scholarly journals Least-Squares Fitting of Multidimensional Spectra to Kubo Lineshape Models

2021 ◽  
Author(s):  
Kevin Robben ◽  
Christopher Cheatum
Keyword(s):  
Least Squares ◽  
Source Code ◽  
Model Fitting ◽  
Scale Invariant ◽  
Linear Absorption ◽  
Time Constants ◽  
Least Squares Fitting ◽  
Propagation Of Uncertainty ◽  
Fitting Algorithm ◽  
Line Slope

We report a comprehensive study of the efficacy of least-squares fitting of multidimensional spectra to generalized Kubo lineshape models and introduce a novel least-squares fitting metric, termed the Scale Invariant Gradient Norm (SIGN), that enables a highly reliable and versatile algorithm. The precision of dephasing parameters is between 8× to 50× better for nonlinear model fitting compared to the CLS method, which effectively increases data acquisition efficiency by one to two orders of magnitude. Whereas the center-line-slope (CLS) method requires sequential fitting of both the nonlinear and linear spectra, our model fitting algorithm only requires nonlinear spectra, but accurately predicts the linear spectrum. We show an experimental example in which the CLS time constants differ by 60% for independent measurements of the same system, while the Kubo time constants differ by only 10% for model fitting. This suggests that model fitting is a far more robust method of measuring spectral diffusion than the CLS method, which is more susceptible to structured residual signals that are not removable by pure solvent subtraction. Statistical analysis of the CLS method reveals a fundamental oversight in accounting for the propagation of uncertainty by Kubo time constants in the process of fitting to the linear absorption spectrum. A standalone desktop app and source code for the least-squares fitting algorithm are freely available with example lineshape models and data. We have written the MATLAB source code in a generic framework where users may supply custom lineshape models. Using this application, a standard desktop fits a 12-parameter generalized Kubo model to a 106 data-point spectrum in a few minutes.

Design and Analysis of High-precision Weighted Linear Least-Squares Fitting Algorithm for Fluorescent Optical Fiber Temperature Sensor

2021 ◽  
pp. 2250031
Author(s):  
Jian Yang ◽  
Xiangliang Jin ◽  
Yan Peng ◽  
Jun Luo
Keyword(s):  
Optical Fiber ◽  
Least Squares ◽  
High Precision ◽  
Temperature Sensor ◽  
Heating Temperature ◽  
Experimental Tests ◽  
Linear Least Squares ◽  
Least Squares Fitting ◽  
Fitting Algorithm ◽  
Microwave Hyperthermia

Microwave hyperthermia is a new method of treating cancer, where the therapeutic effect is determined by the heating temperature. Traditional active temperature sensors are interfered by high frequency so that the accuracy of temperature measurement cannot be guaranteed. It is of great significance to study the high-precision fluorescent optical fiber temperature sensor with complete insulation. This paper has realized a compact and practical fluorescent optical fiber temperature sensor after studying the optical path, circuit, data processing algorithm. In order to improve the accuracy of the system, the weighted linear least-squares fitting algorithm is improved in this paper. Through experimental tests, compared with the standard linear least-squares fitting algorithm and the unimproved weighted linear least-squares fitting algorithm, the accuracy of the algorithm is improved by about 98% and 65.5%, respectively. In addition, the response time is reduced by about 36.5%, compared with the unimproved weighted linear least-squares fitting algorithm. This algorithm fully meets the precision requirements of microwave hyperthermia.

scholarly journals On the UPMSat-2 Attitude Determination and Control Subsystem’s magnetometers integration

2021 ◽  
Vol 2090 (1) ◽  
pp. 012099
Author(s):  
Elena Rodríguez-Rojo ◽  
Javier Cubas ◽  
Santiago Pindado
Keyword(s):  
Least Squares ◽  
Attitude Determination ◽  
Ordinary Least Squares ◽  
Mathematical Methods ◽  
Data Set ◽  
Least Squares Fitting ◽  
Earth Magnetic Field ◽  
Fitting Algorithm ◽  
Magnetometer Calibration ◽  
And Control

Abstract In the present work, a method for magnetometer calibration through least squares fitting is presented. This method has been applied over the magnetometer’s data set obtained during the integration tests of the Attitude Determination and Control Subsystem (ADCS) of UPMSat-2. The UPMSat-2 mission is a 50-kg satellite designed and manufactured by the Technical University of Madrid (Universidad Politécnica de Madrid), and finally launched in September 2020. The satellite has three fluxgate magnetometers (one of them experimental) whose calibration is critical to obtain correct measurements to be used by the ADCS. Among several mathematical methods suitable to obtain the calibration parameters, an ordinary least squares fitting algorithm is selected as a first step of the calibration process. The surface estimated is an ellipsoid, surface represented by the magnetometer’s measures of the Earth magnetic field in a point of the space. The calibration elements of the magnetometers are related to the coefficients of the estimated ellipsoid.

Freehand 3D Ultrasound Calibration Based on Two-Layer Z-Fiducial Phantom

2011 ◽  
Vol 317-319 ◽  
pp. 638-642
Author(s):  
Xiao Yu Wang ◽  
Dong Mei Wu ◽  
Zhi Jiang Du
Keyword(s):  
Coordinate System ◽  
Least Squares ◽  
3D Ultrasound ◽  
Transformation Matrix ◽  
Position Sensor ◽  
Least Squares Fitting ◽  
Fitting Algorithm ◽  
Precision And Accuracy ◽  
Spatial Calibration ◽  
Freehand 3D Ultrasound

Spatial calibration is a key technique in Freehand 3D Ultrasound. In this article, a two-layer Z-fiducial phantom with one “Z” shaped fiducial in each layer is used to perform spatial calibration. After freehand scanning above the phantom, the intersections of the scan plane and Z-fiducial plane in B-scans are segmented, and the calibration transformation matrix between the coordinate system of the position sensor receiver and B-scan is calculated using the least-squares fitting algorithm. At last, the calibration result is evaluated on two criteria: precision and accuracy. The result shows that our phantom is convenient as well as reliable for freehand spatial calibration.

scholarly journals An Error-Reduction Method for Temporal Phase Unwrapping Based on Double Three-Step Phase-Shifting and Least-Squares Fitting

2012 ◽  
Vol 6-7 ◽  
pp. 76-81
Author(s):  
Yong Liu ◽  
Ding Fa Huang ◽  
Yong Jiang
Keyword(s):  
Least Squares ◽  
Reduction Method ◽  
Intermediate Phase ◽  
Error Reduction ◽  
Phase Unwrapping ◽  
Phase Shifting ◽  
Surface Measurement ◽  
Acquisition Time ◽  
Least Squares Fitting ◽  
Temporal Phase

Phase-shifting interferometry on structured light projection is widely used in 3-D surface measurement. An investigation shows that least-squares fitting can significantly decrease random error by incorporating data from the intermediate phase values, but it cannot completely eliminate nonlinear error. This paper proposes an error-reduction method based on double three-step phase-shifting algorithm and least-squares fitting, and applies it on the temporal phase unwrapping algorithm using three-frequency heterodyne principle. Theoretical analyses and experiment results show that this method can greatly save data acquisition time and improve the precision.

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