scholarly journals DOA Estimation and Self-Calibration under Unknown Mutual Coupling

Sensors ◽  
2019 ◽  
Vol 19 (4) ◽  
pp. 978
Author(s):  
Dong Qi ◽  
Min Tang ◽  
Shiwen Chen ◽  
Zhixin Liu ◽  
Yongjun Zhao
Keyword(s):  
Mutual Coupling ◽  
Linear Equations ◽  
Least Square Method ◽  
Calibration Method ◽  
Least Square ◽  
Frequency Distributions ◽  
Steering Vector ◽  
Practical Applications ◽  
Time Frequency ◽  
Self Calibration

In practical applications, the assumption of omnidirectional elements is not effective in general, which leads to the direction-dependent mutual coupling (MC). Under this condition, the performance of traditional calibration algorithms suffers. This paper proposes a new self-calibration method based on the time-frequency distributions (TFDs) in the presence of direction-dependent MC. Firstly, the time-frequency (TF) transformation is used to calculate the space-time-frequency distributions (STFDs) matrix of received signals. After that, the estimated steering vector and corresponding noise subspace are estimated by the steps of noise removing, single-source TF points extracting and clustering. Then according to the transformation relationship between the MC coefficients, steering vector and MC matrix, we deduce a set of linear equations. Finally, with two-step alternating iteration, the equations are solved by least square method in order to estimate DOA and MC coefficients. Simulations results show that the proposed algorithm can achieve direction-dependent MC self-calibration and outperforms the existing algorithms.

scholarly journals Self-Calibration of an Industrial Robot Using a Novel Affordable 3D Measuring Device

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3380 ◽  
Author(s):  
Martin Gaudreault ◽  
Ahmed Joubair ◽  
Ilian Bonev
Keyword(s):  
Industrial Robot ◽  
Low Cost ◽  
Least Square Method ◽  
Calibration Method ◽  
Least Square ◽  
Geometrical Parameters ◽  
Robot Arm ◽  
Measuring Device ◽  
Self Calibration ◽  
Position Errors

This work shows the feasibility of calibrating an industrial robot arm through an automated procedure using a new, low-cost, wireless measuring device mounted on the robot’s flange. The device consists of three digital indicators that are fixed orthogonally to each other on an aluminum support. Each indicator has a measuring accuracy of 3 µm. The measuring instrument uses a kinematic coupling platform which allows for the definition of an accurate and repeatable tool center point (TCP). The idea behind the calibration method is for the robot to bring automatically this TCP to three precisely-known positions (the centers of three precision balls fixed with respect to the robot’s base) and with different orientations of the robot’s end-effector. The self-calibration method was tested on a small six-axis industrial robot, the ABB IRB 120 (Vasteras, Sweden). The robot was modeled by including all its geometrical parameters and the compliance of its joints. The parameters of the model were identified using linear regression with the least-square method. Finally, the performance of the calibration was validated with a laser tracker. This validation showed that the mean and the maximum absolute position errors were reduced from 2.628 mm and 6.282 mm to 0.208 mm and 0.482 mm, respectively.

scholarly journals Minimization of Deviations of Gear Real Tooth Surfaces Determined by Coordinate Measurements

1993 ◽  
Vol 115 (4) ◽  
pp. 995-1001 ◽  
Author(s):  
F. L. Litvin ◽  
C. Kuan ◽  
J. C. Wang ◽  
R. F. Handschuh ◽  
J. Masseth ◽  
...  
Keyword(s):  
Linear Equations ◽  
Least Square Method ◽  
Least Square ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Overdetermined System ◽  
Entire Surface ◽  
First Order ◽  
Tooth Surfaces ◽  
Coordinate Measurements

