A new method for least squares identification of parameters of the transcendental equations

2012 ◽  
Vol 7 (31) ◽  
Author(s):  
Kloppers P.H
Keyword(s):  
Least Squares ◽  
New Method ◽  
Identification Of Parameters ◽  
Transcendental Equations

SINS Installation Error Calibration Based on Multi-Position Combinations

2011 ◽  
Vol 383-390 ◽  
pp. 4213-4220
Author(s):  
Zhen Huan Wang ◽  
Xi Jun Chen ◽  
Qing Shuang Zeng
Keyword(s):  
Theoretical Analysis ◽  
Least Squares ◽  
Rotation Rate ◽  
Scale Factor ◽  
New Method ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Error Calibration ◽  
Sine And Cosine Functions ◽  
Cosine Functions

A new method is proposed to calibrate the installation errors of SINS. According to the method, the installation errors of the gyro and accelerometer can be calibrated simultaneously, which not depend on latitude, gravity, scale factor and earth's rotation rate. By the multi-position combinations, the installation errors of the gyro and accelerometer are modulated into the sine and cosine functions, which can be identified respectively based on the least squares. In order to verify the correctness of the theoretical analysis, the SINS is experimented by a three-axis turntable, and the installation errors of the gyro and accelerometer are identified respectively according to the proposed method. After the compensation of the installation error, the accuracy of the SINS is improved significantly.

scholarly journals Estimation of Soil Nutrient Content Using Hyperspectral Data

Agriculture ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 1129
Author(s):  
Yiping Peng ◽  
Lu Wang ◽  
Li Zhao ◽  
Zhenhua Liu ◽  
Chenjie Lin ◽  
...  
Keyword(s):  
Least Squares ◽  
Soil Nutrients ◽  
Cross Validation ◽  
Regional Scale ◽  
Soil Nutrient ◽  
Nutrient Content ◽  
New Method ◽  
Accurate Estimation ◽  
Support Vector ◽  
Soil Nutrient Content

Soil nutrients play a vital role in plant growth and thus the rapid acquisition of soil nutrient content is of great significance for agricultural sustainable development. Hyperspectral remote-sensing techniques allow for the quick monitoring of soil nutrients. However, at present, obtaining accurate estimates proves to be difficult due to the weak spectral features of soil nutrients and the low accuracy of soil nutrient estimation models. This study proposed a new method to improve soil nutrient estimation. Firstly, for obtaining characteristic variables, we employed partial least squares regression (PLSR) fit degree to select an optimal screening algorithm from three algorithms (Pearson correlation coefficient, PCC; least absolute shrinkage and selection operator, LASSO; and gradient boosting decision tree, GBDT). Secondly, linear (multi-linear regression, MLR; ridge regression, RR) and nonlinear (support vector machine, SVM; and back propagation neural network with genetic algorithm optimization, GABP) algorithms with 10-fold cross-validation were implemented to determine the most accurate model for estimating soil total nitrogen (TN), total phosphorus (TP), and total potassium (TK) contents. Finally, the new method was used to map the soil TK content at a regional scale using the soil component spectral variables retrieved by the fully constrained least squares (FCLS) method based on an image from the HuanJing-1A Hyperspectral Imager (HJ-1A HSI) of the Conghua District of Guangzhou, China. The results identified the GBDT-GABP was observed as the most accurate estimation method of soil TN ( of 0.69, the root mean square error of cross-validation (RMSECV) of 0.35 g kg−1 and ratio of performance to interquartile range (RPIQ) of 2.03) and TP ( of 0.73, RMSECV of 0.30 g kg−1 and RPIQ = 2.10), and the LASSO-GABP proved to be optimal for soil TK estimations ( of 0.82, RMSECV of 3.39 g kg−1 and RPIQ = 3.57). Additionally, the highly accurate LASSO-GABP-estimated soil TK (R2 = 0.79) reveals the feasibility of the LASSO-GABP method to retrieve soil TK content at the regional scale.

