Coordinate Measurement Errors Research Articles

Accuracy of coordinate measurements at phase modulation by digital raster

The development of optical-electronic instruments for measuring linear and angular quantities based on focal-plane array (photomatrices) using a digital phase analyzer (digital raster) is considered. It is shown that, unlike a phase raster with a mechanical drive, a digital raster provides the possibility of automation and increased measurement accuracy, reducing the weight and size characteristics of the measuring instrument. A method for constructing a digital raster is proposed, based on the use of photomatrices in combination with computer technologies. To ensure the required accuracy of the developed opto-electronic devices, the sources and components of the measurement error were investigated. The influence of the discrete structure of a digital raster on the error in measuring image coordinates has been studied. Mathematical expressions are obtained for calculating the limiting values of coordinate measurement errors caused by parasitic phase modulation that occurs when using a digital raster (sampling error). The dependence of these errors on image parameters and pixel size has been determined. It is shown that, based on the permissible maximum sampling error, it is possible to calculate the required dimensions of a photomatrix pixel, while the size of the sampling pixel can be larger than the size of the photomatrix pixel, which is very signifi cant from the point of view of energy relations. The results obtained will be useful in the development of optical-electronic means of angular and linear measurements with digital rasters.

Issue of VHF Continuous Emission Radars Coordinate Measurement Discrepancy

The research delves into the significance of continuous emission radars of very high frequency (VHF) range in detecting small unmanned aircraft and marine targets for navigation safety. Recognising the need for improved radars and reduced coordinate measurement errors, the study aims to analyse discrepancies in azimuth and range determination in radars with fixed-phased antenna arrays. By developing effective tools with low computational complexity for target azimuth determination, the research seeks to enhance radar performance. Employing analytical, classification, functional, and statistical methods, the study comprehensively examines the peculiarities and differences of radars. It meticulously analyses coordinate measurement errors and investigates their causes. The impact of these discrepancies on radar performance and their relevance in various applications, particularly maritime navigation, is carefully evaluated. The findings emphasise the critical role of continuous emission radars in ensuring shipping safety and economic efficiency. The recommendations derived from the study offer valuable insights for improving radar effectiveness, addressing operational limitations, and enhancing overall functionality. By tackling coordinate measurement errors and providing accurate azimuth determination tools, this research contributes to advancing continuous emission radar technology and its practical applications. Through its findings and recommendations, the study aims to optimise radar performance, enhance navigation safety, and improve economic efficiency in diverse sectors.

ПРИНЦИПЫ ПОСТРОЕНИЯ И МОДЕЛИ СИСТЕМЫ АВТОМАТИЧЕСКОГО УПРАВЛЕНИЯ ВТОРЫМ ЛОКОМОТИВОМ ПРИ ВИРТУАЛЬНОЙ СЦЕПКЕ

Automatic control system model of second train locomotive at virtual assessment as well as control quality analysis approaches have been considered. The controlled value represents being calculated in train traffic process the distance between “tail” of a first train and “head” of a second one, providing traffic safety at emergency braking of a first train. This distance is called “virtual replacer length”. Formalization has been introduced allowing to account for synchronization absence at transfer of information on the coordinate and speed of a first locomotive and the control digital system work cycle of a second one. Speed and coordinate measurement errors have been considered which’re connected with lagging at information transfer and possibility of failing in decoding of received by radio channel information by second locomotive receiver. At virtual length assessment, various ways of its upper assessment have been considered, the way has been chosen, taking into account motion speeds and the coordinates of both trains, emergency braking path of a first train, the possibility of emergency braking of a first train at the beginning of the cycle of information transfer, measurement methodological and instrumental errors. Digital proportional integral differentiating control law has been considered as an operator, transforming mismatches at the choice of a control of a second locomotive. Automatic control system model has been developed which relates to impulse system class and which feature is the calculation of control action in train traffic process. The parametric synthesis of automatic control system is recommended to be held by simulation modelling methods. Control quality criteria have been chosen.

Influence of measurement errors of the complex coherence factor on reconstructed image quality of integrated optical interferometric imagers

Interferometric imagers need to measure the phase, modulus, and spatial frequency coordinates of the complex coherence factor to reconstruct images. However, these three measurement parameters are accompanied by certain measurement errors in the actual imaging process, thereby affecting the quality of the reconstructed image. Based on the checkerboard integrated optical imaging system, we simulate the influence of measurement errors of the complex coherence factor on the imaging performance of the integrated optical interferometric imager. The simulation results show that, on the premise that measurement errors follow the normal distribution, the modulus measurement error does not significantly reduce the quality of the reconstructed image, whereas the phase and spatial frequency coordinate measurement errors have a great impact. When the mean value of the phase measurement error is 0, the standard deviation must be <0.18π to ensure the high quality of the reconstructed image. For the measurement error of the spatial frequency coordinates, when the standard deviation of the lenslet position errors is <0.075 times the shortest baseline length, its influence on the quality of the reconstructed image is acceptable. The simulation results are of great help to the engineering, manufacturing, and application of integrated optical interferometric imaging technology.

