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Journal articles on the topic 'Direct Least Square Fitting'

Author: Grafiati
Published: 3 June 2025
Last updated: 22 June 2025

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1

Kesaniemi, Martti, and Kai Virtanen. "Direct Least Square Fitting of Hyperellipsoids." IEEE Transactions on Pattern Analysis and Machine Intelligence 40, no. 1 (2018): 63–76. http://dx.doi.org/10.1109/tpami.2017.2658574.

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2

Fitzgibbon, A., M. Pilu, and R. B. Fisher. "Direct least square fitting of ellipses." IEEE Transactions on Pattern Analysis and Machine Intelligence 21, no. 5 (1999): 476–80. http://dx.doi.org/10.1109/34.765658.

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3

MAINI, ELISEO STEFANO. "ENHANCED DIRECT LEAST SQUARE FITTING OF ELLIPSES." International Journal of Pattern Recognition and Artificial Intelligence 20, no. 06 (2006): 939–53. http://dx.doi.org/10.1142/s021800140600506x.

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This paper presents a robust and direct algorithm for the least-square fitting of ellipses to scattered data. The proposed algorithm makes use of well-known techniques that improve the robustness of the direct least-square fitting with a modest increase of the computational burden. Furthermore, by trivial modifications of the constrained minimization problem the algorithm may be converted to perform the specific fitting of other types of conics such as hyperbola. The method is simple and accurate and can be implemented with fixed time of computation. These characteristics coupled to its robustness and specificity makes the algorithm well-suited for applications requiring real-time machine vision.
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4

Zsombor-Murray, Paul. "Direct and specific least-square fitting of hyperbolæ and ellipses." Journal of Electronic Imaging 13, no. 3 (2004): 492. http://dx.doi.org/10.1117/1.1758951.

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5

Pratt, Vaughan. "Direct least-squares fitting of algebraic surfaces." ACM SIGGRAPH Computer Graphics 21, no. 4 (1987): 145–52. http://dx.doi.org/10.1145/37402.37420.

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6

Moura, L., and R. Kitney. "A direct method for least-squares circle fitting." Computer Physics Communications 64, no. 1 (1991): 57–63. http://dx.doi.org/10.1016/0010-4655(91)90049-q.

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7

O'Leary, P., M. Harker, and P. Zsombor-Murray. "Direct and least square fitting of coupled geometric objects for metric vision." IEE Proceedings - Vision, Image, and Signal Processing 152, no. 6 (2005): 687. http://dx.doi.org/10.1049/ip-vis:20045206.

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8

Sun, Jin Guang, and Yu Cheng Zhou. "Skin Color Detection Method Based on Direct Least Square Ellipse Fitting in CrCbCg Space." Advanced Materials Research 366 (October 2011): 28–31. http://dx.doi.org/10.4028/www.scientific.net/amr.366.28.

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Skin color detection is an important in computer vision.This work presents a new efficient method for skin color detection based on an improved direct least square ellipse fitting in the space CrCbCg. The color distribution statistics of three-dimensional CrCbCg is obtained by fitting the color distribution ellipse boundary in the Cr-Cb, Cr-Cg, Cb-Cg plane exactly ,finally ,the criteria based on the statistics is used to detect skin color area accurately. Experimental results show that this method improves the robustness of the skin color detection to complex environment.
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9

Schöne, R., and T. Hanning. "Least Squares Problems with Absolute Quadratic Constraints." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/312985.

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This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.
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10

Wang, Xuanze, Qian Shi, Da Liu, et al. "Absolute Capacitance Measurement by Direct Digital Fitting of Proportional Coefficient." Applied Sciences 15, no. 8 (2025): 4589. https://doi.org/10.3390/app15084589.

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In the realm of capacitance measurement, traditional methods that gauge capacitance through timing charge and discharge intervals frequently suffer from inaccuracies, particularly due to noise affecting voltage threshold detection. These techniques are also inefficient for high-capacitance components, as their lengthy charge–discharge cycles limit the measurable range within a given period. To this end, a method for directly sampling and analyzing the input and output signals of an RC first-order system under square wave excitation is proposed for a wide range of capacitance measurements. By establishing a proportional relationship between the differentiated output signal and the difference between input and output signals, one can deduce the capacitance. To counteract noise-induced errors during differentiation, data smoothing is applied, enhancing accuracy. This technique achieves a relative standard deviation of less than 0.9% for capacitances from 60 pF to 60,000 pF, using a 100 kΩ reference resistor and continuous square waves. For capacitances above 800 pF, precision further improves to less than 0.2%. The approach leverages least squares fitting and outlier rejection to manage noise effectively. It remains independent of the capacitor’s initial state, ensuring broad-range accuracy and faster measurement times.
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11

Xiong, Boli, Jing M. Chen, Gangyao Kuang, and Nobuhiko Kadowaki. "Estimation of the Repeat-Pass ALOS PALSAR Interferometric Baseline Through Direct Least-Square Ellipse Fitting." IEEE Transactions on Geoscience and Remote Sensing 50, no. 9 (2012): 3610–17. http://dx.doi.org/10.1109/tgrs.2012.2184290.

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12

Jansen, J., R. Peschar, and H. Schenk. "On the determination of accurate intensities from powder diffraction data. I. Whole-pattern fitting with a least-squares procedure." Journal of Applied Crystallography 25, no. 2 (1992): 231–36. http://dx.doi.org/10.1107/s0021889891012104.

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A new algorithm, direct intensity fitting, has been developed which performs a whole-pattern fitting for powder data. The algorithm is related to the fitting technique of Pawley [J. Appl. Cryst. 14, 357–361] but does not require start values for the intensities of the individual reflections. Comparative tests show that direct intensity fitting extracts more accurate intensities from a powder diffractogram and reduces the minimum peak distance for accurate data to half of the half-widths. The structure of the superconductor Ba2YCu3O8−x can be solved in a default direct-methods run with direct-intensity-fitting intensities extracted from a normal laboratory powder diffractogram.
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13

Greenaway-McGrevy, Ryan. "MULTISTEP PREDICTION OF PANEL VECTOR AUTOREGRESSIVE PROCESSES." Econometric Theory 29, no. 4 (2013): 699–734. http://dx.doi.org/10.1017/s0266466612000679.

