• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.486-486
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• 2000

This paper is concerned with a transfer alignment method for the SDINS(StrapDown Inertial Navigation System) under ship motions. Major error sources of transfer alignment are data transfer time-delay, lever-arm velocity and ship body flexure. Specifically, to reduce alignment errors induced by measurement time-delay effects, the error compensation method through delay state augmentation is suggested. A linearized error model for the velocity and attitude matching transfer alignment system is first derived by linearizing the nonlinear measurement equation with respect to its time delay and augmenting the delay state into the conventional linear state equations. And then it is shown via observability analysis and computer simulations that the delay state can be estimated and compensated during ship motions resulting in considerably less alignment errors.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.40 no.5
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• pp.326-332
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• 2003

This paper deals with a model reduction for linear systems with time varying delayed states. A generalized controllability and observability gramians are defined and obtained by solving linear matrix inequalities. Using the generalized controllability and observability gramians, the balanced state space equation is realized. The reduced model can be obtained by truncating states in the balanced realization and the upper bound of model approximation error is also presented. In order to demonstrate efficacy of the suggested method, a numerical example is performed.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.6
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• pp.145-151
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• 1995

The first-order Taylor series expansion can be evaluated analytically from the formulated symbolic nonlinear dynamic equations. A closed-form linear dynamic euation is derived about a nominal trajectory. The state space representation of the linearized dynamics can be derived easily from the closed-form linear dynamic equations. But manual symbolic expansion of dynamic equations and linearization is tedious, time-consuming and error-prone. So it is desirable to manipulate the procedures using a computer. In this paper, the analytic linearization is performed using the symbolic language MATHEMATICA. Two examples are given to illustrate the approach anbd to compare nonlinear model with linear model.

• Communications for Statistical Applications and Methods
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• v.29 no.6
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• pp.695-708
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• 2022

Recently, several studies have been conducted using state space model. In this study, a dynamic linear model with state space model form is applied to stock data. The monthly returns for 135 Korean stocks are fitted to a dynamic linear model, to obtain an estimate of the time-varying 𝛽-coefficient time-series. The model formula used for the return is a capital asset pricing model formula explained in economics. In particular, the transition equation of the state space model form is appropriately modified to satisfy the assumptions of the error term. k-shape clustering is performed to classify the 135 estimated 𝛽 time-series into several groups. As a result of the clustering, four clusters are obtained, each consisting of approximately 30 stocks. It is found that the distribution is different for each group, so that it is well grouped to have its own characteristics. In addition, a common pattern is observed for each group, which could be interpreted appropriately.

• Imaging Science in Dentistry
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• v.46 no.1
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• pp.1-7
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• 2016

Purpose: This study assessed the accuracy of age estimates produced by a regression equation derived from lower third molar development in a Thai population. Materials and Methods: The first part of this study relied on measurements taken from panoramic radiographs of 614 Thai patients aged from 9 to 20. The stage of lower left and right third molar development was observed in each radiograph and a modified Gat score was assigned. Linear regression on this data produced the following equation: Y=9.309+1.673 mG+0.303S (Y=age; mG=modified Gat score; S=sex). In the second part of this study, the predictive accuracy of this equation was evaluated using data from a second set of panoramic radiographs (539 Thai subjects, 9 to 24 years old). Each subject's age was estimated using the above equation and compared against age calculated from a provided date of birth. Estimated and known age data were analyzed using the Pearson correlation coefficient and descriptive statistics. Results: Ages estimated from lower left and lower right third molar development stage were significantly correlated with the known ages (r=0.818, 0.808, respectively, $P{\leq}0.01$). 50% of age estimates in the second part of the study fell within a range of error of ${\pm}1year$, while 75% fell within a range of error of ${\pm}2years$. The study found that the equation tends to estimate age accurately when individuals are 9 to 20 years of age. Conclusion: The equation can be used for age estimation for Thai populations when the individuals are 9 to 20 years of age.

• The Korean Journal of Applied Statistics
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• v.24 no.1
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• pp.207-216
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• 2011

Bootstrap is a resampling technique to find an estimate of parameters or to evaluate the estimate. This technique has been used in estimating parameters in linear model(LM) and generalized linear model(GLM). In this paper, we explore the possibility of applying Bootstrapping Residuals, Pairs, and an Estimating Equation that are most widely used in LM and GLM to the generalized estimating equation(GEE) algorithm for modelling repeatedly measured regression data sets. We compared three bootstrapping methods with coefficient and standard error estimates of GEE models from one simulated and one real data set. Overall, the estimates obtained from bootstrap methods are quite comparable, except that estimates from bootstrapping pairs are somewhat different from others. We conjecture that the strange behavior of estimates from bootstrapping pairs comes from the inconsistency of those estimates. However, we need a more thorough simulation study to generalize it since those results are coming from only two small data sets.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.1-21
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• 2015

This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.

• Journal of the Optical Society of Korea
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• v.20 no.1
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• pp.199-203
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• 2016

An enzyme-free optical method is proposed for estimating high concentrations of glucose in a glucose-lactose mixture, based on a predictive equation that takes advantage of the reflective optical power observed at two discrete wavelengths. Compared to the conventional absorption spectroscopy method based on Beer's Law, which is mainly valid for concentrations below hundreds of mg/dL, the proposed scheme, which relies on reflection signals, can be applied to measure higher glucose concentrations, of even several g/dL in a glucose-lactose mixture. Two probe wavelengths of 1160 and 1300 nm were selected to provide a linear relationship between the reflective power and pure glucose/lactose concentration, where the relevant linear coefficients were derived to complete the predictive equation. Glucose concentrations from 2 to 7 g/dL in a glucose-lactose mixture were efficiently estimated, using the established predictive equation based on monitored reflective powers. The standard error of prediction was 1.17 g/dL.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.23 no.1
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• pp.56-67
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• 2012

In this thesis, to compensate the sweep nonlinearity occurring in the high resolution radar system using FMICW or FMCW, the method of the estimation of the nonlinearity is proposed. The nonlinear phase component caused by the nonlinear characteristic of the radar system is modelled as a linear combination of the sinusoidal functions consisting of various magnitudes and phases(systematic nonlinear phase error) and a random component(stochastic nonlinear phase error). From two IF signals that are measured respectively independently for two reference point targets lying in different distances which are known, a sparse linear equation is made and solved by least squares method to estimate the nonlinear phase component. The estimated component can be used for predistortion method to compensate the sweep nonlinearity.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.709-720
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• 2011

We obtain special type of differential equations which their solution are random variable with known continuous density function. Stochastic differential equations (SDE) of continuous distributions are determined by the Fokker-Planck theorem. We approximate solution of differential equation with numerical methods such as: the Euler-Maruyama and ten stages explicit Runge-Kutta method, and analysis error prediction statistically. Numerical results, show the performance of the Rung-Kutta method with respect to the Euler-Maruyama. The exponential two parameters, exponential, normal, uniform, beta, gamma and Parreto distributions are considered in this paper.