• 한국측량학회지
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• 제36권6호
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• pp.621-628
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• 2018

GPS (Global Positioning System)를 이용하여 위치를 결정하기 위해서는 4개 이상의 가시위성이 있어야 한다. 하지만 도심지역과 같은 환경에서는 이러한 조건을 만족하기 어려운 경우도 있다. 특히, 가시위성이 3개뿐인 경우 외부로부터 위치결정에 필요한 시계오차정보를 활용하는 측위기법이 대안으로 사용되기도 한다. 본 연구에서는 먼저 수신기 시계오차특성을 분석한 후 시계오차의 보간에 적합한 방법으로 LSC (Least-Squares Collocation)을 제안하였다. 실험을 위해 국내 상시관측소와 상시관측소 근처에 설치된 수신기로부터 수신된 GPS 데이터를 이용하였다. DGPS (Differential GPS)기법을 통해 먼저 시계오차를 계산했으며 효율적인 보간을 위해 구간을 나눈 후 보간하는 방법을 적용하였다. 시계오차의 계산이 불가능한 epoch에 대해 LSC 보간법을 적용함으로써 시계오차를 계산하였다. 실험결과를 분석하기 위해 원래 데이터로부터 계산된 시계오차와 보간된 시계오차와의 차이인 잔차를 계산하였다. 계산결과 잔차의 평균은 0.24m 그리고 표준편차는 0.49m로 충분한 정확도의 확보가 가능한 것으로 판단된다.

• 호남수학학술지
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• 제37권3호
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• pp.299-315
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• 2015

In this paper, we study the first-order system least-squares (FOSLS) spectral method for parabolic partial differential equations. There were lots of least-squares approaches to solve elliptic partial differential equations using finite element approximation. Also, some approaches using spectral methods have been studied in recent. In order to solve the parabolic partial differential equations in parallel, we consider a parallel numerical method based on a hybrid method of the frequency-domain method and first-order system least-squares method. First, we transform the parabolic problem in the space-time domain to the elliptic problems in the space-frequency domain. Second, we solve each elliptic problem in parallel for some frequencies using the first-order system least-squares method. And then we take the discrete inverse Fourier transforms in order to obtain the approximate solution in the space-time domain. We will introduce such a hybrid method and then present a numerical experiment.

• 한국측량학회지
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• 제23권4호
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• pp.385-392
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• 2005

본 논문에서는 중력데이터를 사용하여 중력지오이드모델을 개발하고, GPS/Leveling데이터를 사용하여 개선한 KGEOID05모델을 계산하였으며, 그 정밀도를 분석하였다. KGEOID05는 중력지오이드모델에 보정항을 더하여 계산하였으며, 보정항은 GPS/Levelling에 의하여 구한 지오이드고와 중력지오이드고의 차이를 사용하여 모델링 하였다. 모델링을 위한 통계학적 함수는 Markov 2차공분산 함수에 기초한 least squares collocation방법을 사용하였다. 총 373점의 GPS관측점을 보정항 모델링에 사용하였으며, 정밀도분석결과 KGEOID05의 정밀도는 11cm로 계산되었다. $2{\sim}3$점의 수준점에 대한 GPS관측데이터를 사용하여 지역적으로 KGEOID05모델에 대한 fitting을 실시할 경우에 GPS관측에 의한 $2{\sim}3cm$ 정밀도의 표고측정이 가능하다.

• 대한수학회지
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• 제50권6호
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• pp.1291-1310
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• 2013

This paper develops least-squares pseudo-spectral collocation methods for elliptic boundary value problems having interface conditions given by discontinuous coefficients and singular source term. From the discontinuities of coefficients and singular source term, we derive the interface conditions and then we impose such interface conditions to solution spaces. We define two types of discrete least-squares functionals summing discontinuous spectral norms of the residual equations over two sub-domains. In this paper, we show that the homogeneous least-squares functionals are equivalent to appropriate product norms and the proposed methods have the spectral convergence. Finally, we present some numerical results to provide evidences for analysis and spectral convergence of the proposed methods.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2007년도 Proceedings of ISRS 2007
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• pp.386-389
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• 2007

Currently, fast and accurate long baseline positioning in kinematic mode is a challenging topic, but positional accuracy can be improved with the help of the network-derived external ionospheric corrections. To provide not only ionospheric corrections, but also their variances, satellite-by-satellite interpolation for the ionospheric delays is performed using the least-squares collocation (LSC) method. Satellite-by-satellite interpolation has the advantage in that the vertical projection used in single-layer ionospheric model is not required. Also, more reliable user positioning and the corresponding accuracy assessment can be obtained by providing not only external ionospheric corrections but also their variances. The rover positioning with and without the external ionospheric delays in both rapid-static and kinematic mode was performed and analyzed. The numerical results indicate that the improvement in the positioning quality is achieved using the proposed method. With the TAMDEF network in Antarctica, 18 % improvement in mean time-to-fix in kinematic mode was achieved.