The deviations of a gear’s real tooth surface from the theoretical surface are determined by coordinate measurements at the grid of the surface. A method has been developed to transform the deviations from Cartesian coordinates to those along the normal at the measurement locations. Equations are derived that relate the first order deviations with the adjustment to the manufacturing machine tool settings. The deviations of the entire surface are minimized. The minimization is achieved by application of the least-square method for an overdetermined system of linear equations. The proposed method is illustrated with a numerical example for hypoid gear and pinion.

scholarly journals A New Algorithm for Reconstructing Two-Dimensional Temperature Distribution by Ultrasonic Thermometry

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Xuehua Shen ◽  
Qingyu Xiong ◽  
Weiren Shi ◽  
Shan Liang ◽  
Xin Shi ◽  
...  
Keyword(s):  
Temperature Distribution ◽  
Ultrasound Velocity ◽  
Least Square Method ◽  
Reconstruction Algorithm ◽  
Industrial Applications ◽  
Least Square ◽  
Distribution Models ◽  
Practical Applications ◽  
Reconstruction Performance ◽  
Reconstructed Temperature

Temperature, especially temperature distribution, is one of the most fundamental and vital parameters for theoretical study and control of various industrial applications. In this paper, ultrasonic thermometry to reconstruct temperature distribution is investigated, referring to the dependence of ultrasound velocity on temperature. In practical applications of this ultrasonic technique, reconstruction algorithm based on least square method is commonly used. However, it has a limitation that the amount of divided blocks of measure area cannot exceed the amount of effective travel paths, which eventually leads to its inability to offer sufficient temperature information. To make up for this defect, an improved reconstruction algorithm based on least square method and multiquadric interpolation is presented. And then, its reconstruction performance is validated via numerical studies using four temperature distribution models with different complexity and is compared with that of algorithm based on least square method. Comparison and analysis indicate that the algorithm presented in this paper has more excellent reconstruction performance, as the reconstructed temperature distributions will not lose information near the edge of area while with small errors, and its mean reconstruction time is short enough that can meet the real-time demand.

scholarly journals The tides in the south-western Kara sea. Tides calibration method effects

2017 ◽  
pp. 98-115
Author(s):  
G. N. Voinov ◽  
A. K. Naumov
Keyword(s):  
Sea Level ◽  
Least Square Method ◽  
Calibration Method ◽  
Kara Sea ◽  
Least Square ◽  
The South ◽  
Quality Estimation ◽  
Annual Series ◽  
Method Effects ◽  
Statistical Estimations

The estimates of the tides harmonic constants are given over the period from 1962 to 1993. They were received using a least square method according to AARI. Quality estimation of the sea level observations was performed. The annual series with bad observations were transformed by means of tides calibration. The Estimation of the tides fi ne structure – harmonics of the second and third degree of the potential according to analysis over the period from 1962–1985 was received. The statistical estimations of the sea level in the separate typical years were calculated using initial and corrected series.

scholarly journals Statistical inference of prehistoric demography from frequency distributions of radiocarbon dates: a review and a guide for the perplexed

2021 ◽  
Author(s):  
Enrico R. Crema
Keyword(s):  
Frequency Data ◽  
Statistical Nature ◽  
Radiocarbon Dates ◽  
Frequency Distributions ◽  
Practical Applications ◽  
Time Frequency ◽  
Comparative Demography ◽  
Frequency Changes ◽  
Past Population

The last decade saw a rapid increase in the number of applications where time-frequency changes of radiocarbon dates have been used as a proxy for inferring past population dynamics. Although its simple and universal premise is appealing and undoubtedly offers some unique opportunities for research on long-term comparative demography, practical applications are far from trivial and riddled by challenges. Here I review: 1) the most common criticisms concerning the nature of radiocarbon time-frequency data as a demographic proxy; 2) the statistical nature of the problem; and 3) three classes of inferential approaches proposed so far in the literature.

