance by taking into account the aircraft flexures deterministically. The developed procedure neither requires captive carry tests for determination of flexures nor increases the size of the problem, and can be used in real-time missions of any type of military aircraft. The procedure is evaluated for the Velocity Match (VM) method as well as the Velocity and Attitude Match (VAM) method, which are applied through a Kalman Filter (KF). Using a short-time Wing-Rock (WR) manoeuvre, the results of both methods are compared to each other for two cases in which either the flexures are taken into account deterministically, or modelled as noise by assuming that they are unknown. Standard deviations of the errors and the Circular Error Probable (CEP) variations have shown that the TA performance of the VAM method can be much improved if aircraft flexures are incorporated deterministically into the method. The improved performance makes possible target of opportunity missions at shorter weapon ranges, and it decreases target strike errors.

Assessing circular error probable when the errors are elliptical normal

An important problem of continuing interest to engineers is the need to assess the circular error probable (CEP), a measure of the impact accuracy of a projectile or a measure of GPS point positioning accuracy. One of the challenges in addressing this problem is to construct some accurate confidence bounds or intervals for CEP in the small sample settings, where certain amount of systematic biases exist in testing experiments. Currently there is no general method available to deal with this challenge due to the intractability of the distributions of the existing CEP estimators. In this paper, in order to meet this challenge, several new approximate formulas are derived for calculating CEP, which are more accurate than the existing ones but still simple to use. Both exact and empirical expressions for the derivatives of CEP with respect to the population means and variances are also given. Using these formulas, three kinds of confidence bounds or intervals for CEP are proposed, which are based on the parametric bootstrap, the asymptotic distribution, and the Cornish–Fisher expansion, respectively. Moreover, a bias-corrected estimator of CEP is provided. The performances of these procedures are evaluated based on some Monte Carlo simulation studies. Both the theoretical and simulation results show that the Cornish–Fisher expansion-based procedure performs slightly better than the other two procedures when the downrange and cross-range variances are assumed the same. However, when these two variances are different, the simulation demonstrates that the bootstrap approach can be superior to the Cornish–Fisher for the small samples (say n=10), and vice versa for the moderate samples (say n=20).

Reconstructing NC Program-Based Geometrical Error Compensation for Heavy-Duty NC Machine Tool

Heavy-duty NC machine tool is difficult and costly to evidently improve their precision via manufacturing technology only. It is proved being an effective approach to improve machine tool manufacturing precision based on software error compensation. In this paper, an error compensation algorithm based on reconstructing NC program is discussed. Following comprehensive discussion on basic algorithm of positioning error compensation in detail, linear interpolation and circular interpolation movement error compensation algorithm are further sketched in brief. To decrease the machining error, NC program is reconstructed before actual machining. The experiment results show that error compensation methods based on reconstructing NC program can improve profile accuracy of heavy-duty NC machine tools obviously.

Position determination using the DTV segment sync signal

As a supplement to the Global Positioning System (GPS) in an urban center and indoor environment, the digital television (DTV) segment sync signal can be employed to obtain a mobile user’s position. Two DTV receivers and a counter are integrated to measure the time difference of arrival (TDOA) for a pair of received signals from a transmitter and its corresponding repeater (DTVR). Using the measurements from a transmitter and its multiple corresponding DTVR pairs, the mobile user position can be estimated using the recursive least square method. An experiment done in Seoul using two low-grade high resolution digital television (HDTV) receivers and a two-channel universal counter demonstrates that the mean value of the mobile user position measurement is accurate to 42.58 meters circular error probability (CEP).

Measuring positional error of circular curve features in Geographic information systems (GIS)

This paper addresses the task of modeling positional uncertainty of circular features. The specific interest provided by this study is the consideration of the actual curve function in the measurement of circular curve error. This approach differs from the existing methods based on line segment approximation. A least-squares adjustment method, composed of a series of discrete points and the covariance of these parameters, is adopted to estimate the parameters of a circular curve. Two geometric measures are developed, based on the error ellipses of the points on the circular curve: the standard deviation-based measure and the maximum distance-based measure. A comparison of the two measures for circular curves was conducted by means of a simulation experiment. The implementation of the two geometric measures is further illustrated by two case studies; one describes the positional error of digital shorelines and the other digitizes circular road curves.

