Accurate phase extraction algorithm based on Gram–Schmidt orthonormalization and least square ellipse fitting method

Based on the superiority avoiding the matrix equation to be morbid for those fitting functions constructed by orthogonal base, the Legendre orthogonal polynomial is adopted to fit the experimental data of concrete uniaxial compression stress-strain curves under the frame of least-square. With the help of FORTRAN programming, 3 series of experimental data is fitted. And the fitting effect is very satisfactory when the item number of orthogonal base is not less than 5. What’s more, compared with those piecewise fitting functions, the Legendre orthogonal polynomial fitting function obtained can be introduced into the nonlinear harden-soften character of concrete constitute law more convenient because of its uniform function form and continuous derived feature. And the fitting idea by orthogonal base function will provide a widely road for studying the constitute law of concrete material.

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Phase extraction algorithm considering high-order harmonics in fringe image processing

Applied Optics ◽

10.1364/ao.54.004989 ◽

2015 ◽

Vol 54 (16) ◽

pp. 4989 ◽

Cited By ~ 10

Author(s):

Keming Zhang ◽

Jun Yao ◽

Jubing Chen ◽

Hong Miao

Keyword(s):

Image Processing ◽

High Order ◽

Phase Extraction ◽

Extraction Algorithm

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COMPARING TWO DIFFERENT MODES OF MECHANICAL VENTILATION BY THE LEAST SQUARE FITTING METHOD: NAVA VERSUS PSV

Intensive Care Medicine Experimental ◽

10.1186/2197-425x-3-s1-a319 ◽

2015 ◽

Vol 3 (Suppl 1) ◽

pp. A319

Author(s):

S Spadaro ◽

S Grasso ◽

V Cricca ◽

F Dalla Corte ◽

R Di Mussi ◽

...

Keyword(s):

Mechanical Ventilation ◽

Least Square ◽

Least Square Fitting ◽

Fitting Method ◽

Least Square Fitting Method

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The Parameter Estimation of Double Exponential Pulse Based on a Least Infinity Norm Fitting Method

Journal of Physics Conference Series ◽

10.1088/1742-6596/2083/4/042002 ◽

2021 ◽

Vol 2083 (4) ◽

pp. 042002

Author(s):

Yuewu Shi ◽

Wei Wang ◽

Zhizhen Zhu ◽

Xin Nie

Keyword(s):

Estimation Error ◽

Estimation Method ◽

Maximum Amplitude ◽

Least Square Method ◽

Least Square ◽

Physical Parameters ◽

Infinity Norm ◽

Fitting Method ◽

Double Exponential ◽

Exponential Pulse

Abstract This paper presents an estimation method of double exponential pulse (DEP) between the physical parameters rise time (t r), full width at half maximum amplitude (t FWHM) and the mathematical parameters α, β. A newly fitting method based on the least infinity norm criterion is proposed to deal with the estimation problem of DEP. The calculation process and equation of parameters of this method is proposed based on an m-th-order polynomial fitting model. This estimation method is compared with the least square method by the same data and fitting function. The results show that the maximum estimation error of parameters of double exponential pulse obtained by the least infinity norm method is 1.5 %.

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