THE CALIBRATION OF AN ARRAY OF ACCELEROMETERS

2011 ◽  
Vol 35 (2) ◽  
pp. 251-267 ◽  
Author(s):  
Dany Dubé ◽  
Philippe Cardou
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Least Squares ◽  
Calibration Method ◽  
Calibration Procedure ◽  
Rigid Bodies ◽  
New Method ◽  
Scale Factors ◽  
Array Calibration ◽  
The One

An accelerometer-array calibration method is proposed in this paper by which we estimate not only the accelerometer offsets and scale factors, but also their sensitive directions and positions on a rigid body. These latter parameters are computed from the classical equations that describe the kinematics of rigid bodies, and by measuring the accelerometer-array displacements using a magnetic sensor. Unlike calibration schemes that were reported before, the one proposed here guarantees that the estimated accelerometer-array parameters are globally optimum in the least-squares sense. The calibration procedure is tested on OCTA, a rigid body equipped with six biaxial accelerometers. It is demonstrated that the new method significantly reduces the errors when computing the angular velocity of a rigid body from the accelerometer measurements.

Aerodynamic Forces Approximations Calculated With a New Analytical Formulation

2006 ◽  
Author(s):  
Djallel Eddine Biskri ◽  
Ruxandra Mihaela Botez
Keyword(s):  
Least Squares ◽  
Frequency Domain ◽  
Approximation Method ◽  
Unsteady Aerodynamics ◽  
Analytical Form ◽  
New Method ◽  
Aerodynamic Forces ◽  
Laplace Domain ◽  
Analytical Formulation ◽  
Multidisciplinary Study

Aeroservoelasticity is a multidisciplinary study of three main disciplines: unsteady aerodynamics, aeroelasticity and servo-controls. Two classical methods are used in the literature to approximate the unsteady generalized forces from the frequency domain Q (k) to the Laplace domain Q(s) and these methods are: the Least Squares LS and the Minimum State MS. In the present paper, we present a new method, called Corrected Minimum State (CMS), based on the Standard MS approximation method. This new CMS method uses an analytical form of the error as function of Laplace variable similar to the analytical form of the aerodynamic forces calculated with the MS method. We applied this new method to an F/A-18 aircraft and we found that the CMS method brings improvements in the approximation results in comparison with the standard MS method. It is shown that use of the CMS method on an F/A-18 aircraft will give better results in terms of convergence speeds and precision than the MS method.

Détermination directe des coefficients du potentiel de Dunham par une méthode de moindres carrés non linéaire appliquée aux nombres d'ondes des raies. Application au cas de la molécule HBr

1977 ◽  
Vol 55 (21) ◽  
pp. 1829-1834 ◽  
Author(s):  
P. Niay ◽  
P. Bernage ◽  
C. Coquant ◽  
A. Fayt
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Iterative Process ◽  
Nonlinear Least Squares ◽  
Theoretical Framework ◽  
New Method

In this paper, the Dunham potential coefficients are numerically determined by using a nonlinear least squares routine applied directly to the line experimental wave numbers.The results are compared to the ones obtained when using the usual iterative process applied to the H81Br Yi0 and Yi1 equilibrium constants.The al determination new method assumes a theoretical framework (B.O., adiabatic or non-adiabatic) to be valid. One can test this assumption by comparing the experimental data to the calculated ones.

Accurate power series for eigenvalues of spheroidal angle functions and their convergence radii

2011 ◽  
Vol 89 (11) ◽  
pp. 1083-1099
Author(s):  
Tam Do-Nhat
Keyword(s):  
Power Series ◽  
Least Squares ◽  
Complex Plane ◽  
Branch Point ◽  
Upper Bound ◽  
Least Squares Method ◽  
Radius Of Convergence ◽  
New Method ◽  
Recursion Relations

In this paper, the radius of convergence of the spheroidal power series associated with the eigenvalue is calculated without using the branch point approach. Studying the properties of the power series using the recursion relations among its coefficients in the new method offers some insights into the spheroidal power series and its associated eigenfunction. This study also used the least squares method to accurately compute the convergence radii to five or six significant digits. Within the circle of convergence in the complex plane of the parameter c = kF, where k is the wavenumber and F is the semifocal length of the spheroidal system, the extremely fast convergent spheroidal power series are computed with full precision. In addition, a formula for the magnitude of the upper bound of the error is obtained.

A New Method for Stress Categorization on Planes

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
P. B. Godbole ◽  
Supak Pore
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stress Distribution ◽  
Least Squares ◽  
New Method ◽  
Element Analysis ◽  
Least Squares Fit

A new method employing the fitting of a least squares plane to stress distribution obtained from a finite element analysis for evaluating categorized values is presented. The property of a least squares fit, i.e., the preservation of volume under stress distribution and the plane of consideration, is used in evaluating various numerical integrals. The procedure is demonstrated through application to a typical shell nozzle junction.

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