ACCURATEMAPPING OF A DEFECT BORDER BY ERROR ANALYSIS

Precise Point Positioning (PPP) is an increasingly recognized precisely the GPS/GNSS positioning technique. In order to improve the accuracy of PPP, the error sources in PPP measurements should be reduced as much as possible and the ambiguities should be correctly resolved. The correct ambiguity resolution requires a careful control of residual errors that are normally categorized into random and systematic errors. To understand effects from two categorized errors on the PPP ambiguity resolution, those two GPS datasets are simulated by generating in locations in South Korea (denoted as SUWN) and Hong Kong (PolyU). Both simulation cases are studied for each dataset; the first case is that all the satellites are affected by systematic and random errors, and the second case is that only a few satellites are affected. In the first case with random errors only, when the magnitude of random errors is increased, L1 ambiguities have a much higher chance to be incorrectly fixed. However, the size of ambiguity error is not exactly proportional to the magnitude of random error. Satellite geometry has more impacts on the L1 ambiguity resolution than the magnitude of random errors. In the first case when all the satellites have both random and systematic errors, the accuracy of fixed ambiguities is considerably affected by the systematic error. A pseudorange systematic error of 5 cm is the much more detrimental to ambiguity resolutions than carrier phase systematic error of 2 mm. In the 2 nd case when only a portion of satellites have systematic and random errors, the L1 ambiguity resolution in PPP can be still corrected. The number of allowable satellites varies from stations to stations, depending on the geometry of satellites. Through extensive simulation tests under different schemes, this paper sheds light on how the PPP ambiguity resolution (more precisely L1 ambiguity resolution) is affected by the characteristics of the residual errors in PPP observations. The numerical examples recall the PPP data analysts that how accurate the error correction models must achieve in order to get all the ambiguities resolved correctly.

Fossil plant gas-exchange-based CO2 reconstructions use carbon (C) assimilation rates of extant plant species as substitutes for assimilation rates of fossil plants. However, assumptions in model species adoption can lead to systematic error propagation. We used a dataset of c. 2500 extant species to investigate the role of phylogenetic relatedness and ecology in determining C assimilation, an essential variable in gas-exchange-based CO2 models. We evaluated the effect on random and systematic error propagation in atmospheric CO2 caused by adopting different model species. Phylogenetic relatedness, growth form, and solar exposure are important predictors of C assimilation rate. CO2 reconstructions that apply C assimilation rates from modern species based solely on phylogenetic relatedness to fossil species can result in CO2 estimates that are systematically biased by a factor of >2. C assimilation rates used in CO2 reconstructions should be determined by averaging assimilation rates of modern plant species that are (1) in the same family and (2) have a similar habit and habitat as the fossil plant. In addition, systematic bias potential and random error propagation are greatly reduced when CO2 is reconstructed from multiple fossil plant species with different modern relatives at the same site.

Evaluation of errors in the determination of gas chromatographic retention parameters and derivative quantities

To quantify systematic and random patient set-up errors in breast and head and neck conventional irradiation and to evaluate a no-action level (NAL) protocol for systematic set-up error off-line correction in head and neck cancer and breast cancer patients. Verification electronic portal images of orthogonal set-up fields were obtained daily for the initial four consecutive fractions for 20 patients treated for breast cancer and for 20 head and neck cancer patients. The calculated systematic error was used to shift the isocentre accordingly on the fifth treatment day. From then until the end of the treatment course, pair orthogonal portal images of set-up fields were obtained weekly. To assess the impact of the protocol, pre- and post-correction systematic errors were compared and PTV margins were estimated before and after correction using published margin recipes. Population systematic set-up error decreased in the breast cancer patient group after the implementation of NAL protocol from 4.0 to 1.7 mm on the x-axis, from 4.7 to 2.1 mm on the y-axis and from 2.8 to 0.9 mm on the z axis. The percentage of patients with individual systematic set-up error reduction was 80%, 90% and 80% on the x-, y and z-axes respectively. Population systematic set-up error decreased also in the head and neck cancer patient group from 2.3 to 1.1 mm on the x-axis, from 1.6 to 1.4 mm on the y-axis and from 1.7 to 0.7 mm on the z-axis. The percentage of patients with individual systematic set-up error reduction was 70%, 65% and 85% on the x-, y- and z-axes respectively. Margin reduction achievable with NAL protocol implementation on the x-, y- and z-axes was 6.3, 7.2 and 4.8 mm for breast cancer patients and 3.3, 0.6 and 2.8 mm for head and neck cancer patients. NAL off-line protocol is useful for systematic set-up error correction and PTV margin reduction in conventional breast and head and neck irradiation.