Quantifying Circular-Linear Associations: Hippocampal Phase Precession

Event Abstract Back to Event Quantifying Circular-Linear Associations: Hippocampal Phase Precession Richard Kempter1, 2*, Christian Leibold3, 4 and Robert Schmidt1, 2 1 Humboldt-Universität zu Berlin, Bernstein Center for Computational Neuroscience Berlin, Germany 2 Humboldt-Universität zu Berlin, Institute for Theoretical Biology, Germany 3 University of Munich, Bernstein Center for Computational Neuroscience Munich, Germany 4 University of Munich, Department of Biology II, Germany When a rat crosses the place field of a hippocampal pyramidal cell, this cell typically fires a series of action potentials. The phases of these spikes, measured with respect to theta oscillations of the field potential, decrease as a function of the spatial distance traveled (Figure 1). This relation between phase and position of spikes is called phase precession. The degree of association between the circular phase variable and the linear spatial variable is commonly quantified through, however, a linear-linear correlation coefficient: the circular variable is converted to a linear variable by restricting the phase to a chosen range. Here we show how and why this procedure can bias estimates of the correlation as well as the slope and offset of the regression line, and that there is a strong dependence on noise and sample size. To overcome these problems, we introduce a new measure to quantify circular-linear associations. This approach is based on the minimization of a circular error, and it leads to a robust estimate of the slope and phase offset of the regression line. Finally, a correlation coefficient for circular-linear data is derived that is a natural analog of the Pearson's product moment correlation coefficient for linear-linear data. Figure 1: Phase precession in the rat CA1 region from pooled data (top row) and single trials (bottom rows). Spike data (black dots) has been fitted with different methods (grey: linear-linear; red: circular-linear fit constrained to negative slopes; blue: circular-linear fit allowing both positive and negative slopes). Figure 1 Keywords: computational neuroscience Conference: Bernstein Conference on Computational Neuroscience, Berlin, Germany, 27 Sep - 1 Oct, 2010. Presentation Type: Presentation Topic: Bernstein Conference on Computational Neuroscience Citation: Kempter R, Leibold C and Schmidt R (2010). Quantifying Circular-Linear Associations: Hippocampal Phase Precession. Front. Comput. Neurosci. Conference Abstract: Bernstein Conference on Computational Neuroscience. doi: 10.3389/conf.fncom.2010.51.00009 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 08 Sep 2010; Published Online: 22 Sep 2010. * Correspondence: Dr. Richard Kempter, Humboldt-Universität zu Berlin, Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany, r.kempter@biologie.hu-berlin.de Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Richard Kempter Christian Leibold Robert Schmidt Google Richard Kempter Christian Leibold Robert Schmidt Google Scholar Richard Kempter Christian Leibold Robert Schmidt PubMed Richard Kempter Christian Leibold Robert Schmidt Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Horizontal positioning error derived from stationary GPS units: A function of time and proximity to building infrastructure

This investigation quantified Horizontal Positioning Error (HPE) from stationary Global Positioning System (GPS) units. In experiment 1, GPS units were placed within close proximity of each other and data were collected at three times within the same day. In experiment 2, the GPS units were configured in a straight line from the edge of the field (nearby to a stadium), towards the centre. Circular Error Probable of 95% (CEP95) was used to quantify HPE, mean numbers of satellites recorded. CEP95 and the number of satellites were inversely related in both experiments. Changes in satellite availability throughout the day led to significant variability in HPE across trials in experiment 1. In experiment 2, the largest CEP95 was found among units located closest to the stadium. Collectively, these findings identify important considerations for using GPS to map athletes’ positions that have not been adequately addressed in the sports science literature. The number satellites, time between repeated measures testing, and the proximity of nearby buildings, can cause unpredictable changes in measurement error and should be considered in the interpretation of data. Further, we recommend that CEP95 be reported in GPS-based experiments, which may help prevent the misleading interpretation of inaccurate or unstable data.

Gravity modeling in aerospace applications

The science of inertial navigation has evolved to the point that the traditional gravity model is a principal error source in advanced, precise systems. Specifically, the unmodeled vertical deflections of the earth's gravitational field are a major contributor to CEP (circular error probable) divergence in precise terrestrial inertial navigation systems (INS). Over the years, several studies have been undertaken to the development of advanced techniques for accurate, real-time compensation of gravity disturbance vectors. More complex on-board gravity models which compute vertical deflection components will reduce the CEP divergence rate, but imperfect modeling due to on-board processing limitations will still cause residual vertical deflection errors. In order to eliminate or reduce gravity-induced errors in the INS requires measurement of gravity disturbance values and in-flight compensation to the inertial navigator. It is assumed in this paper that gravity disturbance values have been measured prior to the airborne mission and various techniques for compensation are to be considered. As part of a screening process in this study, several gravity compensation techniques (both deterministic and stochastic models) were investigated. The screening process involved identification of gravity models and algorithms, and developments of selection criteria for subsequent screening of the candidates.

