On Calibration Error of Randomized Forecasting Algorithms

2007 ◽  
pp. 388-402
Author(s):  
Vladimir V. V’yugin
Keyword(s):  
Calibration Error

Silicate analysis of carbonated rocks using ICP-AES with calibration by the concentration ratio

2020 ◽  
Vol 86 (5) ◽  
pp. 16-21
Author(s):  
T. A. Karimova ◽  
G. L. Buchbinder ◽  
S. V. Kachin
Keyword(s):  
Inductively Coupled Plasma ◽  
Concentration Ratio ◽  
Total Error ◽  
Atomic Emission ◽  
Emission Spectrometry ◽  
Calibration Error ◽  
Plasma Atomic Emission Spectrometry ◽  
Standard Samples ◽  
Inductively Coupled ◽  
Carbonate Materials

Calibration by the concentration ratio provides better metrological characteristics compared to other calibration modes when using the inductively coupled plasma atomic emission spectrometry (ICP-AES) for analysis of geological samples and technical materials on their base. The main reasons for the observed improvement are: i) elimination of the calibration error of measuring vessels and the error of weighing samples of the analyzed materials from the total error of the analysis; ii) high intensity of the lines of base element; and iii) higher accuracy of measuring the ratio of intensities compared to that of measuring the absolute intensities. Calcium oxide is better suited as a base when using calibration by the concentration ratio in analysis of carbonate rocks, technical materials, slags containing less than 20% SiO2 and more than 20% CaO. An equation is derived to calculate the content of components determined in carbonate materials when using calibration by the concentration ratio. A method of ICP-AES with calibration by the concentration ratio is developed for determination of CaO (in the range of contents 20 – 100%), SiO2 (2.0 – 35%), Al2O3 (0.1 – 30%), MgO (0.1 – 20%), Fe2O3 (0.5 – 40%), Na2O (0.1 – 15%), K2O (0.1 – 5%), P2O5 (0.001 – 2%), MnO (0.01 – 2%), TiO2 (0.01 – 2.0%) in various carbonate materials. Acid decomposition of the samples in closed vessels heated in a HotBlock 200 system is proposed. Correctness of the procedure is confirmed in analysis of standard samples of rocks. The developed procedure was used during the interlaboratory analysis of the standard sample of slag SH17 produced by ZAO ISO (Yekaterinburg, Russia).

scholarly journals Implications of component size and calibration error on digital templating for total hip arthroplasty. A visual matrix from a simple mathematical model

2021 ◽  
Author(s):  
Christoph Kolja Boese ◽  
Tim Rolvien ◽  
Matthias Trost ◽  
Michael Frink ◽  
Jan Hubert ◽  
...  
Keyword(s):  
Total Hip Arthroplasty ◽  
Hip Arthroplasty ◽  
Standard Procedure ◽  
Calibration Error ◽  
Optimal Size ◽  
Linear Calibration ◽  
Component Size ◽  
Digital Templating ◽  
Total Hip ◽  
Implant Size

Abstract Objective Preoperative digital templating is a standard procedure in total hip arthroplasty. Deviations between template size and final implant size may result from inaccurate calibration, templating as well as intraoperative decisions. So far, the explicit effect of calibration errors on templating has not been addressed adequately. Materials and Methods A mathematical simulation of calibration errors up to ± 24% was applied to the templating of acetabular cups (38 to 72 mm diameter). The effect of calibration errors on template component size as deviation from optimal size was calculated. Results The relationship between calibration error and component size deviation is inverse and linear. Calibration errors have a more pronounced effect on larger component sizes. Calibration errors of 2–6% result in templating errors of up to two component sizes. Common errors of up to 12% may result in templating errors of 3–4 sizes for common implant sizes. A tabular matrix visualizes the effect. Conclusion Calibration errors play a significant role in component size selection during digital templating. Orthopedic surgeons should be aware of this effect and try to identify and address this source of error.

scholarly journals KiDS+VIKING-450 and DES-Y1 combined: Cosmology with cosmic shear

