Gait Trajectory Planning Based on Least Squares Fitting - Polynomial for Lower Extremity Rehabilitation

2014 ◽  
Vol 668-669 ◽  
pp. 1569-1572
Author(s):  
Fu Cheng Cao ◽  
Li Min Du
Keyword(s):  
Data Analysis ◽  
Lower Extremity ◽  
Least Squares ◽  
Trajectory Planning ◽  
Curve Fitting ◽  
Polynomial Functions ◽  
Computer Data ◽  
Normal Gait ◽  
Order Polynomial ◽  
Least Squares Curve Fitting

According to the analysis results of normal gait data, a method of gait trajectory planning based least squares curve fitting is proposed. Given the generalized-th order polynomial functions, the coefficients for functions are determined, then, a health hip and knee gait trajectory planning functions were obtained. The computer data analysis results show that the gait trajectory fitted can represent a normal gait accurately.

Statistical characterization of the random errors in the radioimmunoassay dose--response variable.

1976 ◽  
Vol 22 (3) ◽  
pp. 350-358 ◽  
Author(s):  
D Rodbard ◽  
R H Lenox ◽  
H L Wray ◽  
D Ramseth
Keyword(s):  
Least Squares ◽  
Dose Response ◽  
Curve Fitting ◽  
Response Curve ◽  
Dose Response Curve ◽  
Random Errors ◽  
Statistical Characterization ◽  
Response Variable ◽  
Least Squares Curve Fitting ◽  
The Relationship

Abstract We have developed practical methods for evaluating the magnitude of the random errors in radioimmunoassay dose--response variables, and the relationship between this error and position on the dose--response curve. This is important: to obtain appropriate weights for each point on the dose--response curve when utilizing least-squares curve-fitting methods; to evaluate whether the standards and the unknowns are subject to error of the same magnitude; for quality-control purposes; and to study the sources of errors in radioimmunoassay. Both standards and unknowns in radioimmunoassays for cAMP and cGMP were analyzed in triplicate. The same mean (Y), sample standard deviation, sy, and variance (2-y) of the response variable were calculated for each dose level. The relationship between s 2-y and y was calculated utilizing several models. Results for standards and unknowns from several assays were pooled, and a curve smoothing procedure was used to minimize random sampling errors. This pooling increased the reliability of the analysis, and confirmed the presence of the theoretically predicted nonuniformity of variance. Thus, the calculation of results from these radioimmunoassays should utilize a weighted least-squares curve-fitting program. These analyses have been computerized, and can be used as a "pre-processor" for programs for routine analysis of results of radioimmunoassay.

A Fourier Transform Infrared Study of Mineral Matter in Coal: The Application of a Least Squares Curve-Fitting Program

1981 ◽  
Vol 35 (1) ◽  
pp. 102-106 ◽  
Author(s):  
Paul C. Painter ◽  
Susan M. Rimmer ◽  
Randy W. Snyder ◽  
Alan Davis
Keyword(s):  
Fourier Transform ◽  
Least Squares ◽  
Curve Fitting ◽  
Fourier Transform Infrared ◽  
Mineral Matter ◽  
Infrared Study ◽  
Least Squares Curve Fitting ◽  
Mineral Mixtures ◽  
Good Agreement

The application of Fourier transform infrared spectroscopy to the quantitative determination of mineral matter in coal is discussed. The use of a least squares curve-fitting program allows a choice between standards to be made. The results of an analysis of mineral mixtures and a coal low temperature ash are presented. The results are in good agreement with known concentrations and those obtained by other methods of analysis.

An algorithm for least-squares curve-fitting of TL and TSDC peaks

1986 ◽  
Vol 41 (1) ◽  
pp. 35-39 ◽  
Author(s):  
C. Christodoulides ◽  
L. Apekis ◽  
P. Pissis
Keyword(s):  
Least Squares ◽  
Curve Fitting ◽  
Least Squares Curve Fitting

Least-Squares Curve-Fitting of Fourier Transform Infrared Spectra with Applications to Polymer Systems

1977 ◽  
Vol 31 (6) ◽  
pp. 518-524 ◽  
Author(s):  
M. K. Antoon ◽  
J. H. Koenig ◽  
J. L. Koenig
Keyword(s):  
Fourier Transform ◽  
Least Squares ◽  
Infrared Spectra ◽  
Curve Fitting ◽  
Fourier Transform Infrared ◽  
Polymer Systems ◽  
Fourier Transform Infrared Spectra ◽  
Least Squares Curve Fitting ◽  
Xylene Solution

A method is presented for least-squares curve-fitting of Fourier transform infrared spectra. A demonstration of the determination of xylene solution compositions illustrates the accuracy of the method. Least-squares coefficients are shown to be valuable for the analysis of several polymer systems by digital subtraction of spectra.

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