Error Analysis of Integrated Six-Light-Screen Array Measurement Model

The light-screen array measurement method is very suitable for measuring the coordinates of rapid-fire weapons, and the measurement error is determined by the measurement model. In this paper, the separated light-screen array is improved to an integrated light-screen array, which reduces the parameters and optimizes the measurement model. Three kinds of factors affecting the coordinate measurement error of the projectile under the integrated measurement model are analysed, and the influence of the factors on the distribution of coordinate measurement errors is simulated and analysed in the selected 1m×1m target area. Then the error distribution of the separated measurement model and the integrated measurement model is simulated and analysed under the same conditions based on the design values and current technology level. The result shows that compared with the separated measurement model under the same simulation conditions, the comprehensive coordinate measurement error is optimized by about 2.1mm within 1m×1m target area. The research can provide reference for the design and optimization of light-screen array and other similar photoelectric measurement systems, and provide new ideas for improving the coordinate measurement precision of therapid-fire weapons.

Estimating statistical errors in retrievals of ice velocity and deformation parameters from satellite images and buoy arrays

Abstract. The objective of this note is to provide the background and basic tools to estimate the statistical error of deformation parameters that are calculated from displacement fields retrieved from synthetic aperture radar (SAR) imagery or from location changes of position sensors in an array. We focus here specifically on sea ice drift and deformation. In the most general case, the uncertainties of divergence/convergence, shear, vorticity, and total deformation are dependent on errors in coordinate measurements, the size of the area and the time interval over which these parameters are determined, as well as the velocity gradients within the boundary of the area. If displacements are calculated from sequences of SAR images, a tracking error also has to be considered. Timing errors in position readings are usually very small and can be neglected. We give examples for magnitudes of position and timing errors typical for buoys and SAR sensors, in the latter case supplemented by magnitudes of the tracking error, and apply the derived equations on geometric shapes frequently used for deriving deformation from SAR images and buoy arrays. Our case studies show that the size of the area and the time interval for calculating deformation parameters have to be chosen within certain limits to make sure that the uncertainties are smaller than the magnitude of deformation parameters.

Measurement of coordinates of sources of radio emission at high frequencies goniometric and goniometric and range-metering by methods

Coordinates of sources of a radio emission of range of high frequencies using an on-off system azimuth and meridian direction finders are measured by a goniometric method. In the bearing posts active arrays of vertical vibrators and synchronized coherent radio receivers with frequency conversion are used. For minimization of amplitude and phase not identities preliminary calibration of channels of the receiver at frequencies of the taken the bearings signals is executed. By results of measurements average quadratic deviations of coordinates of sources of a radio emission of type of radio stations of meteo-information of airfield networks of the Russian Federation and the neighboring countries, standard frequency stations and time, transmitters of telecode and continuous messages are investigated. The analysis of dependences of achievable accuracy figures of measurements on the space provision of positions of direction finders, lengths of routes and also fluctuations of electro-physical parameters and space distribution of the ionized layers of the atmosphere leading to changes of beam trajectories of distribution and abnormal errors of measurements of the directions of arrival of radio waves to different season and day is carried out. It is shown that in the lower part of range of high frequencies the measurement error of coordinates of sources of a radio emission a goniometric system makes 4.7 %, and in process of approach of frequency to the upper bound of range this indicator increases by 1.2 times. By results of bearing of signals in one point of space and measurements of height of layers of the atmosphere with use of the station of vertical sounding coordinates of sources of a radio emission are determined by a goniometric and range-metering method. Measurements of coordinates of objects by a goniometric and range-metering method can be executed with average quadratic deviation of 11-13 % of range.

ERROR ESTIMATION OF MICROSEISMIC EVENT PARAMETERS

In the paper factors affecting error of microseismic events location are considered. Linearized error estimates are constructed, an accuracy of this approach is shown by the example. The influence of the following factors is demonstrated by examples: coordinate measurement errors of the microseismic antenna, errors in the model used for processing, and lack of information on the static corrections necessary to compensate for the low-velocity zone.

Analyzing measurement errors for navigation parameters in onground short-range navigation systems based on pseudolites

This article discusses coordinate measurement errors in short-range pseudolite navigation systems. An analysis of the components of the measurement error of radio navigating parameters has been performed; the geometric factor values have been calculated for various variants of constructing the system. The peculiarities of measuring the spatial orientation of objects using interferometric methods in on-ground short-range navigation systems have been ascertained.

Basing error in coordinate measurements of cylindrical gears

A mathematical model for determining the basing errors in coordinate measurements of gears by means of pins is formulated on the basis of a best-fit algorithm.

Error estimates in coordinate measurements of the cross section parameters of cylindrical surfaces

A simulation method and the results of simulating the errors in coordinate measurements of the cross section parameters of cylindrical surfaces are discussed. Data are presented from experimental studies that confirm the simulations.

One-stage estimation of the position of a radio source by a combined passive system

An algorithm for one-stage estimation of the radiator position by a combined passive system consisting of narrow-base subsystems is synthesized and analyzed. The Cramer-Rao matrix bound of coordinate measurement errors is calculated for the one-stage algorithm. A comparative analysis of the system based on the synthesized algorithm and the previously studied one-stage wide-and narrow-base systems is performed. It is shown that, in a number of cases, the system based on the proposed algorithm can ensure a considerable advantage over the known systems in terms of measurement accuracy.