2020 ◽  
Vol 638 ◽  
pp. L1 ◽  
Author(s):  
S. Joudaki ◽  
H. Hildebrandt ◽  
D. Traykova ◽  
N. E. Chisari ◽  
C. Heymans ◽  
...  
Keyword(s):  
Dark Energy ◽  
Cosmic Microwave Background ◽  
Gravitational Lensing ◽  
Error Model ◽  
Calibration Error ◽  
Microwave Background ◽  
Weak Gravitational Lensing ◽  
Dark Energy Survey ◽  
Cosmic Shear ◽  
Energy Survey

We present a combined tomographic weak gravitational lensing analysis of the Kilo Degree Survey (KV450) and the Dark Energy Survey (DES-Y1). We homogenize the analysis of these two public cosmic shear datasets by adopting consistent priors and modeling of nonlinear scales, and determine new redshift distributions for DES-Y1 based on deep public spectroscopic surveys. Adopting these revised redshifts results in a 0.8σ reduction in the DES-inferred value for S​8, which decreases to a 0.5σ reduction when including a systematic redshift calibration error model from mock DES data based on the MICE2 simulation. The combined KV450+DES-Y1 constraint on S8 = 0.762−0.024+0.025 is in tension with the Planck 2018 constraint from the cosmic microwave background at the level of 2.5σ. This result highlights the importance of developing methods to provide accurate redshift calibration for current and future weak-lensing surveys.

scholarly journals Polarization calibration techniques and scheduling for the Daniel K. Inouye Solar Telescope

2014 ◽  
Vol 10 (S305) ◽  
pp. 102-107
Author(s):  
David F. Elmore
Keyword(s):  
Advanced Technology ◽  
Optical Coatings ◽  
Calibration Error ◽  
Solar Telescope ◽  
Critical Importance ◽  
Common Path ◽  
Solar Research ◽  
Telescope Optics ◽  
The Individual ◽  
Calibration Techniques

AbstractThe Daniel K. Inouye Solar Telescope (DKIST), formerly Advanced Technology Solar Telescope when it begins operation in 2019 will be by a significant margin Earth's largest solar research telescope. Science priorities dictate an initial suite of instruments that includes four spectro-polarimeters. Accurate polarization calibration of the individual instruments and of the telescope optics shared by those instruments is of critical importance. The telescope and instruments have been examined end-to-end for sources of polarization calibration error, allowable contributions from each of the sources quantified, and techniques identified for calibrating each of the contributors. Efficient use of telescope observing time leads to a requirement of sharing polarization calibrations of common path telescope components among the spectro-polarimeters and for those calibrations to be repeated only as often as dictated by degradation of optical coatings and instrument reconfigurations. As a consequence the polarization calibration of the DKIST is a facility function that requires facility wide techniques.

scholarly journals First Odin sub-mm retrievals in the tropical upper troposphere: humidity and cloud ice signals

2007 ◽  
Vol 7 (2) ◽  
pp. 459-469 ◽  
Author(s):  
M. Ekström ◽  
P. Eriksson ◽  
B. Rydberg ◽  
D. P. Murtagh
Keyword(s):  
Careful Analysis ◽  
Systematic Difference ◽  
Horizontal Distribution ◽  
Calibration Error ◽  
Main Concern ◽  
Random Component ◽  
Worst Case ◽  
First Results ◽  
Ice Content ◽  
Cloud Ice

