Application of the Weighted Least Squares Parameter Estimation Method to the Robot Calibration

1994 ◽  
Vol 116 (3) ◽  
pp. 890-893 ◽  
Author(s):  
G. Zak ◽  
B. Benhabib ◽  
R. G. Fenton ◽  
I. Saban
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Kinematic Model ◽  
Measurement Data ◽  
Estimation Method ◽  
Kinematic Parameter ◽  
Measuring System ◽  
Parameter Estimates ◽  
Robot Calibration

Significant attention has been paid recently to the topic of robot calibration. To improve the robot’s accuracy, various approaches to the measurement of the robot’s position and orientation (pose) and correction of its kinematic model have been proposed. Little attention, however, has been given to the method of estimation of the kinematic parameters from the measurement data. Typically, a least-squares solution method is used to estimate the corrections to the parameters of the model. In this paper, a method of kinematic parameter estimation is proposed where a standard least-squares estimation procedure is replaced by weighted least-squares. The weighting factors are calculated based on all the a priori available statistical information about the robot and the pose-measuring system. By giving greater weight to the measurements made where the standard deviation of the noise in the data is expected to be lower, a significant reduction in the error of the kinematic parameter estimates is made possible. The improvement in the calibration results was verified using a calibration simulation algorithm.

scholarly journals Novel Optimization-Based Parameter Estimation Method for the Bass Diffusion Model

SAGE Open ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 215824402110269
Author(s):  
Lang Liang
Keyword(s):  
Parameter Estimation ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Estimation Method ◽  
Reference Value ◽  
Diffusion Problem ◽  
Bass Model ◽  
Weighted Least Squares Method ◽  
Estimated Parameters ◽  
Bass Diffusion Model

The Bass model is the most popular model for forecasting the diffusion process of a new product. However, the controlling parameters in it are unknown in practice and need to be determined in advance. Currently, the estimation of the controlling parameters has been approached by various techniques. In this case, a novel optimization-based parameter estimation (OPE) method for the Bass model is proposed in the theoretical framework of system dynamics ( SD). To do this, the SD model of the Bass differential equation is first established and then the corresponding optimization mathematical model is formulated by introducing the controlling parameters as design variable and the discrepancy of the adopter function to the reference value as objective function. Using the VENSIM software, the present SD optimization model is solved, and its effectiveness and accuracy are demonstrated by two examples: one involves the exact solution and another is related to the actual user diffusion problem from Chinese Mobile. The results show that the present OPE method can produce higher predicting accuracy of the controlling parameters than the nonlinear weighted least squares method and the genetic algorithms. Moreover, the reliability interval of the estimated parameters and the goodness of fitting of the optimal results are given as well to further demonstrate the accuracy of the present OPE method.

scholarly journals Distributed Weighted Least-Squares and Gaussian Belief Propagation: An Integrated Approach

2021 ◽  
Author(s):  
Dino Zivojevic ◽  
Muhamed Delalic ◽  
Darijo Raca ◽  
Dejan Vukobratovic ◽  
Mirsad Cosovic
Keyword(s):  
Least Squares ◽  
Large Scale ◽  
Belief Propagation ◽  
Weighted Least Squares ◽  
Measurement Data ◽  
Integrated Approach ◽  
Factor Graph ◽  
State Variables ◽  
Large Scale Systems ◽  
Distributed Approach

The purpose of a state estimation (SE) algorithm is to estimate the values of the state variables considering the available set of measurements. The centralised SE becomes impractical for large-scale systems, particularly if the measurements are spatially distributed across wide geographical areas. Dividing the large-scale systems into clusters (\ie subsystems) and distributing the computation across clusters, solves the constraints of centralised based approach. In such scenarios, using distributed SE methods brings numerous advantages over the centralised ones. In this paper, we propose a novel distributed approach to solve the linear SE model by combining local solutions obtained by applying weighted least-squares (WLS) of the given subsystems with the Gaussian belief propagation (GBP) algorithm. The proposed algorithm is based on the factor graph operating without a central coordinator, where subsystems exchange only ``beliefs", thus preserving privacy of the measurement data and state variables. Further, we propose an approach to speed-up evaluation of the local solution upon arrival of a new information to the subsystem. Finally, the proposed algorithm provides results that reach accuracy of the centralised WLS solution in a few iterations, and outperforms vanilla GBP algorithm with respect to its convergence properties.

