Comparing of Coordinate Transformation Based on Total Least Squares and Least Squares

2014 ◽  
Vol 522-524 ◽  
pp. 1211-1214
Author(s):  
Qing Wu Meng ◽  
Lu Meng
Keyword(s):  
Least Squares ◽  
Coordinate Transformation ◽  
Least Square Method ◽  
Coefficient Matrix ◽  
Total Least Squares ◽  
Least Square ◽  
Experimental Results ◽  
Transformation Models ◽  
Total Least Square

The coordinate transformation models based on least square method and total least square are built and discussed. The least square model only includes the errors of observation vectors, the total least square model simultaneously takes into consideration to the errors of observation vectors and the errors of coefficient matrix. The both models are verified and compared in experiment. The experimental results showed that the model of total least square is more in line with actual, and more reasonable than by least square theoretically, and the coordinate transformation solution result of total least square with least square is more near.

Localization of Mobile Robot Based on Least Square Method

2013 ◽  
Vol 347-350 ◽  
pp. 808-811
Author(s):  
Jia Lu Li ◽  
Lin Bing Long ◽  
Bao Feng Zhang
Keyword(s):  
Motion Estimation ◽  
Mobile Robot ◽  
Mobile Robots ◽  
Least Squares ◽  
Least Square Method ◽  
Least Square ◽  
Experimental Results ◽  
Sift Algorithm ◽  
Key Techniques ◽  
Point Detection

Localization is the basis for navigation of mobile robots. This paper focuses on key techniques of localization for mobile robots based on vision. Firstly, the specific measures and steps of the algorithm are analyzed and researched in depth. In the study, SIFT algorithm combined with epipolar geometry constraint is used on the environment feature point detection, matching and tracking. And the method of RANSAC combined with the least squares is used to obtain accurate results of the motion estimation. Then the necessary experiments are carried out to verify the correctness and effectiveness of algorithms. The experimental results verified the accuracy of the improved algorithm.

Fuzzy C-Regression Models

2013 ◽  
Vol 278-280 ◽  
pp. 1323-1326
Author(s):  
Yan Hua Yu ◽  
Li Xia Song ◽  
Kun Lun Zhang
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Methods ◽  
Statistical Regression ◽  
Fuzzy Linear Regression ◽  
Fuzzy Degree

Fuzzy linear regression has been extensively studied since its inception symbolized by the work of Tanaka et al. in 1982. As one of the main estimation methods, fuzzy least squares approach is appealing because it corresponds, to some extent, to the well known statistical regression analysis. In this article, a restricted least squares method is proposed to fit fuzzy linear models with crisp inputs and symmetric fuzzy output. The paper puts forward a kind of fuzzy linear regression model based on structured element, This model has precise input data and fuzzy output data, Gives the regression coefficient and the fuzzy degree function determination method by using the least square method, studies the imitation degree question between the observed value and the forecast value.

Determination of Johnson Cook Material Model Constants and Their Influence on Machining Simulations of Tungsten Heavy Alloy

2018 ◽  
Author(s):  
Chithajalu Kiran Sagar ◽  
Amrita Priyadarshini ◽  
Amit Kumar Gupta ◽  
Sidharth Kumar Shukla
Keyword(s):  
Least Square Method ◽  
Material Model ◽  
Least Square ◽  
Experimental Results ◽  
Tungsten Heavy Alloy ◽  
Fe Model ◽  
Abc Algorithm ◽  
Bee Colony ◽  
Aircraft Manufacturing ◽  
Heavy Alloys

Tungsten Heavy Alloys (WHA) are used in counterbalance and ballast weights for aerodynamic balancing in fixed and rotary wing aircraft. Manufacturing these components for closer tolerances using machining is a challenging task. The present work aims to develop a 2D Finite Element (FE) model to simulate the chip formation process during machining of WHA using Johnson Cook Material Model (JCMM). The model constants for 95%WHA are determined based on the high strain rate test data using least square method. The calculated values are further optimized using Genetic Algorithm (GA) and Artificial Bee Colony (ABC) algorithm, which are then used as material inputs for FE simulation of machining WHA. The predicted results such as cutting force, chip geometry, shear stress, shear angle are presented and compared with the experimental results under similar cutting conditions. It has been observed that the constants obtained from ABC algorithm show minimum error in the cutting performance measures for all the experimental results.