Abstract. Odin-SMR is a limb-sounder operating in the 500 GHz region with the capability of performing measurements down to altitudes of about 10 km with relatively low influence of ice clouds. Until now spectra from tropospheric tangent altitudes have been disregarded due to inadequate handling of scattering. A first method to extract upper tropospheric quantities has now been developed, yielding the humidity in two layers around 200 and 130 hPa and information on cloud ice content above 200 hPa. First results are compared with in situ MOZAIC measurements and presented to give a global view of the horizontal distribution. The seasonal structures are in agreement with other satellite measurements. The main concern for these retrievals is the calibration performance. A careful analysis indicates a systematic calibration error of about 1 K, but also a random component that differs between the two bands. The random calibration uncertainty results in retrieval errors of 10–60% depending on humidity and band. Presently this prohibits use of single retrievals, but averages can be presented with good accuracy. The fixed calibration error can largely be removed, leaving the spectroscopic uncertainties to dominate the humidity retrieval accuracy, with a worst case estimate of 30%. However, the comparison of MOZAIC data and the measurements for the 200 hPa layer shows a systematic difference of <10%. This indicates that the actual systematic error is low and gives further confidence in the capability of Odin-SMR to measure humidity in the upper tropical troposphere.

scholarly journals Registration Error Analysis for Augmented Reality

1997 ◽  
Vol 6 (4) ◽  
pp. 413-432 ◽  
Author(s):  
Richard L. Holloway
Keyword(s):  
Augmented Reality ◽  
Error Analysis ◽  
Optical Distortion ◽  
Calibration Error ◽  
Head Tracking ◽  
System Delay ◽  
System Calibration ◽  
The Real ◽  
Registration Error ◽  
Real Environment

Augmented reality (AR) systems typically use see-through head-mounted displays (STHMDs) to superimpose images of computer-generated objects onto the user's view of the real environment in order to augment it with additional information. The main failing of current AR systems is that the virtual objects displayed in the STHMD appear in the wrong position relative to the real environment. This registration error has many causes: system delay, tracker error, calibration error, optical distortion, and misalignment of the model, to name only a few. Although some work has been done in the area of system calibration and error correction, very little work has been done on characterizing the nature and sensitivity of the errors that cause misregistration in AR systems. This paper presents the main results of an end-to-end error analysis of an optical STHMD-based tool for surgery planning. The analysis was done with a mathematical model of the system and the main results were checked by taking measurements on a real system under controlled circumstances. The model makes it possible to analyze the sensitivity of the system-registration error to errors in each part of the system. The major results of the analysis are: (1) Even for moderate head velocities, system delay causes more registration error than all other sources combined; (2) eye tracking is probably not necessary; (3) tracker error is a significant problem both in head tracking and in system calibration; (4) the World (or reference) coordinate system adds error and should be omitted when possible; (5) computational correction of optical distortion may introduce more delay-induced registration error than the distortion error it corrects, and (6) there are many small error sources that will make submillimeter registration almost impossible in an optical STHMD system without feedback. Although this model was developed for optical STHMDs for surgical planning, many of the results apply to other HMDs as well.

scholarly journals Calculating uncertainty for the RICE ice core continuous flow analysis water isotope record

2018 ◽  
Vol 11 (8) ◽  
pp. 4725-4736 ◽  
Author(s):  
Elizabeth D. Keller ◽  
W. Troy Baisden ◽  
Nancy A. N. Bertler ◽  
B. Daniel Emanuelsson ◽  
Silvia Canessa ◽  
...  
Keyword(s):  
High Resolution ◽  
Continuous Flow ◽  
Ice Core ◽  
Flow Analysis ◽  
Calibration Error ◽  
Data Set ◽  
Total Uncertainty ◽  
Continuous Flow Analysis ◽  
Uncertainty Estimates ◽  
Water Isotope

Abstract. We describe a systematic approach to the calibration and uncertainty estimation of a high-resolution continuous flow analysis (CFA) water isotope (δ2H, δ18O) record from the Roosevelt Island Climate Evolution (RICE) Antarctic ice core. Our method establishes robust uncertainty estimates for CFA δ2H and δ18O measurements, comparable to those reported for discrete sample δ2H and δ18O analysis. Data were calibrated using a time-weighted two-point linear calibration with two standards measured both before and after continuously melting 3 or 4 m of ice core. The error at each data point was calculated as the quadrature sum of three factors: Allan variance error, scatter over our averaging interval (error of the variance) and calibration error (error of the mean). Final mean total uncertainty for the entire record is δ2H=0.74 ‰ and δ18O=0.21 ‰. Uncertainties vary through the data set and were exacerbated by a range of factors, which typically could not be isolated due to the requirements of the multi-instrument CFA campaign. These factors likely occurred in combination and included ice quality, ice breaks, upstream equipment failure, contamination with drill fluid and leaks or valve degradation. We demonstrate that our methodology for documenting uncertainty was effective across periods of uneven system performance and delivered a significant achievement in the precision of high-resolution CFA water isotope measurements.