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This paper considers the conventional recursive (otherwise known as plug-in) and direct multistep forecasts in a panel vector autoregressive framework. We derive asymptotic expressions for the mean square prediction error (MSPE) of both forecasts as N (cross sections) and T (time periods) grow large. Both the bias and variance of the least squares fitting are manifest in the MSPE. Using these expressions, we consider the effect of model specification on predictor accuracy. When the fitted lag order (q) is equal to or exceeds the true lag order (p), the direct MSPE is larger than the recursive MSPE. On the other hand, when the fitted lag order is underspecified, the direct MSPE is smaller than the recursive MSPE. The recursive MSPE is increasing in q for all q ≥ p. In contrast, the direct MSPE is not monotonic in q within the permissible parameter space. Extensions to bias-corrected least squares estimators are considered.
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14

Łuczak, Dominik. "Nonlinear Identification with Constraints in Frequency Domain of Electric Direct Drive with Multi-Resonant Mechanical Part." Energies 14, no. 21 (2021): 7190. http://dx.doi.org/10.3390/en14217190.

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Knowledge of a direct-drive model with a complex mechanical part is important in the synthesis of control algorithms and in the predictive maintenance of digital twins. The identification of two-mass drive systems with one low mechanical resonance frequency is often described in the literature. This paper presents an identification workflow of a multi-resonant mechanical part in direct drive with up to three high-frequency mechanical resonances. In many methods, the identification of a discrete time (DT) model is applied, and its results are transformed into a continuous-time (CT) representation. The transformation from a DT model to a CT model has limitations due to nonlinear mapping of discrete to continuous frequencies. This problem may be overcome by identification of CT models in the frequency domain. This requires usage of a discrete Fourier transform to obtain frequency response data as complex numbers. The main work presented in this paper is the appropriate fitting of a CT model of a direct-drive mechanical part to complex number datasets. Fitting to frequency response data is problematic due to the attraction of unexcited high frequency ranges, which lead to wrong identification results of multi-mass (high order) drive systems. Firstly, a CT fitting problem is a nonlinear optimization problem, and, secondly, complex numbers may be presented in several representations, which leads to changes in the formulation of the optimization problem. In this paper, several complex number representations are discussed, and their influence on the optimization process by simulation evaluation is presented. One of the best representations is then evaluated using a laboratory setup of direct drive with unknown parameters of three high mechanical resonance frequencies. The mechanical part of the examined direct drive is described by three mechanical resonances and antiresonances, which are characteristic of a four-mass drive system. The main finding is the addition of frequency boundaries in the identification procedure, which are the same as those in the frequency range of the excitation signal. Neither a linear least-square algorithm nor a nonlinear least-square algorithm is suitable for this approach. The usage of nonlinear least-square algorithm with constraints as a fitting algorithm allows one to solve the issue of modeling multi-mass direct-drive systems in the frequency domain. The second finding of this paper is a comparison of different cost functions evaluated to choose the best complex number representation for the identification of multi-mass direct-drive systems.
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15

Fang, Changqing, Huiyu Sun, and Jianping Gu. "Powell’s method-based nonlinear least-squares data fitting for the Mittag-Leffler relaxation function." Mathematics and Mechanics of Solids 22, no. 5 (2015): 1058–67. http://dx.doi.org/10.1177/1081286515616284.

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The Mittag-Leffler relaxation function, [Formula: see text], with [Formula: see text], plays an important role in the fractional viscoelastic models. The Mittag-Leffler function is an infinite series whose analytic derivatives are unexplored, thus a direct search method based on Powell’s method is introduced to solve the minimization problem of nonlinear least-squares data fitting for Mittag-Leffler relaxation function in this paper. A simple and effective method is provided for the determination of the initial values and an acceleration strategy is proposed for this direct search method. Numerical results show this direct search method is efficient in the parameter estimation of the Mittag-Leffler relaxation function. Furthermore, the acceleration strategy proves to be conducive to improving the computational efficiency of this direct search method.
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16

Chen, Nongtian, Youchao Sun, Zongpeng Wang, and Chong Peng. "Correction and Fitting Civil Aviation Flight Data EGT Based on RPM: Polynomial Least Squares Analysis." Applied Sciences 12, no. 5 (2022): 2545. http://dx.doi.org/10.3390/app12052545.

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There are different missing flight data due to various reasons in the process of acquisition and storage, especially in general aviation, which cause inconvenience for flight data analysis. Effectively explaining the relationship between flight data parameters and selecting a simple and effective method for fitting and correcting flight data suitable for engineering applications are the main points of the paper. Herein, a convenient and applicable approach of missing data correction and fitting based on the least squares polynomial method is introduced in this work. Firstly, the polynomial fitting model based on the least squares method is used to establish multi-order polynomial by existing flight data since the order of the least squares polynomial has a direct impact on the fitting effect. The order is too high or too small, over-fitting or deviation will occur, resulting in improper data. Therefore, the optimization and selection of the model order are significant for flight data correction and fitting. Because the flight data of the aircraft engine exhaust gas temperature (EGT) are often lost because of the immature detection technology, a series of the multi-order polynomial are established by the relationship of aircraft engine exhaust gas temperature and Revolutions Per Minute (RPM). Case study results confirm the optimal model order is four for the fitting and correction of aircraft engine exhaust temperature, and the least squares polynomial method is applicable and effective for EGT flight data correction and fitting based on RPM data.
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17

Malissiovas, Georgios, Frank Neitzel, Sven Weisbrich, and Svetozar Petrovic. "Weighted Total Least Squares (WTLS) Solutions for Straight Line Fitting to 3D Point Data." Mathematics 8, no. 9 (2020): 1450. http://dx.doi.org/10.3390/math8091450.

