Error estimation and bias correction in phase-improvement calculations

1999 ◽  
Vol 55 (9) ◽  
pp. 1555-1567 ◽  
Author(s):  
Kevin Cowtan
Keyword(s):  
Error Estimates ◽  
Error Estimation ◽  
Bayesian Methods ◽  
Bias Correction ◽  
Phase Error ◽  
Acta Cryst

With the rise of Bayesian methods in crystallography, the error estimates attached to estimated phases are becoming as important as the phase estimates themselves. Phase improvement by density modification can cause problems in this environment because the quality of the resulting phases is usually overestimated. This problem is addressed by an extension of the γ correction [Abrahams (1997). Acta Cryst. D53, 371–376] to arbitrary density-modification techniques. The degree to which the improved phases are biased by the features of the initial map is investigated in order to determine the limits of the resulting procedure and the quality of the phase-error estimates.

A Numerical Analysis of the Weak Galerkin Method for the Helmholtz Equation with High Wave Number

2017 ◽  
Vol 22 (1) ◽  
pp. 133-156 ◽  
Author(s):  
Yu Du ◽  
Zhimin Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimates ◽  
Phase Error ◽  
Three Dimensions ◽  
Wave Number ◽  
Weak Galerkin ◽  
High Wave Number ◽  
Large Wave ◽  
Element Method

AbstractWe study the error analysis of the weak Galerkin finite element method in [24, 38] (WG-FEM) for the Helmholtz problem with large wave number in two and three dimensions. Using a modified duality argument proposed by Zhu and Wu, we obtain the pre-asymptotic error estimates of the WG-FEM. In particular, the error estimates with explicit dependence on the wave numberkare derived. This shows that the pollution error in the brokenH1-norm is bounded byunder mesh conditionk7/2h2≤C0or (kh)2+k(kh)p+1≤C0, which coincides with the phase error of the finite element method obtained by existent dispersion analyses. Herehis the mesh size,pis the order of the approximation space andC0is a constant independent ofkandh. Furthermore, numerical tests are provided to verify the theoretical findings and to illustrate the great capability of the WG-FEM in reducing the pollution effect.

scholarly journals σ2 R , a reciprocal-space measure of the quality of macromolecular electron-density maps

1999 ◽  
Vol 55 (6) ◽  
pp. 1174-1178 ◽  
Author(s):  
Thomas C. Terwilliger
Keyword(s):  
Standard Deviation ◽  
Ab Initio ◽  
Electron Density ◽  
Reciprocal Space ◽  
Rapid Evaluation ◽  
Reliable Measure ◽  
Similar Measure ◽  
Acta Cryst ◽  
Density Maps

It has previously been shown that the presence of distinct regions of solvent and protein in macromolecular crystals leads to a high value of the standard deviation of local r.m.s. electron density and that this can in turn be used as a reliable measure of the quality of macromolecular electron-density maps [Terwilliger & Berendzen (1999a). Acta Cryst. D55, 501–505]. Here, it is demonstrated that a similar measure, \sigma_{R}^{2}, the variance of the local roughness of the electron density, can be calculated in reciprocal space. The formulation is suitable for rapid evaluation of macromolecular crystallographic phases, for phase improvement and for ab initio phasing procedures.

Ab initiostructure solution by iterative phase-retrieval methods: performance tests on charge flipping and low-density elimination

2010 ◽  
Vol 43 (1) ◽  
pp. 89-100 ◽  
Author(s):  
Frank Fleischer ◽  
Thomas Weber ◽  
Sofia Deloudi ◽  
Lukáš Palatinus ◽  
Walter Steurer
Keyword(s):  
Figure Of Merit ◽  
Phase Retrieval ◽  
Periodic Structures ◽  
Correction Term ◽  
Low Density ◽  
Performance Tests ◽  
Acta Cryst ◽  
Model Independent ◽  
Novel Model

