• International Journal of Aeronautical and Space Sciences
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• v.14 no.1
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• pp.85-90
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• 2013

This paper presents a study on terrain referenced navigation (TRN). The extended Kalman filter (EKF) is adopted as a filter method. A Jacobian matrix of measurement equations in the EKF consists of terrain slope terms, and accurate slope estimation is essential to keep filter stability. Two slope estimation methods are proposed in this study. Both methods are based on the least-squares approach. One is planar regression searching the best plane, in the least-squares sense, representing the terrain map over the region, determined by position error covariance. It is shown that the method could provide a more accurate solution than the previously developed linear regression approach, which uses lines rather than a plane in the least-squares measure. The other proposed method is weighted planar regression. Additional weights formed by Gaussian pdf are multiplied in the planar regression, to reflect the actual pdf of the position estimate of EKF. Monte Carlo simulations are conducted, to compare the performance between the previous and two proposed methods, by analyzing the filter properties of divergence probability and convergence speed. It is expected that one of the slope estimation methods could be implemented, after determining which of the filter properties is more significant at each mission.

• Communications for Statistical Applications and Methods
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• v.17 no.2
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• pp.141-151
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• 2010

Hybrid fuzzy regression analysis is used for integrating randomness and fuzziness into a regression model. Least squares support vector machine(LS-SVM) has been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate hybrid fuzzy linear and nonlinear regression models with crisp inputs and fuzzy output using weighted fuzzy arithmetic(WFA) and LS-SVM. LS-SVM allows us to perform fuzzy nonlinear regression analysis by constructing a fuzzy linear regression function in a high dimensional feature space. The proposed method is not computationally expensive since its solution is obtained from a simple linear equation system. In particular, this method is a very attractive approach to modeling nonlinear data, and is nonparametric method in the sense that we do not have to assume the underlying model function for fuzzy nonlinear regression model with crisp inputs and fuzzy output. Experimental results are then presented which indicate the performance of this method.

• Proceedings of the Korea Water Resources Association Conference
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• 2002.05a
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• pp.541-546
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• 2002

• The Korean Journal of Applied Statistics
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• v.21 no.1
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• pp.159-168
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• 2008

Since the term structure of interest rates (TSIR) has longitudinal data, we should consider as input variables both time left to maturity and time simultaneously to get a more useful and more efficient function estimation. However, since the resulting data set becomes very large, we need to develop a fast and reliable estimation method for large data set. Furthermore, it tends to overestimate TSIR because data are correlated. To solve these problems we propose a mixture of weighted least squares support vector machines. We recognize that the estimate is well smoothed and well explains effects of the third stock market crash in USA through applying the proposed method to the US Treasury bonds data.

• The Korean Journal of Nuclear Medicine
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• v.37 no.5
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• pp.288-300
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• 2003

Purpose: To obtain regional blood flow and tissue-blood partition coefficient with time-activity curves from ${H_2}^{15}O$ PET, fitting of some parameters in the Kety model is conventionally accomplished by nonlinear least squares (NLS) analysis. However, NLS requires considerable compuation time then is impractical for pixel-by-pixel analysis to generate parametric images of these parameters. In this study, we investigated several fast parameter estimation methods for the parametric image generation and compared their statistical reliability and computational efficiency. Materials and Methods: These methods included linear least squres (LLS), linear weighted least squares (LWLS), linear generalized least squares (GLS), linear generalized weighted least squares (GWLS), weighted Integration (WI), and model-based clustering method (CAKS). ${H_2}^{15}O$ dynamic brain PET with Poisson noise component was simulated using numerical Zubal brain phantom. Error and bias in the estimation of rCBF and partition coefficient, and computation time in various noise environments was estimated and compared. In audition, parametric images from ${H_2}^{15}O$ dynamic brain PET data peformed on 16 healthy volunteers under various physiological conditions was compared to examine the utility of these methods for real human data. Results: These fast algorithms produced parametric images with similar image qualify and statistical reliability. When CAKS and LLS methods were used combinedly, computation time was significantly reduced and less than 30 seconds for $128{\times}128{\times}46$ images on Pentium III processor. Conclusion: Parametric images of rCBF and partition coefficient with good statistical properties can be generated with short computation time which is acceptable in clinical situation.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.686-689
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• 2002

This paper proposes a weighted least-squares(WLS) method for designing variable one-dimensional (1-D) FIR digital filters with simultaneously variable magnitude and variable non-integer phase-delay responses. First, the coefficients of a variable FIR filter are represented as the two-dimensional (2-D) polynomials of a pair of spectral parameters: one is for tuning the magnitude response, and the other is for varying its non-integer phase-delay response. Then the optimal coefficients of the 2-D polynomials are found by minimizing the total weighted squared error of the variable frequency response. Finally, we show that the resulting variable FIR filter can be implemented in a parallel form, which is suitable for high-speed signal processing.

• Magazine of the Korean Society of Agricultural Engineers
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• v.32 no.1
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• pp.103-109
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• 1990

The application of the Log-Pearson Type m distribution recommended by Water Resources Council, U. S. A. for flood frequency analysis requires the estimation of the regionalized skew coefficient. In this study, regionalized skew coefficients are estimated using a weighted regression model which relates at-site skews based on logarithms of observed annual flood peak series to both basin characteristics and precipitation data in the Han river and the Nakdong river basin. The model is developed with weighted least squares method in which the weights are determined by separating residual variance into that due to model error and due to sampling error. As the result of analysis, regionalized skews are estimated as - 0.732 and - 0.575 in the Han river and the Nakdong river basin, respectively.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.4 no.1
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• pp.45-61
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• 2010

In the communication channel, the received signal is affected by many factors that can cause errors. These effects mean that received signal strength (RSS) based methods incur more errors in measuring distance and consequently result in low precision in the location detection process. As one of the approaches to overcome these problems, we propose using direction calibration to improve the performance of the RSS-based method for distance measurement, and sequentially a weighted least squares (WLS) method using reliability factors in conjunction with a conventional RSS weighting matrix is proposed to solve an over-determined localization process. The proposed scheme focuses on the features of the RSS method to improve the performance, and these effects are proved by the simulation results.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.41 no.3
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• pp.311-319
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• 1992

In this paper, a direct adaptive pole placement controller for an unknown linear time-invariant single-input single-output nonminimum phase plant is proposed. To design this direct adaptive pole placement controller, the auxiliary signals are introduced. Consequently, a linear equation error model is formulated for estimating both the controller parameters and the additional auxiliary parameters. To estimate the controller parameters and the additional auxiliary parameters, the exponentially weighted least-squares algorithm is implemented, and a method of selecting the characteristic polynomials of the sensitivity function filters is proposed. In this method, all the past measurement data are weighted exponentially. A series of simulations for a nonminimum phase plant is presented to illustrate some features of both the parameter estimation and the output response of this adaptive pole placement controller.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.733-739
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• 2011

The linear absolute shrinkage and selection operator(Lasso) method improves the low prediction accuracy and poor interpretation of the ordinary least squares(OLS) estimate through the use of $L_1$ regularization on the regression coefficients. However, the Lasso is not robust to outliers, because the Lasso method minimizes the sum of squared residual errors. Even though the least absolute deviation(LAD) estimator is an alternative to the OLS estimate, it is sensitive to leverage points. We propose a robust Lasso estimator that is not sensitive to outliers, heavy-tailed errors or leverage points.