Parameter Estimation in Marketing Models in the Presence of Influential Response Data: Robust Regression and Applications

1984 ◽  
Vol 21 (3) ◽  
pp. 268-277 ◽  
Author(s):  
Vijay Mahajan ◽  
Subhash Sharma ◽  
Yoram Wind
Keyword(s):  
Parameter Estimation ◽  
Regression Analysis ◽  
Least Squares ◽  
Robust Regression ◽  
Ordinary Least Squares ◽  
Regression Coefficients ◽  
Parameter Estimates ◽  
Response Data ◽  
Marketing Models ◽  
Marketing Data

In marketing models, the presence of aberrant response values or outliers in data can distort the parameter estimates or regression coefficients obtained by means of ordinary least squares. The authors demonstrate the potential usefulness of the robust regression analysis in treating influential response values in marketing data.

scholarly journals IMU-Based Online Kinematic Calibration of Robot Manipulator

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Guanglong Du ◽  
Ping Zhang
Keyword(s):  
Kalman Filter ◽  
Robot Manipulator ◽  
Experimental Studies ◽  
Estimation Method ◽  
Kinematic Parameter ◽  
Corner Detection ◽  
Measurement Unit ◽  
Robot Calibration ◽  
Self Calibration ◽  
Calibration Methods

Robot calibration is a useful diagnostic method for improving the positioning accuracy in robot production and maintenance. An online robot self-calibration method based on inertial measurement unit (IMU) is presented in this paper. The method requires that the IMU is rigidly attached to the robot manipulator, which makes it possible to obtain the orientation of the manipulator with the orientation of the IMU in real time. This paper proposed an efficient approach which incorporates Factored Quaternion Algorithm (FQA) and Kalman Filter (KF) to estimate the orientation of the IMU. Then, an Extended Kalman Filter (EKF) is used to estimate kinematic parameter errors. Using this proposed orientation estimation method will result in improved reliability and accuracy in determining the orientation of the manipulator. Compared with the existing vision-based self-calibration methods, the great advantage of this method is that it does not need the complex steps, such as camera calibration, images capture, and corner detection, which make the robot calibration procedure more autonomous in a dynamic manufacturing environment. Experimental studies on a GOOGOL GRB3016 robot show that this method has better accuracy, convenience, and effectiveness than vision-based methods.

scholarly journals Determination of Lateral Modulation Apodization Functions Using a Regularized, Weighted Least Squares Estimation

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Chikayoshi Sumi
Keyword(s):  
Least Squares ◽  
Spatial Resolution ◽  
Soft Tissues ◽  
Displacement Vector ◽  
Weighted Least Squares ◽  
Strain Tensor ◽  
Estimation Method ◽  
Modulation Method ◽  
Value Decomposition

Recently, work in this group has focused on the lateral cosine modulation method (LCM) which can be used for next-generation ultrasound (US) echo imaging and tissue displacement vector/strain tensor measurements (blood, soft tissues, etc.). For instance, in US echo imaging, a high lateral spatial resolution as well as a high axial spatial resolution can be obtained, and in tissue displacement vector measurements, accurate measurements of lateral tissue displacements as well as of axial tissue displacements can be realized. For an optimal determination of an apodization function for the LCM method, the regularized, weighted minimum-norm least squares (WMNLSs) estimation method is presented in this study. For designed Gaussian-type point spread functions (PSFs) with lateral modulation as an example, the regularized WMNLS estimation in simulations yields better approximations of the designed PSFs having wider lateral bandwidths than a Fraunhofer approximation and a singular-value decomposition (SVD). The usefulness of the regularized WMNLS estimation for the determination of apodization functions is demonstrated.

scholarly journals Analysis of algebraic weighted least-squares estimators for enzyme parameters

1992 ◽  
Vol 288 (2) ◽  
pp. 533-538 ◽  
Author(s):  
M E Jones
Keyword(s):  
Least Squares ◽  
Coefficient Of Variation ◽  
Constant Coefficient ◽  
Weighted Least Squares ◽  
Simulated Data ◽  
Standard Errors ◽  
Parameter Estimates ◽  
Spreadsheet Program ◽  
Least Squares Estimators ◽  
Constant Coefficient Of Variation

An algorithm for the least-squares estimation of enzyme parameters Km and Vmax. is proposed and its performance analysed. The problem is non-linear, but the algorithm is algebraic and does not require initial parameter estimates. On a spreadsheet program such as MINITAB, it may be coded in as few as ten instructions. The algorithm derives an intermediate estimate of Km and Vmax. appropriate to data with a constant coefficient of variation and then applies a single reweighting. Its performance using simulated data with a variety of error structures is compared with that of the classical reciprocal transforms and to both appropriately and inappropriately weighted direct least-squares estimators. Three approaches to estimating the standard errors of the parameter estimates are discussed, and one suitable for spreadsheet implementation is illustrated.

