• Journal of the Korean Statistical Society
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• v.28 no.2
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• pp.151-165
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• 1999

This paper considers the trimmed least squares estimator of the autoregression parameter in the unstable AR(1) model: X\ulcorner=ØX\ulcorner+$\varepsilon$\ulcorner, where $\varepsilon$\ulcorner are iid random variables with mean 0 and variance $\sigma$$^2$> 0, and Ø is the real number with │Ø│=1. The trimmed least squares estimator for Ø is defined in analogy of that of Welsh(1987). The limiting distribution of the trimmed least squares estimator is derived under certain regularity conditions.

• Journal of Electrical Engineering and Technology
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• v.7 no.4
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• pp.606-614
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• 2012

A practical recursive linear robust estimation scheme is proposed for target localization in the sensor network which provides range difference of arrival (RDOA) measurements. In order to radically solve the known practical difficulties such as sensitivity for initial guess and heavy computational burden caused by intrinsic nonlinearity of the RDOA based target localization problem, an uncertain linear measurement model is newly derived. In the suggested problem setting, the target localization performance of the conventional linear estimation schemes might be severely degraded under the low SNR condition and be affected by the target position in the sensor network. This motivates us to devise a new sensor network localization algorithm within the framework of the recently developed robust least squares estimation theory. Provided that the statistical information regarding RDOA measurements are available, the estimate of the proposition method shows the convergence in probability to the true target position. Through the computer simulations, the omnidirectional target localization performance and consistency of the proposed algorithm are compared to those of the existing ones. It is shown that the proposed method is more reliable than the total least squares method and the linear correction least squares method.

• Journal of Power System Engineering
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• v.7 no.1
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• pp.74-81
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• 2003

A system identification is to estimate the mathematical model on the base of input output data and to measure the output in the presence of adequate input for the controlled system. In the traditional system control field, most identification problems have been thought as estimating the unknown modeling parameters on the assumption that the model structures are fixed. In the system identification, it is possible to estimate the true parameter values by the adjusted least squares method in the input output case of no observed noise, and it is possible to estimate the true parameter values by the total least squares method in the input output case with the observed noise. We suggest the adjusted least squares method as a consistent estimation method in the system identification in the case where there is observed noise only in the output. In this paper the adjusted least squares method has been developed from the least squares method and the efficiency of the estimating results was confirmed by the generating data with the computer simulations.

• The Journal of the Acoustical Society of Korea
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• v.29 no.6
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• pp.374-380
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• 2010

It is known that the problem of FIR filtering with noisy input and output data can be solved by a total least squares (TLS) estimation. It is also known that the performance of the TLS estimation is very sensitive to the ratio between the variances of the input and output noises. In this paper, we propose a convex combination algorithm between the ordinary recursive LS based TLS (RTLS) and the ordinary recursive LS (RLS). This combined algorithm is robust to the noise variance ratio and has almost the same complexity as the RTLS. Simulation results show that the proposed algorithm performs near TLS in noise variance ratio ${\gamma}{\approx}1$ and that it outperforms TLS and LS in the rage of 2 < $\gamma$ < 20. Consequently, the practical workability of the TLS method applied to noisy data has been significantly broadened.

• Proceedings of the KIPE Conference
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• 2018.11a
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• pp.175-176
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• 2018

This paper presents a method to estimate the parameter of permanent magnet synchronous motor using a least squares method. The approximate solution of the linear simultaneous equations is obtained by the pseudoinverse least squares method of the input current and output voltage data of the current controller. It is possible to obtain the current response of the same bandwidth to the general control target by using the Pole-zero Cancellation technique. This paper verifies the performance of the proposed method by comparing the results of estimation of parameters of different motors by simulation.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.10
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• pp.978-982
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• 2007

This paper presents the velocity estimation of a mobile robot using a regular polygonal array of optical mice that are installed at the bottom of a mobile robot. First, the basic principle of the proposed velocity estimation method is explained. Second, the velocity kinematics from a mobile robot to an array of optical mice is derived as an overdetermined linear system. Third, for a given set of optical mouse readings, the mobile robot velocity is estimated based on the least squares solution to the obtained system. Finally, simulation results are given to demonstrate the validity of the proposed velocity estimation method.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1557-1571
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• 2017

The L-curve method is a parametric plot of interrelation between the residual norm of the least squares problem and the solution norm. However, the L-curve method may be hard to apply to the total least squares problem due to its no closed form solution of the regularized total least squares problems. Thus the sequence of the solution norm under the fixed regularization parameter and its corresponding residual need to be found with an efficient manner. In this paper, we suggest an efficient algorithm to find the sequence of the solutions and its residual in order to plot the L-curve for the total least squares problems. In the numerical experiments, we present that the proposed algorithm successfully and efficiently plots fairly 'L' like shape for some practical regularized total least squares problems.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2003.10a
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• pp.15-19
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• 2003

The Total Least Squares (TLS) method is introduced in comparison with the conventional Least Squares (LS) method. The principles and mathematical models for both methods are summarized and the comparison results from their applications to a simple geometric example, fitting a straight line to a set of 2D points are presented. As conceptually reasoned, the results clearly indicate that LS is more susceptible of producing wrong parameters with worse precision rather than TLS. For many applications in surveying, can adjustment computation and parameter estimation based on TLS provide better results.

• Journal of the Korean Data and Information Science Society
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• v.14 no.4
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• pp.1091-1102
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• 2003

The Weibull variate is commonly used as a lifetime distribution in reliability applications. Estimation of parameters is revisited in the two-parameter Weibull distribution. The method of product spacings, the method of quantile estimates and the method of least squares are applied to this distribution. A comparative study between a simple minded estimate, the maximum likelihood estimate, the product spacings estimate, the quantile estimate, the least squares estimate, and the adjusted least squares estimate is presented.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.409-417
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• 2003

There are two rotation matrix parameters in a model, pro-posed by Prentice in 1989, for pairs of rotations in 3 dimensional space. For the least squares estimates of the two parameters, an algorithm was also presented, but it turned out that the algorithm could fail to get the least squares estimates. This article provides another algorithm for the least squares estimates and its performance is demonstrated by simulation results.