Penerbitan Maklumat Tiga Dimensi Sebuah Lukisan Garisan Menggunakan Kaedah Jumlah Kuasa Dua Terkecil

2012 ◽  
Author(s):  
Habibollah Haron ◽  
Dzulkifli Mohamed
Keyword(s):  
Linear System ◽  
Line Drawing ◽  
Least Square Method ◽  
Least Square ◽  
Geometric Information ◽  
Ordinary Least Square ◽  
Total Least Square ◽  
Regular Line ◽  
Space Image

Pengekstrakan lukisan garisan melibatkan proses menukar lukisan garisan tidak sekata kepada lukisan sekata, mendapatkan entiti asas simpang, garisan serta kawasan dan seterusnya mendapatkan maklumat tiga dimensi lukisan. Proses penukaran lukisan tidak sekata akan menghasilkan maklumat dua dimensi lukisan dan maklumat geometri dua dimensi lukisan iaitu simpang, garisan dan kawasan masing-masing yang mewakili unjuran bucu, pinggir dan permukaan dalam tiga dimensi. Berdasarkan maklumat geometri dua dimensi ini, jenis kenalaran imej ditentukan untuk membentuk set sistem linear lebih tentu. Grimstead menggunakan empat kenalaran imej dan menggunakan lelaran kuasa dua terkecil untuk menyelesaikan sistem linear lebih tentu yang dihasilkan. Kertas kerja ini akan mencadangkan kaedah jumlah kuasa dua terkecil untuk menyelesaikan sistem linear lebih tentu yang dibentuk oleh dua kenalaran imej. Perbandingan dengan kaedah Grimstead akan ditunjukkan dan penerangan akan dibantu oleh kes kajian dan paparan output. Kata kunci: Terjemahan garisan; Jumlah Kuasa Dua Terkecil; ruang gradien; kenalaran imej; sistem linear Line drawing interpretation involves process of converting irregular line drawing to regular line drawing. The converting process produces junctions, lines and regions that are two-dimensional projection of vertices, edges, and faces of a solid model respectively. Based on the geometric information obtained, image regularities are determined and a over-determined sets of linear systems is developed. Grimstead used the three image regularities in the linear system and iterative ordinary least square to solve them. The paper is intended to propose Total Least Square method in solving over-determined sets of linear system of image regularities of a line drawing. Two image regularities have been used. The solutions obtained are visualized with the help of MATLAB tool. Case study is given to assist the explaination. Key words: Line Interpretation; Total Least Square Method; Gradient Space; Image Regularities; Linear System

Error Model and Calibration Analysis of the Flexible Coordinate Measuring Machine

2011 ◽  
Vol 121-126 ◽  
pp. 3273-3277 ◽  
Author(s):  
Fang Li ◽  
Shu Gui Liu ◽  
Lei Zhao
Keyword(s):  
Mathematical Model ◽  
Coordinate Measuring Machine ◽  
Least Square Method ◽  
Coefficient Matrix ◽  
Error Model ◽  
Least Square ◽  
Parameter Calibration ◽  
Measuring Machine ◽  
Improving Accuracy ◽  
The Mathematical Model

A new 5-DOF flexible coordinate measuring machine (CMM) is introduced in this paper, which uses REVO system produced by Renishaw. According to the D-H method, the mathematical model is built, and then the error model of the flexible CMM is derived. The parameter calibration based on the nonlinear least square method is analyzed theoretically. Due to the disadvantages of Gauss-Newton method, LM method is researched, which improved the singularity of the coefficient matrix. The calibration analysis is a basis for improving accuracy of the flexible CMM.

Solitary waves of the RLW equation via least squares method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ozlem Ersoy Hepson ◽  
Idris Dag ◽  
Bülent Saka ◽  
Buket Ay
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Spline Functions ◽  
Algebraic Equations ◽  
B Spline ◽  
B Splines ◽  
Rlw Equation ◽  
Set Up

Abstract Integration using least squares method in space and Crank–Nicolson approach in time is managed to set up an algorithm to solve the RLW equation numerically. Trial functions in the least square method consist of a combination of the quartic B-spline functions. Integration of the RLW equation gives a system of algebraic equations. The solutions consisting of a combination of the quartic B-splines are given for some initial and boundary value problems of RLW equation.

scholarly journals Scaled weighted total least-squares adjustment for partial errors-in-variables model

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
J. Zhao
Keyword(s):  
Least Squares ◽  
Variance Component ◽  
Maximum Likelihood Method ◽  
Coefficient Matrix ◽  
Total Least Squares ◽  
Likelihood Method ◽  
Errors In Variables ◽  
Weighted Total Least Squares ◽  
Least Squares Adjustment ◽  
Observation Vector

AbstractScaled total least-squares (STLS) unify LS, Data LS, and TLS with a different choice of scaled parameter. The function of the scaled parameter is to balance the effect of random error of coefficient matrix and observation vector for the estimate of unknown parameter. Unfortunately, there are no discussions about how to determine the scaled parameter. Consequently, the STLS solution cannot be obtained because the scaled parameter is unknown. In addition, the STLS method cannot be applied to the structured EIV casewhere the coefficient matrix contains the fixed element and the repeated random elements in different locations or both. To circumvent the shortcomings above, the study generalize it to a scaledweighted TLS (SWTLS) problem based on partial errors-in-variable (EIV) model. And the maximum likelihood method is employed to derive the variance component of observations and coefficient matrix. Then the ratio of variance component is proposed to get the scaled parameter. The existing STLS method and WTLS method is just a special example of the SWTLS method. The numerical results show that the proposed method proves to bemore effective in some aspects.

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