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In this contribution the fitting of a straight line to 3D point data is considered, with Cartesian coordinates xi, yi, zi as observations subject to random errors. A direct solution for the case of equally weighted and uncorrelated coordinate components was already presented almost forty years ago. For more general weighting cases, iterative algorithms, e.g., by means of an iteratively linearized Gauss–Helmert (GH) model, have been proposed in the literature. In this investigation, a new direct solution for the case of pointwise weights is derived. In the terminology of total least squares (TLS), this solution is a direct weighted total least squares (WTLS) approach. For the most general weighting case, considering a full dispersion matrix of the observations that can even be singular to some extent, a new iterative solution based on the ordinary iteration method is developed. The latter is a new iterative WTLS algorithm, since no linearization of the problem by Taylor series is performed at any step. Using a numerical example it is demonstrated how the newly developed WTLS approaches can be applied for 3D straight line fitting considering different weighting cases. The solutions are compared with results from the literature and with those obtained from an iteratively linearized GH model.
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18

Muchtadi-Alamsyah, Intan, Mohamad Nur Heriawan, Gantina Rachmaputri, Elvira Rahmadiantri, and Made Putri Lawiyuniarti. "Application of Three-Dimensional Direct Least Square Method for Ellipsoid Anisotropy Fitting Model of Highly Irregular Drill Hole Patterns." Applied Sciences 12, no. 15 (2022): 7848. http://dx.doi.org/10.3390/app12157848.

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Ellipsoid or geometric anisotropy is a widely used method in geostatistical analysis to obtain variograms with different ranges in different directions (azimuth) and relatively similar sill variance. Ellipsoid anisotropy is indispensable in mining when a resource geologist intends to understand the spatial continuity of variables related to any geological controls of the mineralization. For example, when dealing with mineralization related to tabular deposits, a porphyritic deposit with an irregular drill hole pattern (fan drilling), three-dimensional ellipsoid anisotropy is quite challenging to model. We assume that the variables’ spatial continuity is isotropic, and we model it using a three-dimensional omnidirectional variogram. However, if the actual spatial continuity of the variables has a three-dimensional anisotropy, then assuming a three-dimensional omnidirectional variogram will generate imprecise resource estimations. This study presents a new practical three-dimensional ellipsoid model-fitting method using a three-dimensional direct least square method. We investigated a zinc (Zn) dataset from thousands of irregular drill hole patterns from a porphyritic system associated with skarn orebodies for the case study.
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19

Zhang, Wei, Hong Bo Yi, and Xiao Wen Wang. "Coal Dust Recognition Based on Concave Point Extraction and Ellipse Fitting." Applied Mechanics and Materials 654 (October 2014): 296–99. http://dx.doi.org/10.4028/www.scientific.net/amm.654.296.

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A new coal dust particle recognition algorithm based on concave points extraction and ellipse fitting is proposed for the features of irregularities and particle overlap. The new algorithm includes contour processing and ellipse fitting in this paper. In the part of contour processing, the feature points are obtained with polygonal approximation on the edge of a binary dust particles image, and then concave points of overlapping particles are extracted by the method of angle combined with size, finally the edge is segmented by concave points. To solve the problem that direct least square ellipse fitting is easily affected by noise points, bare bones particle swarm optimization is introduced to find global optimum fitting parameters and the segmented edge is ellipse fitted. Experiment results show this proposed algorithm obtains better recognition performance.
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20

Jiang, Chao, Fuliang Wang, and Yan Ning. "Application of least squares fitting algorithm in transformer terminal unit electrical quantities acquisition." IOP Conference Series: Earth and Environmental Science 983, no. 1 (2022): 012021. http://dx.doi.org/10.1088/1755-1315/983/1/012021.

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Abstract In order to accurately estimate the frequency and harmonics of voltage and current signals acquired in transformer terminal unit (TTU), the least squares fitting algorithm is applied to its harmonic analysis. The principle of the algorithm and its flowchart are presented, and the implementation of the algorithm in TTU is primarily discussed. The noisy voltage signals with harmonics and signal frequencies ranging from 49.8 Hz to 50.2 Hz are generated and the real ones are acquired. The harmonic analysis results of the least squares fitting algorithm and the Hanning window and interpolation algorithm reveal that the errors in the signal frequency, direct current (DC) component, amplitude and phase of fundamental and harmonics of the former are only about 1/3 of that of the latter.
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21

Heller, René, Michael Hippke, and Kai Rodenbeck. "Transit least-squares survey." Astronomy & Astrophysics 627 (July 2019): A66. http://dx.doi.org/10.1051/0004-6361/201935600.

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The extended Kepler mission (K2) has revealed more than 500 transiting planets in roughly 500 000 stellar light curves. All of these were found either with the box least-squares algorithm or by visual inspection. Here we use our new transit least-squares (TLS) algorithm to search for additional planets around all K2 stars that are currently known to host at least one planet. We discover and statistically validate 17 new planets with radii ranging from about 0.7 Earth radii (R⊕) to roughly 2.2 R⊕ and a median radius of 1.18 R⊕. EPIC 201497682.03, with a radius of 0.692+0.059−0.048, is the second smallest planet ever discovered with K2. The transit signatures of these 17 planets are typically 200 ppm deep (ranging from 100 ppm to 2000 ppm), and their orbital periods extend from about 0.7 d to 34 d with a median value of about 4 d. Fourteen of these 17 systems only had one known planet before, and they now join the growing number of multi-planet systems. Most stars in our sample have subsolar masses and radii. The small planetary radii in our sample are a direct result of the higher signal detection efficiency that TLS has compared to box-fitting algorithms in the shallow-transit regime. Our findings help in populating the period-radius diagram with small planets. Our discovery rate of about 3.7% within the group of previously known K2 systems suggests that TLS can find over 100 additional Earth-sized planets in the data of the Kepler primary mission.
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22

Tazreiter, Martin, Paul Christian, Robert Schennach, Thomas Grießer, and Anna Maria Coclite. "Simple method for the quantitative analysis of thin copolymer films on substrates by infrared spectroscopy using direct calibration." Analytical Methods 9, no. 36 (2017): 5266–73. http://dx.doi.org/10.1039/c7ay01748k.

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23

Hu Donggang. "Potato shape detection based on stable direct least square method of ellipses fitting and it��s application prospect in Land Science." International Journal of Digital Content Technology and its Applications 6, no. 20 (2012): 161–71. http://dx.doi.org/10.4156/jdcta.vol6.issue20.18.

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24

Lei, Iat-Long, Phoey Lee Teh, and Yain-Whar Si. "Direct least squares fitting of ellipses segmentation and prioritized rules classification for curve-shaped chart patterns." Applied Soft Computing 107 (August 2021): 107363. http://dx.doi.org/10.1016/j.asoc.2021.107363.