Topographic surveys inevitably contain error, introducing uncertainty into estimates of volumetric or mean change based on the differencing of repeated surveys. In the geomorphic community, uncertainty has often been framed as a problem of separating out real change from apparent change due purely to error, and addressed by removing measured change considered indistinguishable from random noise from analyses (thresholding). Thresholding is important when quantifying gross changes (i.e. total erosion or total deposition), which are systematically biased by random errors in stable parts of a landscape. However, net change estimates are not substantially influenced by those same random errors, and the use of thresholds results in inherently biased, and potentially misleading, estimates of net change and uncertainty. More generally, thresholding is unrelated to the important process of propagating uncertainty in order to place uncertainty bounds around final estimates. Error propagation methods for uncorrelated, correlated, and systematic errors are presented. Those equations demonstrate that uncertainties in modern net change analyses, as well as in gross change analyses using reasonable thresholds, are likely to be dominated by low‐magnitude but highly correlated or systematic errors, even after careful attempts to reduce those errors. In contrast, random errors with little to no correlation largely cancel to negligible levels when averaged or summed. Propagated uncertainty is then typically insensitive to the precision of individual measurements, and is instead defined by the relative mean error (accuracy) over the area of interest. Given that real‐world mean elevation changes in many landscape settings are often similar in magnitude to potential mean errors in repeat topographic analyses, reducing highly correlated or systematic errors will be central to obtaining accurate change estimates, while placing uncertainty bounds around those results provides essential context for their interpretation. Published 2018. This article is a U.S. Government work and is in the public domain in the USA.

A common question in movement studies is how the results should be interpreted with respect to systematic and random errors. In this study, simulations are made in order to see how a rigid body's orientation in space (i.e. helical angle between two orientations) is affected by (1) a systematic error added to a single marker (2) a combination of this systematic error and Gaussian white noise. The orientation was estimated after adding a systematic error to one marker within the rigid body. This procedure was repeated with Gaussian noise added to each marker. In conclusion, results show that the systematic error's effect on estimated orientation depends on number of markers in the rigid body and also on which direction the systematic error is added. The systematic error has no effect if the error is added along the radial axis (i.e. the line connecting centre of mass and the affected marker).

The position errors of array elements, which include systematic and random errors, are inevitable and could lead to the degradation of the radiation performance. For an array antenna, the systematic errors come from the continuous deformation of the reflector while the random errors come from the manufacturing and assembly of array elements. The accurate representation of position errors is important to evaluate the effects of position errors on performance in the design of an array antenna. In previous studies, many methods have been proposed to represent the systematic and random errors. However, few studies have considered the high‐order position relevance of array elements resulting from the systematic errors, which could lead to the inaccurate representation of position errors. Here, a γ‐conical representation method is proposed to consider the γ‐order position relevance of successive array elements. The existing conical representation method and the proposed γ‐conical representation method are used as comparisons to generate simulation data of position errors. The corresponding electrical performance of position errors is calculated with antenna theories and Feko. Prediction models are built based on a linear programming support vector regression algorithm to evaluate the ability of different representation methods. Finally, experiments are conducted on a platform with 8 × 8 array elements to demonstrate the superiority of the γ‐conical representation method.

Purpose:To empirically derive margin formulas from existing clinical radiotherapy plans accounting for respiratory motion and setup uncertainties.Methods:We simulated realistic treatment scenarios, including respiratory motion and setup errors. Individual probability density functions (PDF) from respiratory data were used to simulate respiratory motion. Random (σ) and systematic (Σ) setup errors were modeled as Gaussian distributions. One‐dimensional dose profiles were extracted from existing radiotherapy plans and convolved with respiratory PDFs and random error distributions to produce blurred dose profiles. Each blurred dose profile was then shifted 1000 times by randomly sampling the simulated systematic error distribution. Margins were determined from the distance between the simulated treatment and the original 95% isodose level. An equation was fit for each (σ, Σ) combination to derive margin formulas for 90% of the population receiving 95% dose. This methodology can be applied to different tumor sites. Here, dose profiles were extracted from partial breast 3DCRT plans in the anterior‐posterior (AP) and superior‐inferior (SI) directions. Respiratory motion data was from healthy volunteers, and a clinically relevant range of random and systematic setup errors (standard deviations 1 – 4 mm) was determined from the literature.Results:The PBI margin formulas in the AP and SI directions for 95% dose coverage for 90% of the population were very similar: M= 0.68σ + 1.54Σ and M= 0.72σ + 1.50Σ, respectively. Systematic setup errors had the largest influence on required margin size, whereas realistic respiratory amplitude had minimal impact. The derived formulas resulted in a smaller systematic component than commonly‐used theoretical margin recipes.Conclusion:We have demonstrated a method to derive empirical margin formulas from existing patient radiotherapy plans, incorporating realistic respiratory motion and appropriate ranges of random and systematic error. Site‐specific margin formulas may be better suited to patient populations than theoretically derived, ideal geometry general margin formulas.