scholarly journals A Nonlinear Calibration Method Based on Sinusoidal Excitation and DFT Transformation for High-Precision Power Analyzers

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Wenjian Zhou ◽  
Sheng Yang ◽  
Li Wang ◽  
Hanmin Sheng ◽  
Yang Deng
Keyword(s):  
High Precision ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Calibration Method ◽  
Calibration Error ◽  
Initial Moment ◽  
Calibration Process ◽  
Calibration Methods ◽  
Nonlinear Calibration ◽  
Sinusoidal Excitation

For most high-precision power analyzers, the measurement accuracy may be affected due to the nonlinear relationship between the input and output signal. Therefore, calibration before measurement is important to ensure accuracy. However, the traditional calibration methods usually have complicated structures, cumbersome calibration process, and difficult selection of calibration points, which is not suitable for situations with many measurement points. To solve these issues, a nonlinear calibration method based on sinusoidal excitation and DFT transformation is proposed in this paper. By obtaining the effective value data of the current sinusoidal excitation from the calibration source, the accurate calibration process can be done, and the calibration efficiency can be improved effectively. Firstly, through Fourier transform, the phase value at the initial moment of the fundamental frequency is calculated. Then, the mapping relationship between the sampling value and the theoretical calculation value is established according to the obtained theoretical discrete expression, and a cubic spline interpolation method is used to further reduce the calibration error. Simulations and experiments show that the calibration method presented in this paper achieves high calibration accuracy, and the results are compensation value after calibration with a deviation of ± 3 × 10 − 4 .

scholarly journals Global Calibration of Multi-Cameras Based on Refractive Projection and Ray Tracing

2017 ◽  
Author(s):  
Mingchi Feng ◽  
Xiang Jia ◽  
Jingshu Wang ◽  
Song Feng ◽  
Taixiong Zheng
Keyword(s):  
Ray Tracing ◽  
Real Data ◽  
Calibration Method ◽  
Calibration Error ◽  
Multiple Cameras ◽  
Projection Model ◽  
Vision Measurement ◽  
3D Computer Vision ◽  
Global Calibration ◽  
Calibration Methods

Multi-cameras system is widely applied in 3D computer vision especially when multiple cameras are distributed on both sides of the measured object. The calibration methods of multi-cameras system are critical to the accuracy of vision measurement and the key is to find an appropriate calibration target. In this paper, a high-precision camera calibration method for multi-cameras system based on transparent glass checkerboard and ray tracing is described, which is used to calibrate multiple cameras distributed on both sides of the glass checkerboard. Firstly, the intrinsic parameters of each camera is obtained by Zhang&rsquo;s calibration method. Then, multiple cameras capture several images from the front and back of the glass checkerboard with different orientations, and all images contain distinct grid corners. As the cameras on one side are not affected by the refraction of glass checkerboard, extrinsic parameters can be directly calculated. However, the cameras on another side are influenced by the refraction of glass checkerboard, and the direct use of projection model will produce calibration error. A multi-cameras calibration method using refractive projection model and ray tracing is developed to eliminate this error. Furthermore, both synthetic and real data are employed to validate the proposed approach. The experimental results of refractive calibration show that the error of the 3D reconstruction is smaller than 0.2 mm, the relative errors of both rotation and translation are less than 0.014%, and the mean and standard deviation of reprojection error of 4-cameras system are 0.00007 and 0.4543 pixel. The proposed method is flexible, high accurate, and simple to carry out.

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