New classes of estimators for dispersion parameter of a chi-distributed radial error with application to target analysis

In this paper we have investigated some classes of shrinkage estimators for estimating dispersion parameter σ in p-dimensional analogue of the probable error of a single variate. The need to study this parameter arises due to its importance in target analysis problems to estimate Circular Probable Error (CPE) and Spherical Probable Error (SPE). It is assumed that the prior information or guessed value of the parameter σ say σ0 is available from the past experiences. The properties of the developed shrinkage estimators have been studied when center of impact is known and when it is unknown by using appropriate numerical integration method (10-point Gauss-Laguerre integration method). Simulation studies confirm the high efficiency of the developed classes of shrunken estimators when compared with the usual maximum likelihood estimators (MLE), unbiased estimators and minimum mean squared error (MMSE) estimators.

English

The accuracy of traditional unmanned aerial vehicle (UAV) geo-location based on single image is too low to meet the needs of precise strike. In this paper, a new UAV geo-location method is presented. The mathematical models are constructed by linearization of the collinearity equations to iteratively compute the pose angles and focal length of the camera. At least three images of the target, along with at least three identifiable common points among the images, are needed for reckoning camera pose angles and focal length. The three dimensional (3D) coordinates of ground target are calculated using forward intersection. The new method can get the target coordinates with no dependence on digital elevation model (DEM) and the measured values of camera pose angles, therefore two of the three primary error sources in the traditional UAV target location approach are eliminated. Simulation and real image experiment results show that the accuracy of the estimated target location is close to that of the UAV position, and that target location error is within 5m circular error probable (CEP) on condition that the UAV is navigated by differential global positioning systems (DGPS).Defence Science Journal, 2009, 59(1), pp.43-48, DOI:http://dx.doi.org/10.14429/dsj.59.1483

Comparison of Semidistributed Multinode TOA-DOA Fusion Localization and GPS-Aided TOA (DOA) Fusion Localization for MANETs

This paper evaluates the performance of a semidistributed multinode time-of-arrival (TOA) and direction-of-arrival (DOA) fusion localization technique in terms of localization circular error probability (CEP). The localization technique is applicable in mobile ad hoc networks (MANETs) when global positioning system (GPS) is not available (GPS denied environments). The localization CEP of the technique is derived theoretically and verified via simulations. In addition, we theoretically derive the localization CEP of GPS-aided TOA fusion and GPS-aided DOA fusion techniques, which are also applicable in MANETs. Finally, we compare these three localization techniques theoretically and via simulations. The comparison confirms that in moderate scale MANETs, the multinode TOA-DOA fusion localization technique achieves the best performance; while in large scale MANETs, GPS-aided TOA fusion leads to the best performance.

Measurement Method for Measuring Circular Motion Error of CNC Machine Tools

The dynamic characteristic of CNC (computer numerical control) machine tools is a critical role to decide the accuracy and speed of machine. It is very important to improve the precision and reduce the motion error so as to manufacture complex and fine products. In general, the motion error is estimated by a two or three-dimensional ball bar measurement system. Although this technology is capable of dynamical measurement, its condition should be confined to a low speed or a large radius. A new measurement method for measuring circular motion error of CNC machine tools is proposed in this paper. The instrument consists of a dual-frequency laser interferometer, a beam splitter and two corner cubes. In order to evaluate the exactness of the results we get from our measurement system, we use RSF’s grid encoder to do another experiment and compare both the results. According to the results shown, our measurement system can measure both of the X and Y axes of the plane of the CNC stage in a small scale at the same time and can simplify the calibration procedure as well as shorten the time of measurement. This method can accomplish the two-axis measurement at a high speed, without being restricted by radius variations. It is a good, simple and effective measurement method.

Measurement and analysis of typical motion error traces from a circular test

The circular test provides a rapid and efficient way of measuring the contouring accuracy of a machine tool. To get the actual point coordinate in the work plane, an improved measurement instrument - a new ball bar test system - is presented in this paper to identify both the radial error and the rotation angle error when the machine is manipulated to move in circular traces. Based on the measured circular error, a combination of Fourier components is chosen to represent the systematic form error that fluctuates in the radial direction. The typical motion errors represented by the corresponding Fourier components can thus be identified. The values for machine compensation can be calculated and adjusted until the desired results are achieved.

Effects of Telemetry Location Error on Space‐Use Estimates Using a Fixed‐Kernel Density Estimator

ABSTRACT Fixed‐kernel density estimates using radiotelemetry locations are frequently used to quantify home ranges of animals, interactions, and resource selection. However, all telemetry data have location error and no studies have reported the effects of error on utilization distribution and area estimates using fixed‐kernel density estimators. We simulated different home range sizes and shapes by mixing bivariate‐normal distributions and then drawing random samples of various sizes from these distributions. We compared fixed‐kernel density estimates with and without error to the true underlying distributions. The effects of telemetry error on fixed‐kernel density estimates were related to sample size, distribution complexity, and ratio of median Circular Error Probable to home range size. We suggest a metric to assess the adequacy of the telemetry system being used to estimate an animal's space use before a study is undertaken. Telemetry location error is unlikely to significantly affect fixed‐kernel density estimates for most wildlife telemetry studies with adequate sample sizes.