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25

Marhaban, M. H., Rakeeb S. Kaid, and Samsul B. Mohd Noor. "Automatic Estimation of Gestational Age in Ultrasound Images Based on Direct Least-Squares Fitting of Ellipse." IEEJ Transactions on Electrical and Electronic Engineering 5, no. 5 (2010): 569–73. http://dx.doi.org/10.1002/tee.20574.

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26

Nekut, A. G. "Direct inversion of time‐domain electromagnetic data." GEOPHYSICS 52, no. 10 (1987): 1431–35. http://dx.doi.org/10.1190/1.1442256.

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This note describes a simple method for converting transient electromagnetic (EM) sounding data into profiles of conductivity versus depth, based on an approximate image representation for the decaying induced ground currents. The method can provide one‐dimensional (1-D) inversion for any kind of time‐domain EM sounding data; the discussion here is limited to the case of central‐loop sounding. In particular, I apply the inversion to some time‐derivative central‐loop sounding data and demonstrate that essentially the same interpretation of the geoelectric section is obtained with the simple image method as is obtained using traditional iterative least‐squares fitting to layered models. This simple inverse can be computed much more quickly than an iterative least‐squares inverse, making it possible to estimate the geoelectric section concomitant with data acquisition.
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27

Brenna, J. T., and K. E. Yeager. "Direct determination of deuterium in untreated water and urine by NMR: application to DLW analysis." American Journal of Physiology-Endocrinology and Metabolism 268, no. 5 (1995): E1018—E1026. http://dx.doi.org/10.1152/ajpendo.1995.268.5.e1018.

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Determination of deuterium (D) concentration in tap water and urine is demonstrated to average error approximately 0.5% (coefficient of variation) using a 400-MHz nuclear magnetic resonance (NMR) instrument. Time domain data are obtained using 0.75-ml samples in a broadband probe. Peak areas derived from absorption and magnitude mode Fourier transforms and least-squares fitting of the time domain free induction decays (FIDs) are all investigated as means to derive D concentrations from raw data. Least-squares fits using a sum of exponentially damped sinusoids, which yields estimates for the amplitude, damping constant (relaxation time), wavelength (resulting from mixing of precession and reference frequencies), and phase for each of the two components, are shown to provide the best precision for unfiltered FID. Amplitudes are proportional to the number of spins at each frequency, as analysis of untreated urine from doubly labeled water experiments yield highly linear washout data (r2 > 0.99998) for baseline-corrected log-transformed data. The procedure is general and should extend to other body fluids with minimal modifications. These data show that least-squares curve fitting is the most precise method of quantitative NMR data reduction for a wide range of experimental conditions.
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28

Holden, J. E., L. Eriksson, P. E. Roland, S. Stone-Elander, L. Widen, and M. Kesselberg. "Direct Comparison of Single-Scan Autoradiographic with Multiple-Scan Least-Squares Fitting Approaches to PET CMRO2 Estimation." Journal of Cerebral Blood Flow & Metabolism 8, no. 5 (1988): 671–80. http://dx.doi.org/10.1038/jcbfm.1988.114.

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The time course of local cerebral radioactivity concentration after bolus inhalation of oxygen gas labeled with O-15 was measured in a rapid dynamic sequence of positron tomographic images. Four normal subjects were studied at rest. In each study, 15 multiple-slice image sets were acquired over a 3-min period in a Scanditronix model 384 tomograph. The radioactivity concentration in arterial blood was measured at 1-s intervals by means of a pump-fed flow-through detector. Pump effluent was directed to discrete samples that were separated into plasma and cell fractions to estimate the accumulation of labeled, recirculating water arising from systemic metabolism. Stereotactically matched scans of local cerebral blood flow and volume were acquired in the same imaging session, and the derived values were used as fixed parameters in the model fits of the time courses of pixel radioactivity in the oxygen study. Rapid nonlinear least-squares parameter optimization was used to estimate simultaneously the local CMRO2 and the brain/blood relative distribution volume for water in each image pixel. The same scan data were combined into effective single frames of various starting times and durations for analysis using the single-scan (“autoradiographic”) approach to CMRO2 estimation, which requires a presumed value for relative distribution volume. Oxygen use values derived using this approach were observed to be strongly dependent on the relative distribution volume value chosen, particularly for long study durations. However, for each gray matter region of interest studied, a uniform value for the relative distribution volume existed such that the estimated CMRO2 values were independent of the starting time and duration of the single scan used, and were furthermore the same as that yielded by the multiple-scan least-squares fitting of the total time course in the same region. We conclude that the properties of the single-scan and multiple-scan approaches are very similar at the same total study duration, provided that the value selected for the water relative distribution volume brings the measured and computed tissue time courses into correspondence.
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Wang, Shibo, and Bin Tang. "A Comparative Study of Parameter Identification Methods for Asymmetric Nonlinear Systems with Quadratic and Cubic Stiffness." Sensors 22, no. 15 (2022): 5854. http://dx.doi.org/10.3390/s22155854.

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Understanding the nonlinear dynamic characteristics of engineering structures is challenging, especially for the systems that exhibit asymmetric nonlinear behavior. This paper compared four parameter identification methods for asymmetric nonlinear systems incorporating quadratic and cubic stiffness nonlinearities. Hilbert transform, zero-crossing, direct quadrature, and wavelet transform were used to obtain the backbone, envelope, and restoring force curves from the free vibration time history. A nonlinear curve-fitting method was then applied to estimate the stiffness parameters of the asymmetric systems, and a linear least square fitting approach was utilized to estimate the damping parameters of the asymmetric systems. We used the Helmholtz–Duffing oscillator as a numerical example and a nonlinear vibration absorber with geometric imperfections to verify the feasibility and accuracy of these methods. The advantages and disadvantages of these methods and the deviations in estimated results are discussed.
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30

Rab, Shanay, Sanjay Yadav, Afaqul Zafer, et al. "Comparison of Monte Carlo Simulation, Least Square Fitting and Calibration Factor Methods for the Evaluation of Measurement Uncertainty Using Direct Pressure Indicating Devices." MAPAN 34, no. 3 (2019): 305–15. http://dx.doi.org/10.1007/s12647-019-00333-9.

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31

Liu, Zong Jie, and Roland Van Rapenbusch. "A fast, direct algorithm for the least-squares fitting of two sets of atomic coordinates of macromolecular structures." Journal of Computational Chemistry 9, no. 6 (1988): 596–99. http://dx.doi.org/10.1002/jcc.540090603.