• 한국해안해양공학회지
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• 제6권4호
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• pp.353-363
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• 1994

유량함수 비선형 파랑이론에 입각한 수치모형들의 공학응용성에 대한 판단의 기준을 정하기 위해 수정된 Dean 표(Chaplin, 1980)의 입력제원을 사용하여 collocation 모형과 최소자승법 모형의 결과를 직접 비교하였다. 파장이 긴 천해파와 쇄파에 가까운 파랑을 제외한 모든 경우에 두 모형은 정밀하고 거의 동일한 결과를 보였다. 전반적인 비교를 통해 최소자승법 모형이 공학응용에 적합한 것으로 판단된다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.501-506
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• 2007

A generalized finite difference method for solving solid mechanics problems such as elasticity and crack problems is presented. The method is constructed in framework of Taylor polynomial based on the Moving Least Squares method and collocation scheme based on the diffuse derivative approximation. The governing equations are discretized into the difference equations and the nodal solutions are obtained by solving the system of equations. Numerical examples successfully demonstrate the robustness and efficiency of the proposed method.

• Structural Engineering and Mechanics
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• 제66권5호
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• pp.557-568
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• 2018

An investigation is made in the present work on the post-buckling and geometrically nonlinear behaviors of moderately thick perfect and imperfect rectangular plates made-up of functionally graded materials. Spectral collocation approach based on Legendre basis functions is developed to analyze the functionally graded plates while they are subjected to end-shortening strain. The material properties in this study are varied through the thickness according to the simple power law distribution. The fundamental equations for moderately thick rectangular plates are derived using first order shear deformation plate theory and taking into account both geometric nonlinearity and initial geometric imperfections. In the current study, the domain of interest is discretized with Legendre-Gauss-Lobatto nodes. The equilibrium equations will be obtained by discretizing the Von-Karman's equilibrium equations and also boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Due to effect of geometric nonlinearity, the final set of equilibrium equations is nonlinear and therefore the quadratic extrapolation technique is used to solve them. Since the number of equations in this approach will always be more than the number of unknown coefficients, the least squares technique will be used. Finally, the effects of boundary conditions, initial geometric imperfection and material properties are investigated and discussed to demonstrate the validity and capability of proposed method.

• Interaction and multiscale mechanics
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• 제2권4호
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• pp.333-352
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• 2009

We introduce a radial basis collocation method to solve axially moving beam problems which involve $2^{nd}$ order differentiation in time and $4^{th}$ order differentiation in space. The discrete equation is constructed based on the strong form of the governing equation. The employment of multiquadrics radial basis function allows approximation of higher order derivatives in the strong form. Unlike the other approximation functions used in the meshfree methods, such as the moving least-squares approximation, $4^{th}$ order derivative of multiquadrics radial basis function is straightforward. We also show that the standard weighted boundary collocation approach for imposition of boundary conditions in static problems yields significant errors in the transient problems. This inaccuracy in dynamic problems can be corrected by a statically condensed semi-discrete equation resulting from an exact imposition of boundary conditions. The effectiveness of this approach is examined in the numerical examples.

• Korean Journal of Geomatics
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• 제5권1호
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• pp.21-26
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• 2005

According to revisions of survey law taking effect on January 1, 2003, the Korean geodetic datum has been changed from a local geodetic to a world geodetic system. In this study, the datum transformation parameters especially for the maritime geographical data are determined. From database constructed through MGIS, a total of 492 coordinate pairs were selected and used in the parameter determination after outlier testing. Based on the parameter estimation, the Molodensky model is selected for datum transformation. For higher accuracy, Application of network optimization and a least squares collocation with Gaussian model has resulted in the accuracy better than 15 cm in coordinate transformation.