Comprehensive tests on the density-modification methods charge flipping [Oszlányi & Sütő (2004).Acta Cryst.A60, 134–141] and low-density elimination [Shiono & Woolfson (1992).Acta Cryst.A48, 451–456] for solving crystal structures are performed on simulated diffraction data of periodic structures and quasicrystals. A novel model-independent figure of merit, which characterizes the reliability of the retrieved phase of each reflection, is introduced and tested. The results of the performance tests show that the quality of the phase retrieval highly depends on the presence or absence of an inversion center and on the algorithm used for solving the structure. Charge flipping has a higher success rate for solving structures, while low-density elimination leads to a higher accuracy in phase retrieval. The best results can be obtained by combining the two methods,i.e.by solving a structure with charge flipping followed by a few cycles of low-density elimination. It is shown that these additional cycles dramatically improve the phases not only of the weak reflections but also of the strong ones. The results can be improved further by averaging the results of several runs and by applying a correction term that compensates for a reduction of the structure-factor amplitudes by averaging of inconsistently observed reflections. It is further shown that in most cases the retrieved phases converge to the best solution obtainable with a given method.

An Adaptive Phase Tracking Scheme of OFDM Wireless Communication System

2013 ◽  
Vol 336-338 ◽  
pp. 1798-1803
Author(s):  
Qian Du ◽  
Wen Wu Xie
Keyword(s):  
Kalman Filter ◽  
Wireless Communication ◽  
Channel Estimation ◽  
Error Estimation ◽  
Communication System ◽  
Phase Error ◽  
Basic Structure ◽  
Adaptive Kalman Filter ◽  
Phase Tracking ◽  
New Phase

This paper proposes a new phase tracking algorithm for the 802.11a system. Since this system illuminates the basic structure of 802.11a system, and introduces the OFDM frame generation principle based the transmitter, phase error estimation and channel estimation. On the basis of this, this paper presents a phase tracking scheme based on adaptive Kalman filter, and then simulates the process based on 802.11a system. The result indicates that the BER has been improved because of this adaptive phase tracking scheme.

ExtSym: a program to aid space-group determination from powder diffraction data

2008 ◽  
Vol 41 (6) ◽  
pp. 1177-1181 ◽  
Author(s):  
Anders J. Markvardsen ◽  
Kenneth Shankland ◽  
William I. F. David ◽  
John C. Johnston ◽  
Richard M. Ibberson ◽  
...  
Keyword(s):  
Error Estimates ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
National Laboratory ◽  
Powder Diffraction Data ◽  
Acta Cryst ◽  
Data Set ◽  
Crystal System ◽  
Wide Range ◽  
Integrated Intensities

Once unit-cell dimensions have been determined from a powder diffraction data set and therefore the crystal system is known (e.g.orthorhombic), the method presented by Markvardsen, David, Johnson & Shankland [Acta Cryst.(2001), A57, 47–54] can be used to generate a table ranking the extinction symbols of the given crystal system according to probability. Markvardsenet al.tested a computer program (ExtSym) implementing the method against Pawley refinement outputs generated using theTF12LSprogram [David, Ibberson & Matthewman (1992). Report RAL-92-032. Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, UK]. Here, it is shown thatExtSymcan be used successfully with many well known powder diffraction analysis packages, namelyDASH[David, Shankland, van de Streek, Pidcock, Motherwell & Cole (2006).J. Appl. Cryst.39, 910–915],FullProf[Rodriguez-Carvajal (1993).Physica B,192, 55–69],GSAS[Larson & Von Dreele (1994). Report LAUR 86-748. Los Alamos National Laboratory, New Mexico, USA],PRODD[Wright (2004).Z. Kristallogr.219, 1–11] andTOPAS[Coelho (2003). Bruker AXS GmbH, Karlsruhe, Germany]. In addition, a precise description of the optimal input forExtSymis given to enable other software packages to interface withExtSymand to allow the improvement/modification of existing interfacing scripts.ExtSymtakes as input the powder data in the form of integrated intensities and error estimates for these intensities. The output returned byExtSymis demonstrated to be strongly dependent on the accuracy of these error estimates and the reason for this is explained.ExtSymis tested against a wide range of data sets, confirming the algorithm to be very successful at ranking the published extinction symbol as the most likely.