Camera Calibration Based on Snell’s Law

2005 ◽  
Vol 128 (3) ◽  
pp. 548-557 ◽  
Author(s):  
Psang Dain Lin ◽  
Chi-Kuen Sung
Keyword(s):  
Camera Calibration ◽  
Least Square Method ◽  
Calibration Method ◽  
Least Square ◽  
Camera System ◽  
Optical Elements ◽  
Snell’S Law ◽  
Snell's Law ◽  
Geometric Relationship ◽  
Pinhole Model

In this paper we present a camera calibration method using Snell’s Law. Traditional camera calibration is based on the pinhole model, which is an approximation algorithm using untrue geometrical assumptions and giving a single lumped result for the various optical elements in the camera system. Using full modeling of lens geometry, the proposed method establishes the geometric relationship between images and objects via Snell’s Law. A matrix equation that relates the intrinsic/extrinsic parameters of image the plane and six pose parameters of each element is determined from sensitivity analysis. These parameters can be identified using the least square method by observing points with known coordinates. An illustrative example using a two-camera stereo coordinate measurement system demonstrates that system performance via the proposed method is better than the pinhole model.

Study on Two-Step Method for Robot Dynamics Parameters Calibration

2012 ◽  
Vol 605-607 ◽  
pp. 1557-1562 ◽  
Author(s):  
Qing Xuan Jia ◽  
Tong Li ◽  
Gang Chen
Keyword(s):  
Inverse Method ◽  
Least Square Method ◽  
Calibration Method ◽  
Least Square ◽  
Second Step ◽  
Robot Dynamics ◽  
Joint Movement ◽  
Step Method ◽  
Multidimensional Matrix ◽  
Pseudo Inverse

In order to obtain accurate dynamics parameters, a two-step method for robot dynamics parameters calibration is presented. In the first step a multidimensional matrix is constituted through transforming the configurations of robot manipulators and the product of quality and centroid coordinate about links is solved by using the least square method. In the second step decoupling dynamic equation of robot is deduced based on Newton-Euler algorithm, and through planning specific joint movement, the inertia tensor and centroid coordinate of robot links are calibrated making use of the pseudo inverse method. By the above two steps, the entire calibration of robot dynamic parameters is achieved. The correctness and feasibility of the presented calibration method is manifested by simulations and experiments.

A Camera Calibration Method Based on Free Points

2011 ◽  
Vol 130-134 ◽  
pp. 1885-1888
Author(s):  
Jing Lei Zhang ◽  
Kai Bo Fan ◽  
Yan Jiao Wang
Keyword(s):  
Standard Deviation ◽  
Ccd Camera ◽  
Least Square Method ◽  
Calibration Method ◽  
Initial Guess ◽  
Least Square ◽  
Camera Model ◽  
Extrinsic Parameters ◽  
The Mean ◽  
Constraint Method

A new accurate calibrating technique for intrinsic parameters and extrinsic parameters of CCD camera is described. The camera model is derived by the pinhole projection theory. Then other parameters of the model are resolved under the radial alignment constraints and orthogonal constraints. In order to get a fine initial guess for the nonlinear searching solution, the least square method is introduced, and finally uses radial alignment constraint method to get the results. The experimental results show that the mean absolute differences in x direction and y direction are 0.0070 and 0.1430 separately while the standard deviation are 0.5006 and 1.2046 separately.

System Identification of a Class of Second-Order Continuous System

2014 ◽  
Vol 651-653 ◽  
pp. 528-533 ◽  
Author(s):  
Zhi Gang Jia ◽  
Xing Xuan Wang
Keyword(s):  
Linear Equations ◽  
Continuous System ◽  
Least Square Method ◽  
Second Order ◽  
Least Square ◽  
Step Response ◽  
Order System ◽  
Simulation Results ◽  
Order Continuous ◽  
Identification Model

An identification method of a class of second-order continuous system is proposed. This method constructs a discrete-time identification model, forms a set of linear equations. The parameters can be obtained by least square method. Simulation results show that the method is effective for a class of second-order system, and is not only for step response but also for square wave signal.

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