Integrating Parameter Estimation Solutions From the Time and Time-Scale Domains

2009 ◽  
Author(s):  
James R. McCusker ◽  
Kourosh Danai
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Time Scale ◽  
Prediction Error ◽  
Nonlinear Least Squares ◽  
Integrated Approach ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Single Model ◽  
Iterative Estimation

A method of parameter estimation was recently introduced that separately estimates each parameter of the dynamic model [1]. In this method, regions coined as parameter signatures, are identified in the time-scale domain wherein the prediction error can be attributed to the error of a single model parameter. Based on these single-parameter associations, individual model parameters can then be estimated for iterative estimation. Relative to nonlinear least squares, the proposed Parameter Signature Isolation Method (PARSIM) has two distinct attributes. One attribute of PARSIM is to leave the estimation of a parameter dormant when a parameter signature cannot be extracted for it. Another attribute is independence from the contour of the prediction error. The first attribute could cause erroneous parameter estimates, when the parameters are not adapted continually. The second attribute, on the other hand, can provide a safeguard against local minima entrapments. These attributes motivate integrating PARSIM with a method, like nonlinear least-squares, that is less prone to dormancy of parameter estimates. The paper demonstrates the merit of the proposed integrated approach in application to a difficult estimation problem.

scholarly journals A QUASI-LIKELIHOOD APPROACH TO PARAMETER ESTIMATION FOR SIMULATABLE STATISTICAL MODELS

2014 ◽  
Vol 33 (2) ◽  
pp. 107 ◽  
Author(s):  
Markus Baaske ◽  
Felix Ballani ◽  
Karl Gerald Van den Boogaart
Keyword(s):  
Parameter Estimation ◽  
Statistical Models ◽  
Estimation Method ◽  
Score Function ◽  
Boolean Model ◽  
Parameter Estimates ◽  
Random Errors ◽  
Likelihood Functions ◽  
Simulation Based ◽  
Likelihood Approach

This paper introduces a parameter estimation method for a general class of statistical models. The method exclusively relies on the possibility to conduct simulations for the construction of interpolation-based metamodels of informative empirical characteristics and some subjectively chosen correlation structure of the underlying spatial random process. In the absence of likelihood functions for such statistical models, which is often the case in stochastic geometric modelling, the idea is to follow a quasi-likelihood (QL) approach to construct an optimal estimating function surrogate based on a set of interpolated summary statistics. Solving these estimating equations one can account for both the random errors due to simulations and the uncertainty about the meta-models. Thus, putting the QL approach to parameter estimation into a stochastic simulation setting the proposed method essentially consists of finding roots to a sequence of approximating quasiscore functions. As a simple demonstrating example, the proposed method is applied to a special parameter estimation problem of a planar Boolean model with discs. Here, the quasi-score function has a half-analytical, numerically tractable representation and allows for the comparison of the model parameter estimates found by the simulation-based method and obtained from solving the exact quasi-score equations.

Ridge estimation iterative algorithm to ill-posed uncertainty adjustment model

2020 ◽  
Author(s):  
tieding lu
Keyword(s):  
Parameter Estimation ◽  
Iterative Algorithm ◽  
Measurement Data ◽  
Estimation Method ◽  
Coefficient Matrix ◽  
Observation Equation ◽  
Validity And Reliability ◽  
Ridge Estimation ◽  
Adjustment Model ◽  
Ill Posed

<p> Uncertainties usually exist in the process of acquisition of measurement data, which affect the results of the parameter estimation. The solution of the uncertainty adjustment model can effectively improve the validity and reliability of parameter estimation. When the coefficient matrix of the observation equation has a singular value close to zero, i.e., the coefficient matrix is ill-posed, the ridge estimation can effectively suppress the influence of the ill-posed problem of the observation equation on the parameter estimation. When the uncertainty adjustment model is ill-posed, it is more seriously affected by the error of the coefficient matrix and observation vector. In this paper, the ridge estimation method is applied to ill-posed uncertainty adjustment model, deriving an iterative algorithm to improve the stability and reliability of the results. The derived algorithm is verified by two examples, and the results show that the new method is effective and feasible.</p>

Sign in / Sign up

Export Citation Format

Share Document