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32

Craig, BL, and PV Smith. "Parametrisation of the LCAO Bandstructure of BCC Transition Metals." Australian Journal of Physics 41, no. 6 (1988): 797. http://dx.doi.org/10.1071/ph880797.

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In this paper we present a direct parameter fitting scheme appropriate to a linear combination of atomic orbitals (LCAO) model� Hamiltonian representation of the BCC transition metals incorporating first and second neighbour interactions. Explicit expressions are given for the one-electron eigenvalues at all of the important symmetry points of the BCC Brillouin zone. This direct parameter fitting scheme is shown to produce an excellent representation of the bandstructure of paramagnetic iron, and yields parameter values little different from those obtained from a full least-squares optimisation of the LCAO model Hamiltonian bandstructure. The extension of this scheme to include more distant interactions, and relativistic and spin-orbit effects, is also discussed.
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33

Elshambaky, Hossam Talaat. "Using direct transformation approach as an alternative technique to fuse global digital elevation models with GPS/levelling measurements in Egypt." Journal of Applied Geodesy 13, no. 3 (2019): 159–77. http://dx.doi.org/10.1515/jag-2018-0050.

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Abstract Open global digital elevation models (GDEMs) represent a free and important source of information that is available to any country. Fusion processing between global and national digital elevation models is neither easy nor inexpensive. Hence, an alternative solution to fuse a GDEM (GTOPO30 or SRTM 1) with national GPS/levelling measurements is adopted. Herein, a transformation process between the GDEMs and national GPS/levelling measurements is applied using parametric and non-parametric equations. Two solutions are implemented before and after the filtration of raw data from outliers to assess the ability of the generated corrector surface model to absorb the effect of the outliers’ existence. In addition, a reliability analysis is conducted to select the most suitable transformation technique. We found that when both the fitting and prediction properties have equal priority, least-squares collocation integrated with a least-squares support vector machine inherited with a linear or polynomial kernel function exhibits the most accurate behavior. For the GTOPO30 model, before filtration of the raw data, there is an improvement in the mean and root mean square of errors by 39.31 % and 68.67 %, respectively. For the SRTM 1 model, the improvement in mean and root mean square values reached 86.88 % and 75.55 %, respectively. Subsequently, after the filtration process, these values became 3.48 % and 36.53 % for GTOPO30 and 85.18 % and 47.90 % for SRTM 1. Furthermore, it is found that using a suitable mathematical transformation technique can help increase the precision of classic GDEMs, such as GTOPO30, making them to be equal or more accurate than newer models, such as SRTM 1, which are supported by more advanced technologies. This can help overcome the limitation of shortage of technology or restricted data, particularly in developed countries. Henceforth, the proposed direct transformation technique represents an alternative faster and more economical way to utilize unfiltered measurements of GDEMs to estimate national digital elevations in areas with limited data.
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34

Landi, Gregorio, and Giovanni E. Landi. "The Cramer—Rao Inequality to Improve the Resolution of the Least-Squares Method in Track Fitting." Instruments 4, no. 1 (2020): 2. http://dx.doi.org/10.3390/instruments4010002.

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The Cramer–Rao–Frechet inequality is reviewed and extended to track fitting. A diffused opinion attributes to this inequality the limitation of the resolution of the track fits with the number N of observations. It will be shown that this opinion is incorrect, the weighted least squares method is not subjected to that N-limitation and the resolution can be improved beyond those limits. In previous publications, simulations with realistic models and simple Gaussian models produced interesting results: linear growths of the peaks of the distributions of the fitted parameters with the number N of observations, much faster than the N of the standard least-squares. These results could be considered a violation of a well-known 1 / N -rule for the variance of an unbiased estimator, frequently reported as the Cramer–Rao–Frechet bound. To clarify this point beyond any doubt, a direct proof of the consistency of those results with this inequality would be essential. Unfortunately, such proof is lacking. Hence, the Cramer–Rao–Frechet developments are applied to prove the efficiency (optimality) of the simple Gaussian model and the consistency of the linear growth. The inequality remains valid even for irregular models supporting the similar improvement of resolution for the realistic models.
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35

Mann, Charles K., Thomas J. Vickers, and James D. Womack. "Detection and Determination of Minor Components in Nominally Pure Solids by Raman Spectroscopy." Applied Spectroscopy 41, no. 8 (1987): 1324–29. http://dx.doi.org/10.1366/0003702874447068.

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The problems encountered in applying Raman spectroscopy to direct qualitative and quantitative analysis for minor impurities in nominally pure, colorless solids have been examined. Samples of sulfamethoxazole spiked with 0.5 to 5% of sulfanilamide and sulfanilic acid were used as test materials. A procedure is described which permits detection of spectral features of the specified impurities at the 0.5% level. Least-squares fitting and cross-correlation data treatment procedures for the determination of sulfanilamide in sulfamethoxazole, with limits of detection of about 0.1% for either approach, are described. Computer simulations have been used to examine detection of impurity peaks for a variety of conditions, including the worst-case scenario in which the impurity features coincide with the strongest features of the spectrum of the host material. A least-squares fitting approach is described which permits detection of the impurity peak at the 0.5% level, even under worst case conditions.
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36

Berveglieri, A., R. O. Oliveira, and A. M. G. Tommaselli. "A feasibility study on the measurement of tree trunks in forests using multi-scale vertical images." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-5 (June 5, 2014): 87–92. http://dx.doi.org/10.5194/isprsarchives-xl-5-87-2014.

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The determination of the Diameter at Breast Height (DBH) is an important variable that contributes to several studies on forest, e.g., environmental monitoring, tree growth, volume of wood, and biomass estimation. This paper presents a preliminary technique for the measurement of tree trunks using terrestrial images collected with a panoramic camera in nadir view. A multi-scale model is generated with these images. Homologue points on the trunk surface are measured over the images and their ground coordinates are determined by intersection of rays. The resulting XY coordinates of each trunk, defining an arc shape, can be used as observations in a circle fitting by least squares. Then, the DBH of each trunk is calculated using an estimated radius. Experiments were performed in two urban forest areas to assess the approach. In comparison with direct measurements on the trunks taken with a measuring tape, the discrepancies presented a Root Mean Square Error (RMSE) of 1.8 cm with a standard deviation of 0.7 cm. These results demonstrate compatibility with manual measurements and confirm the feasibility of the proposed technique.
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37

Toraya, Hideo. "A practical approach to the direct-derivation method for QPA: use of observed powder patterns of individual components without background subtraction in whole-powder-pattern fitting." Journal of Applied Crystallography 52, no. 3 (2019): 520–31. http://dx.doi.org/10.1107/s1600576719003406.