Effects of habitat on GPS collar performance: using data screening to reduce location error

Summary Global positioning system (GPS) technology enables researchers to evaluate wildlife movements, space use and resource selection in detail for extended periods of time. Two types of errors, missed location fixes and location error, are inherent to GPS telemetry and can bias location data sets. Habitat characteristics can influence both types of errors, but no studies have reported how continuous ranges of canopy cover and terrain simultaneously affect location error at different positional dilution of precision (PDOP) and signal quality levels. This information can assist in developing a protocol for removing large location errors from GPS data sets. The objectives of this study were to quantify how canopy cover and terrain affected GPS collar performance within a mountainous region of northern Idaho, USA, and evaluate different data‐screening options for GPS location data sets from stationary test collars and free‐ranging black bears Ursus americanus. The fix rate for test collars was very high in all habitats (mean 99·5%, SE 0·14, range 97·9–100%) and was not related to canopy cover or terrain obstruction. However, habitat variables strongly influenced location error, PDOP values and proportion of three‐dimensional (3‐D) fixes. The 95% circular error probable (CEP) equalled 106·8 m for locations at all test sites, and varied substantially with canopy cover, terrain obstruction and signal quality categories, ranging from 14·3 m to 557·0 m. Location errors for two‐dimensional (2‐D) fixes were more variable at higher PDOP values and were significantly larger compared with 3‐D fixes. Data screening increased the accuracy of test collar location data sets by removing large location errors that were associated with high PDOP values. Data‐screening options that focused on screening 2‐D locations were most effective in reducing location error and retaining the greatest number of locations. For black bear data sets, the four data screening options resulted in data reduction ranging from 8% to 35%. Synthesis and applications. We have demonstrated how location data can be analysed and screened based on 2‐D and 3‐D fixes in relation to PDOP values to eliminate locations with potentially large location errors. This information can be applied to GPS location data for individual animals to increase data accuracy for analyses.

Pedestrian tracking and navigation using an adaptive knowledge system based on neural networks

The primary objective of the research presented here is to develop theoretical foundations and implementation algorithms, which integrate the Global Positioning System (GPS), micro-electromechanical inertial measurement unit (MEMS IMU), digital barometer, electronic compass, and human pedometry to provide navigation and tracking of military and rescue ground personnel. This paper discusses the design, implementation and the performance analyses of the personal navigator prototype, with a special emphasis on dead-reckoning (DR) navigation supported by the human locomotion model. The adaptive knowledge system, based on the Artificial Neural Networks (ANN), is implemented to support this functionality. The knowledge system is trained during the GPS signal reception and is used to support navigation under GPS-denied conditions. The human locomotion parameters, step frequency (SF) and step length (SL), are extracted from GPS-timed impact switches (step frequency) and GPS/IMU data (step length), respectively, during the system calibration period. SL is correlated with several data types, such as acceleration, acceleration variation, SF, terrain slope, etc. that constitute the input parameters to the ANN-based knowledge system. The ANN-predicted SL, together with the heading information from the compass and gyro, support DR navigation. The current target accuracy of the system is 3–5 m CEP (circular error probable) 50%.

Multi-Sensor Personal Navigator: System Design and Calibration

This paper presents the current design status and some preliminary calibration/performance analyses of the prototype of a multi-sensor personal navigator currently under development at The Ohio State University. The main purpose of this research project is to develop a theoretical foundation and algorithms which integrate the Global Positioning System (GPS), Micro-electro-mechanical inertial measurement unit (MEMS IMU), barometer and compass to provide seamless position information to support navigation and tracking of ground military and rescue personnel. The system is designed with an open-ended architecture, which would be able to incorporate additional navigation and imaging sensor data, extending the system's operations to the indoor environments. The current target accuracy of the system is at 3–5 m CEP (circular error probable). In the current prototype implementation, the following sensors are integrated in the tightly coupled Extended Kalman Filter (EKF): GPS carrier phase and pseudorange data, Crossbow MEMS IMU400C, PTB220A barometer, and KVH Azimuth 1000 digital compass. This paper focuses on the design architecture of the integrated system and the preliminary performance analysis, with a special emphasis on the navigation during the loss of GPS signal. A brief description of the individual sensors and their calibration is presented, together with the navigation performance of the system of sensors.