Relationships between the Camera Calibration Accuracy and the Imaging Condition

For the 3 D measurements using the images taken with cameras, it is necessary to know the values of the camera's intrinsic parameters, such as the image coordinates of principal point, i.e., the projection of the projection center to the image plane, the principal distance between the principal point and the projection center, and the image distortion coefficients. In the 3D measurements, we need to estimate the calibration accuracy of the camera's intrinsic parameters. Therefore, the authors examined a two-plane calibration method with respect to the calibration accuracy. Paying attention of the fact that the image coordinate measurement errors of the fiducial points propagate to the calibrated intrinsic parameter values, and the magnitude of the error could be formulized according to the setup of the fiducial points, the authors presented many useful relationships between the calibration accuracies and the fiducial point setups.

Hydroacoustic coordinate-measuring system of the NT-200 Baikal neutrino telescope

The hydroacoustic coordinate-measuring system of the NT-200 Baikal neutrino telescope is described. It is a ranging long-base hydroacoustic system constantly operating in an automated or interactive mode and capable of measuring the coordinates of the detecting modules of the NT-200 to within 20 cm. Special attention is given to the justification of the estimate of the coordinate measurement errors. As an illustration, some results of measuring the coordinates of the elements of the NT-200 and the hydrophysical characteristics of lake Baikal are presented.

Vertical control point network and global shape of Io

We have analyzed Galileo and Voyager images of Io to derive global control point networks, involving 402 (Galileo) and 158 (Voyager) surface points as well as combinations of the two data sets. Using block adjustment techniques, three‐dimensional coordinates of the control points are derived with an accuracy of 4.7 km (Galileo) and 8.6 km (Voyager). Three‐axial ellipsoids are fitted to the Galileo control points, for which we find the following: a = 1831.1 ± 0.3 km, b = 1820.4 ± 0.4 km, and c = 1816.6 ± 0.5 km. Our results on size and shape confirm that Io (in synchronous rotation and exposed to strong tidal and rotational forces) is in hydrostatic equilibrium and has a pronounced mass concentration toward the center, in agreement with suggested Fe‐ and Fe/S cores of 740 and 1000 km radius, respectively. However, our shape model is unable to resolve long‐wavelength topography beyond the ellipsoidal parameters. Studies of synthetic Galileo and Voyager control point data sets are carried out to track error propagation in our control point networks and to compare the geometric performance of the two spacecraft cameras. We find that Voyager Vidicon images suffer from residual geometric errors on the order of 1/3 of a pixel, which adds to the typical image coordinate measurement errors (slightly less than 1/2 pixel) that apply for Galileo or Voyager images alike. We therefore suggest that previous authors have overestimated the accuracy of their Voyager‐based control point networks and global topographic maps significantly.

An Uncertainty Analysis Method for Coordinate Referencing in Manufacturing Systems

Accurate and consistent transformations between design and manufacturing coordinate systems are essential for high quality part production. Fixturing and coordinate measurement are common coordinate referencing techniques which are used to locate points or measurement points on workpiece reference surfaces to establish these coordinate transformations. However, uncertainty sources such as geometric form deviations in workpiece surfaces, tolerances on fixture locators, and errors in coordinate measurements exist. A result is that coordinate transformations established using the locating and measurement points are in herently uncertain. An uncertainty analysis method for coordinate referencing is presented in this paper. The uncertainty interval concept is used to describe essential characteristics of uncertainty sources in coordinate referencing and coordinate transformation relationships. The method is applied to estimating uncertainties in simple and compound coordinate transformation obtained using coordinate referencing in an experimental mold manufacturing system. Results of Monte Carlo simulations are used to show that the uncertainty analysis method gives a consistent and high percentage of coverage in evaluating coordinate referencing in the examples studied.

Uncertainties in the Acquisition and Utilization of Coordinate Frames in Manufacturing Systems

Summary Accurate and consistent transformations between design and manufacturing coordinate frames are essential for precision part production. These coordinate transformations establish surface position and orientation relationships as manufactured pans pass from design through production processes to inspection and surface error analysis. Unfortunately, these coordinate transformations can be uncertain due to factors such as geometric form errors in workpiece reference surfaces, fixture locating point variations, and coordinate measurement errors. A method for representing and estimating these uncertainties and their propagation through multi-stage manufacturing processes is presented in this paper. The method is applicable to systems with combinations of fixturing and coordinate measurements.

Errors in kinematic parameters of a planar joint: Guidelines for optimal experimental design

Kinematic characteristics of a body joint performing planar motion are precisely defined by the centers and angles of rotation as the joint undergoes its full range of physiological movement. These potentially (clinically) useful non-invasive kinematic parameters are, however, highly sensitive to input coordinate measurement errors and the experimental design. This paper compares results of an experimental study and a statistically based mathematical model of the errors in the centers and angles of rotation. Guidelines are provided to design optimal kinematic experiments so that, for given measurement equipment, the highest possible precision may be achieved in the results.