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The direct-derivation (DD) method for quantitative phase analysis (QPA) can be used to derive weight fractions of individual phases in a mixture from the sums of observed intensities along with the chemical composition data [Toraya (2016). J. Appl. Cryst. 49, 1508–1516]. The whole-powder-pattern fitting (WPPF) technique can be used as one of the tools for deriving the observed intensities of individual phases. In WPPF, the observed powder pattern of a single-phase sample after background (BG) subtraction can be used as the fitting function in combination with the fitting functions widely used in Pawley and Rietveld refinements. The direct fitting of the observed pattern is a very useful technique when the target component is a low-crystallinity or amorphous material [Toraya (2018). J. Appl. Cryst. 51, 446–455]. Technical problems in utilizing the BG-subtracted pattern are the uncertainty associated with the determination of BG height and the parameter interaction between the BG function (BGF) and the BG-subtracted pattern in the least-squares fit. In this study, a practical approach in which single-phase observed patterns are used for the direct fitting without subtracting their BG intensities is proposed. In QPA, the contribution of BG intensities can be neutralized by converting the sum of BG-included intensities into the sum of BG-subtracted intensities by multiplying by a conversion factor. When the magnitudes of the conversion factors are almost identical for all components, they can be canceled out under the normalization condition in deriving weight fractions, and they are not required in QPA. The magnitude of the conversion factor for each component can be determined by one of two experimental techniques: using a single-phase powder of the target component or a mixture containing the target component in a known weight ratio. The theoretical basis of the present procedure is given, and the procedure is experimentally verified. In this procedure, the interaction between the BGF and the BG-included observed pattern is negligibly small. Least-squares fitting with a few adjustable parameters is very fast and stable. Accurate QPA could be conducted, as indicated by the average deviation of 0.05% from weighed values in QPA of α-Al2O3 + γ-Al2O3 mixtures with five different weight ratios and 0.4% in QPA of an α-SiO2 + SiO2 glass mixture
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38

SHEN, Q., J. XU, C. X. CHEN, Z. H. YE, and R. WANG. "A NEW METHOD TO CALCULATE THE MECHANICS PARAMETERS OF SLIP SURFACES." International Journal of Modern Physics B 22, no. 09n11 (2008): 1558–63. http://dx.doi.org/10.1142/s0217979208047079.

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Obtaining the more exact parameters of slip surfaces is proved to be crucial in the analysis of landslide stability, and there are four study methods available i.e. in-site test, laboratory test, back analysis and theoretical analysis. In general, the former two are the basic one, whereas the latter two are secondary. A set of test values about shearing stress and direct stress can be obtained through in-situ and lab tests, then the parameters of slip surface should be calculated to fitting for the test value by the least square method usually, but the effect of anomalous values should increase markedly because the quadratic sum of residual errors is adopted in calculations. In order to reduce the effect of anomalous value, a new method based on the robust regression analysis and the particle swarm optimization method are adopted to calculate the mechanics parameter of landslides in this paper. In the new method, the sum of residual absolute values is used to replace the quadratic sum of residual error, and then the quadratic sum of anomalous value can be avoided. Comparing to the least square method, the new method can reduce availably the effect of abnormal values, and the results are more credible. Furthermore, an engineering example is cited to show the validity.
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39

Ghosal, Kajal, and Sarbani Dey Ray. "Alginate/hydrophobic HPMC (60M) particulate systems: new matrix for site-specific and controlled drug delivery." Brazilian Journal of Pharmaceutical Sciences 47, no. 4 (2011): 833–44. http://dx.doi.org/10.1590/s1984-82502011000400021.

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This study aimed to obtain site-specific and controlled drug release particulate systems. Some particulates were prepared using different concentrations of sodium alginate (Na-Alg) alone and others were formulated using different proportions of Na-Alg with hydroxypropyl methylcellulose (HPMC) stearoxy ether (60M viscosity grade), a hydrophobic form of conventional HPMC, using diclofenac potassium (DP) by ion-exchange methods. Beads were characterized by encapsulation efficiency, release profile, swelling, and erosion rate. The suitability of common empirical (zero-order, first-order and Higuchi) and semi-empirical (Ritger-Peppas and Peppas-Sahlin) models was studied to describe the drug release profile. The Weibull model was also studied. Models were tested by non-linear least-square curve fitting. A general purpose mathematical software (MATLAB) was used as an analysis tool. In addition, instead of the widely used linear fitting of log-transformed data, direct fitting was used to avoid any sort of truncation or transformation errors. The release kinetics of the beads indicated a purely relaxation-controlled delivery, referred to as case II transport. Weibull distribution showed a close fit. The release of DP from Na-Alg particulates was complete in 5-6 hours, whereas from Na-Alg hydrophobic HPMC particulate systems, release was sustained up to 10 hours. Hydrophobic HPMC with Na-Alg is an excellent matrix to formulate site-specific and controlled drug release particulate systems.
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40

Taakagi, Satoshi. "Analyses of direct verification data of Rockwell diamond indenters by iterative regression method." ACTA IMEKO 3, no. 3 (2014): 15. http://dx.doi.org/10.21014/acta_imeko.v3i3.99.

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For the verification of Rockwell diamond indenters exactly compliant to the international definition, an iterative method with the least square circle fitting was introduced. This method was applied to the analysis of verification data obtained with a laser probe 3D profile measurement instrument. The geometry of a Rockwell diamond indenter was verified with the equipment as an example. Conventional analyses on cross sections of an indenter is demonstrated as well as three dimensional analysis of indenter geometry. The analyses on cross sections showed that the technique can be used to express the geometrical parameters described in the definition of CIPM/CCM/WGH properly, whereas three dimensional analysis enables to express the imperfection of geometry with fewer parameters. In addition, this technique can be applicable to determine equivalent geometrical parameters obtained with the optical measurement system currently used at the National Metrology Institute of Japan (NMIJ) to establish the national standard indenters. It is shown that the proposed method describes the geometry of indenter better than currently used method. These results suggest that the uncertainty of the national standard indenter could be improved through this high resolution geometry measurement and the multiple regression analysis NMIJ is using.
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41

Gorgoso-Varela, Jose Javier, Friday Nwabueze Ogana, and Rafael Alonso Ponce. "Evaluation of direct and indirect methods for modelling the joint distribution of tree diameter and height data with the bivariate Johnson’s SBB function to forest stands." Forest Systems 28, no. 1 (2019): e004. http://dx.doi.org/10.5424/fs/2019281-14104.