Impact of bias correction techniques on an ensemble of seasonal discharge forecast for the Danube upstream of Vienna

2021 ◽  
Author(s):  
Ignacio Martin Santos ◽  
Mathew Herrnegger ◽  
Hubert Holzmann
Keyword(s):  
Bias Correction ◽  
Hydrological Model ◽  
Systematic Errors ◽  
Seasonal Forecasts ◽  
Scaling Factors ◽  
Quantile Mapping ◽  
Forecasting System ◽  
Mapping Techniques ◽  
Seasonal Discharge

<p>The skill of seasonal hydro-meteorological forecasts with a lead time of up to six months is currently limited, since they frequently exhibit random but also systematic errors. Bias correction algorithms can be applied and provide an effective approach in removing historical biases relative to observations. Systematic errors in hydrology model outputs can be consequence of different sources: i) errors in meteorological data used as input data, ii) errors in the hydrological model response to climate forcings, iii) unknown/unobservable internal states and iv) errors in the model parameterizations, also due to unresolved subgrid scale variability.</p><p>Normally, bias correction techniques are used to correct meteorological, e.g. precipitation data, provided by climate models. Only few studies are available applying these techniques to hydrological model outputs. Standard bias correction techniques used in literature can be classified into scaling-, and distributional-based methods. The former consists of using multiplicative or additive scaling factors to correct the modeled simulations, while the later methods are quantile mapping techniques that fit the distribution of the simulation to fit to the observations. In this study, the impact of different bias correction techniques on the seasonal discharge forecasts skill is assessed.</p><p>As a case study, a seasonal discharge forecasting system developed for the Danube basin upstream of Vienna, is used. The studied basin covers an area of around 100 000 km<sup>2</sup> and is subdivided in 65 subbasins, 55 of them gauged with a long historical record of observed discharge. The forecast system uses the calibrated hydrological model, COSERO, which is fed with an ensemble of seasonal temperature and precipitation forecasts. The output of the model provides an ensemble of seasonal discharge forecasts for each of the (gauged) subbasins. Seasonal meteorological forecasts for the past (hindcast), together with historical discharge observations, allow to assess the quality of the seasonal discharge forecasting system, also including the effects of different bias correction methods. The corrections applied to the discharge simulations allow to eliminate potential systematic errors between the modeled and observed values.</p><p>Our findings generally suggest that the quality of the seasonal forecasts improve when applying bias correction. Compared to simpler methods, which use additive or multiplicative scaling factors, quantile mapping techniques tend to be more appropriate in removing errors in the ensemble seasonal forecasts.</p>

DOA and Phase Error Estimation for a Partly Calibrated Array With Arbitrary Geometry

2020 ◽  
Vol 56 (1) ◽  
pp. 497-511 ◽  
Author(s):  
Xuejing Zhang ◽  
Zishu He ◽  
Xuepan Zhang ◽  
Yue Yang
Keyword(s):  
Error Estimation ◽  
Phase Error ◽  
Arbitrary Geometry

scholarly journals Strip-Mode Microwave Staring Correlated Imaging with Self-Calibration of Gain–Phase Errors

Sensors ◽  
2019 ◽  
Vol 19 (5) ◽  
pp. 1079 ◽  
Author(s):  
Rui Xia ◽  
Yuanyue Guo ◽  
Weidong Chen ◽  
Dongjin Wang
Keyword(s):  
Error Estimation ◽  
Phase Error ◽  
Super Resolution ◽  
Image Splicing ◽  
Initial Value ◽  
Self Calibration ◽  
Phase Errors ◽  
Imaging Model ◽  
Multiple Imaging ◽  
Imaging Performance

Microwave staring correlated imaging (MSCI) can realize super resolution imaging without the limit of relative motion with the target. However, gain–phase errors generally exist in the multi-transmitter array, which results in imaging model mismatch and degrades the imaging performance considerably. In order to solve the problem of MSCI with gain–phase error in a large scene, a method of MSCI with strip-mode self-calibration of gain–phase errors is proposed. The method divides the whole imaging scene into multiple imaging strips, then the strip target scattering coefficient and the gain–phase errors are combined into a multi-parameter optimization problem that can be solved by alternate iteration, and the error estimation results of the previous strip can be carried into the next strip as the initial value. All strips are processed in multiple rounds, and the gain–phase error estimation results of the last strip can be taken as the initial value and substituted into the first strip for the correlated processing of the next round. Finally, the whole imaging in a large scene can be achieved by multi-strip image splicing. Numerical simulations validate its potential advantages to shorten the imaging time dramatically and improve the imaging and gain–phase error estimation performance.

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