Error propagation is the extrapolation and cumulation of uncertainty (variance) above total amounts of special nuclear material, for example, uranium or /sup 235/U, that are present in a defined location at a given time. The uncertainty results from the inevitable inexactness of individual measurements of weight, uranium concentration, /sup 235/U enrichment, etc. The extrapolated and cumulated uncertainty leads directly to quantified limits of error on inventory differences (LEIDs) for such material. The NLO error propagation exercise was planned as a field demonstration of the utilization of statistical error propagation methodology at the Feed Materials Production Center in Fernald, Ohio from April 1 to July 1, 1983 in a single material balance area formed specially for the exercise. Major elements of the error propagation methodology were: variance approximation by Taylor Series expansion; variance cumulation by uncorrelated primary error sources as suggested by Jaech; random effects ANOVA model estimation of variance effects (systematic error); provision for inclusion of process variance in addition to measurement variance; and exclusion of static material. The methodology was applied to material balance area transactions from the indicated time period through a FORTRAN computer code developed specifically for this purpose on the NLO HP-3000 computer. This paper contains a complete description of the error propagation methodology and a full summary of the numerical results of applying the methodlogy in the field demonstration. The error propagation LEIDs did encompass the actual uranium and /sup 235/U inventory differences. Further, one can see that error propagation actually provides guidance for reducing inventory differences and LEIDs in future time periods.

Bladder dose–surface maps and urinary toxicity: Robustness with respect to motion in assessing local dose effects

Dosimetric comparison of 3-dimensional conformal radiation therapy and intensity modulated radiation therapy and impact of setup errors in lower limb sarcoma radiation therapy

Abstract. A high-fidelity lidar turbulence measurement technique relies on accurate estimates of radial velocity variance that are subject to both systematic and random errors determined by the autocorrelation function of radial velocity, the sampling rate, and the sampling duration. Using both statistically simulated and observed data, this paper quantifies the effect of the volumetric averaging in lidar radial velocity measurements on the autocorrelation function and the dependence of the systematic and random errors on the sampling duration. For current-generation scanning lidars and sampling durations of about 30 min and longer, during which the stationarity assumption is valid for atmospheric flows, the systematic error is negligible but the random error exceeds about 10 %.

The introduction of IMRT poses new challenges for delivering intended target dose and minimizing dose and toxicity to critical normal structures. For head and neck cancer, reproducible patient positioning throughout the whole treatment course is particularly important due to the proximity of many critical organs. Deviations from the planned irradiation geometry during a treatment session may be systematic or random. Systematic errors occur if the mean irradiation geometry in the fractionated treatment differs differs from the geometry in the treatment plan. The mean deviations are then called systematic errors. Fraction-to-fraction variations around the mean deviation are called random errors. The purpose of this study is to measure the interfraction setup variation of patient undergoing IMRT of head and neck cancer. The data is used to define adequate treatment clinical target volume to planning target volume (CTV-to-PTV) margin. During March to November 2006, the data was collected from 9 head and neck cancer patients treated with dynamic IMRT using 6 MV X-ray beam from Varian Clinac 23EX. Weekly portal images of setup fields which were anterior-posterior and lateral portal images were acquired for each patient with an amorphous silicon EPID, Varian aS500. These images were matched with the reference images from Varian Acuity simulator using the VARiS Vision software, version 7.3.10 Six anatomical landmarks were selected for comparison. The displacement of portal image from the reference image was recorded in X (Left-Right, L-R), Y (Superior-Inferior, S-I) direction for anterior field and Z (Anterior-Posterior, A-P), Y (S-I) direction for lateral field. The systematic and random error for individual and population were calculated. Then the population-based margins were obtained. The total of 168 images ( 27 simulation images and 141 portal images) and 564 match points were evaluated. The results showed that the systematic error ranged from 0 to 7.5 mm and the random error ranged from 0.3 to 4.8 mm for all direction. The population-based margin ranged from 2.4 to 4.9 mm (L-R), 3.9 to 5.0 mm (S-I) for anterior field and 3.4 to 4.7 mm (A-P), 2.6 to 3.7 mm (S-I) for the lateral field. The difference in population-based margins along S-I axis between anterior field and lateral field were observed because the clavicles chosen for anterior field at the shoulder level were less stable than anatomical landmarks chosen for lateral field i.e. skull bones, C1 and C4. These margins were comparable to the margin that prescribed at King Chulalongkorn Memorial Hospital (5-10 mm) for head and neck cancer. These results showed that the population-based margin is less than 5 mm, thus the margin provides sufficient coverage for all of the patients.

Use of stacked Gaussian processes regression method to improve prediction of groundwater solute transport model

The effects of equilibrium transcytolemmal water exchange on the determination of contrast reagent concentration in vivo