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Aim of study: In this study, both the direct and indirect methods by conditional maximum likelihood (CML) and moments for fitting Johnson’s SBB were evaluated. To date, Johnson’s SBB has been fitted by either indirect (two-stage) method using well-known procedures for the marginal diameter and heights, or direct methods, where all parameters are estimated at once. Application of bivariate Johnson’s SBB for predicting height and improving volume estimation requires a suitable fitting method.Area of study: E. globulus, P. pinaster and P. radiata stands in northwest Spain.Material and methods: The data set comprised of 308, 184 and 96 permanent sample plots (PSPs) from the aforementioned species. The suitability of the method was evaluated based on height and volume prediction. Indices including coefficient of determination (R2), root mean square Error (RMSE), model efficiency (MEF), Bayesian Information Criterion (BIC) and Hannan-Quinn Criterion (HQC) were used to assess the model predictions. Significant difference between observed and predicted tree height and volumes were tested using paired sample t-test at 5% level for each plot by species.Main results: The indirect method by CML was the most suitable method for height and volume prediction in the three species. The R2 and RMSE for height prediction ranged from 0.994 – 0.820 and 1.454 – 1.676, respectively. The percentage of plot in which the observed and predicted heights were significant was 0.32%. The direct method was the least performed method especially for height prediction in E. globulus.Research highlights: The indirect (two-stage) method, especially by conditional maximum likelihood, was the most suitable method for the bivariate Johnson’s SBB distribution.Keywords: conditional maximum likelihood; moments; two-stage method; direct method; tree volume.
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42

Shen, Xin Pu, and Xiao Chun Wang. "Parameter Identification of a Plastic Damage Model." Applied Mechanics and Materials 599-601 (August 2014): 568–73. http://dx.doi.org/10.4028/www.scientific.net/amm.599-601.568.

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Studies on parameter identification of a plasticity-based damage constitutive model for concrete are presented in this paper. Differences between the stress-strain curves experimentally obtained and the ones numerically obtained at local level were used as the objective functional of a regularized least square method. For solving the inverse problem, the solution of the direct problem at local level obtained by a driver subroutine was embedded in the iterative solution procedure for the inverse problem proposed in this paper. The sensitivity matrix was calculated numerically by the finite difference method. Numerical examples are given for fitting the numerically obtained stress-strain curves on to a set of experimental results. Parameter identifications under various loading cases, which include uniaxial extension and triaxial compression with different confining stresses, were performed. Results indicate that the numerical scheme is stable and has reasonable accuracy.
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43

Wang, Jin Tao, Zi Yong Liu, Long Zhang, Li Gong Guo, Xue Song Bao, and Lin Tong. "Research on Course Radius Measurement for Vertical Petroleum Tank Volume Metrology Based on 3D Laser Scan Principle." Key Engineering Materials 439-440 (June 2010): 1105–10. http://dx.doi.org/10.4028/www.scientific.net/kem.439-440.1105.

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One course radius measurement method for vertical petroleum tank volume metrology based on 3D laser scan principle was researched. Method of distance measurement by laser phase-shift technology and angular measurement by optical grating was applied to acquire coordinates of points in each course under the control of servo system. The permitted error of measured point location is 2mm. Fitting algorithms base on direct iterative method (DIM) and least square method (LSM) were used to process measured data and deduce equivalent radius of each course. In comparison experiment, one 1000m3 vertical tank was used as test object. Compared to strapping method (international mandatory standard), the maximal deviation radius value of method discussed is 2.8mm. The maximal difference of radius value calculated by DIM and LSM is 0.1mm. The experimental results verified the method discussed in this paper.
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44

Wang, Jin Tao, Zi Yong Liu, Long Zhang, Li Gong Guo, Xue Song Bao, and Lin Tong. "Research on Course Radius Measurement for Vertical Petroleum Tank Volume Metrology Based on 3D Laser Scan Principle." Key Engineering Materials 439-440 (June 2010): 983–88. http://dx.doi.org/10.4028/www.scientific.net/kem.439-440.983.

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One course radius measurement method for vertical petroleum tank volume metrology based on 3D laser scan principle was researched. Method of distance measurement by laser phase-shift technology and angular measurement by optical grating was applied to acquire coordinates of points in each course under the control of servo system. The permitted error of measured point location is 2mm. Fitting algorithms base on direct iterative method (DIM) and least square method (LSM) were used to process measured data and deduce equivalent radius of each course. In comparison experiment, one 1000m3 vertical tank was used as test object. Compared to strapping method (international mandatory standard), the maximal deviation radius value of method discussed is 2.8mm. The maximal difference of radius value calculated by DIM and LSM is 0.1mm. The experimental results verified the method discussed in this paper.
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45

Ho, R., Z. Jia, A. P. Somlyo, and Z. Shao. "Quantitating Calcium in Biological Specimens by Direct Fittingof X-ray Spectra." Microscopy and Microanalysis 7, S2 (2001): 994–95. http://dx.doi.org/10.1017/s1431927600031044.

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Electron probe microanalysis has been a useful method for biological research for some years. Its advantages include the low background of x-ray spectra and range to include characteristic peaks of most biological elements. The traditional method of analyzing biological X-ray spectra filtering both the experimental and reference spectra with a top-hat filter, before performing a linear least squares fit, to remove the slowly varying background. We show that, as expected, this procedure introduces an additional error in the quantitation results, and reduces the sensitivity and precision of this method. Our experience with quantitating trace elements with EELS shows that direct fit of unfiltered spectra yields the highest sensitivity, when the data contain only statistical errors. Biological specimens usually contain high K and low Ca, and in X-ray spectra the K Kβ peak is overlapped with the Ca Kα peak. A small error in extracting the K signal will dramatically affect the quantitation of Ca. We demonstrate here the application of a direct fitting procedure, which focuses on the Ca and K region of the X-ray spectra (2800 ∼ 4900 eV), and yields smaller fitting uncertainties compared to the traditional filtered fit method in trace Ca quantitation.
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46

Tarlowski, C., and I. Koch. "On the problem of estimating the depth to the magnetic basement." GEOPHYSICS 53, no. 10 (1988): 1362–63. http://dx.doi.org/10.1190/1.1442415.

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In many applications in aeromagnetics, the estimation of the depth to the crystalline magnetic basement is of great importance. Of many approaches to this problem, the most widely applied appear to be based upon Fourier analysis (see Ruotoistenmäki, 1987) or on fitting hypothetical models to observed data using a least‐squares principle (for example, Leite and Leão, 1985). Recently, some interest has been focused on direct approaches to the problem (Strakhov and Brodsky, 1986; Koch and Tarlowski, 1986; and Jonca and Vogel, 1987).
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47

Andraud, M., C. Chauvin, P. Sanders, and M. Laurentie. "Pharmacodynamic Modeling ofIn VitroActivity of Marbofloxacin againstEscherichia coliStrains." Antimicrobial Agents and Chemotherapy 55, no. 2 (2010): 756–61. http://dx.doi.org/10.1128/aac.00865-10.

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ABSTRACTA mathematical pharmacodynamic model was developed to describe the bactericidal activity of marbofloxacin againstEscherichia colistrains with reduced susceptibility levels (determined using MICs) under optimal and intestinal growth conditions. Model parameters were estimated using nonlinear least-square curve-fitting procedures for eachE. colistrain. Parameters related to bactericidal activity were subsequently analyzed using a maximum-effect (Emax) model adapted to account for a direct and a delayed effect. While net growth rates did not vary significantly with strain susceptibility, culture medium had a major effect. The bactericidal activity of marbofloxacin was closely associated with the concentration and the duration of exposure of the bacteria to the antimicrobial agent. The value of the concentration inducing a half-maximum effect (C50) was highly correlated with MIC values (R2= 0.87 andR2= 0.94 under intestinal and optimal conditions, respectively). Our model reproduced the time-kill kinetics with good accuracy (R2of >0.90) and helped explain observed regrowth.
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48

Jiang, Xiuqiang, Shuang Li, Long Gu, Jun Sun, and Dongdong Xiao. "Optical Image Generation and High-precision Line-of-Sight Extraction for Mars Approach Navigation." Journal of Navigation 72, no. 1 (2018): 229–52. http://dx.doi.org/10.1017/s0373463318000450.

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A high-precision line-of-sight extraction technique is essential for autonomous optical navigation during the Mars approach phase. To support future Mars exploration missions, an optical image simulation system is a necessary ground verification facility for Mars image generation and line-of-sight extraction algorithm tests. In this paper, an optical image generation procedure is first developed according to projection relationships, reference flight profiles and camera parameters. Next, a hybrid image processing and subpixel-level line-of-sight extraction algorithm is proposed through modification of moment-based sub-pixel edge detection and improvement of direct least-square fitting approaches. Finally, an optical image simulation system is established, and the experimental results show that the proposed procedure can effectively simulate the optical image in the field-of-view of a Mars spacecraft, and the hybrid extraction algorithm can obtain high-precision Mars centroid information.
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49

Xu, Luting, Yanru Li, Xiao Wang, Lei Liu, Ming Ma, and Junhui Yang. "A Machine Learning Approach to Estimating Solar Radiation Shading Rates in Mountainous Areas." Sustainability 16, no. 2 (2024): 931. http://dx.doi.org/10.3390/su16020931.

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Quantification of shading effects from complex terrain on solar radiation is essential to obtain precise data on incident solar radiation in mountainous areas. In this study, a machine learning (ML) approach is proposed to rapidly estimate the shading effects of complex terrain on solar radiation. Based on two different ML algorithms, namely, Ordinary Least Squares (OLS) and Gradient Boosting Decision Tree (GBDT), this approach uses terrain-related factors as input variables to model and analyze direct and diffuse solar radiation shading rates. In a case study of western Sichuan, the annual direct and diffuse radiation shading rates were most correlated with the average terrain shading angle within the solar azimuth range, with Pearson correlation coefficients of 0.901 and 0.97. The GBDT-based models achieved higher accuracy in predicting direct and diffuse radiation shading rates, with R2 values of 0.982 and 0.989, respectively, surpassing the OLS-based models by 0.081 and 0.023. In comparisons between ML models and classic curve-fitting models, the GBDT-based models consistently performed better in predicting both the direct radiation shading rate and the diffuse radiation shading rate, with a standard deviation of residuals of 0.330% and 0.336%. The OLS-based models also showed better performance compared to the curve-fitting models.
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50

Tong, Chen, Chaotan Sima, Muqi Chen, et al. "Laser Linewidth Analysis and Filtering/Fitting Algorithms for Improved TDLAS-Based Optical Gas Sensor." Sensors 23, no. 11 (2023): 5130. http://dx.doi.org/10.3390/s23115130.

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Tunable Diode Laser Absorption Spectroscopy (TDLAS) has been widely applied in in situ and real-time monitoring of trace gas concentrations. In this paper, an advanced TDLAS-based optical gas sensing system with laser linewidth analysis and filtering/fitting algorithms is proposed and experimentally demonstrated. The linewidth of the laser pulse spectrum is innovatively considered and analyzed in the harmonic detection of the TDLAS model. The adaptive Variational Mode Decomposition-Savitzky Golay (VMD-SG) filtering algorithm is developed to process the raw data and could significantly eliminate the background noise variance by about 31% and signal jitters by about 12.5%. Furthermore, the Radial Basis Function (RBF) neural network is also incorporated and applied to improve the fitting accuracy of the gas sensor. Compared with traditional linear fitting or least squares method (LSM), the RBF neural network brings along the enhanced fitting accuracy within a large dynamic range, achieving an absolute error of below 50 ppmv (about 0.6%) for the maximum 8000 ppmv methane. The proposed technique in this paper is universal and compatible with TDLAS-based gas sensors without hardware modification, allowing direct improvement and optimization for current optical gas sensors.
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