• Journal of the Korean Data and Information Science Society
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• 제14권4호
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• pp.1007-1012
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• 2003

A recursive procedure for finding the Cholesky root of the inverse of sample covariance matrix, leading to a direct solution for the inverse of a positive definite matrix, is developed using the likelihood equation for the maximum likelihood estimation of the Cholesky root under normality assumptions. An example of the Hilbert matrix is considered for an illustration of the procedure.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.913-921
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• 2010

The derivative influence measure is adapted to the Cholesky decomposition of a covariance matrix. Formulas for the derivative influence of observations on the Cholesky root and the inverse Cholesky root of a sample covariance matrix are derived. It is easy to implement this influence diagnostic method for practical use. A numerical example is given for illustration.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1998년도 하계학술대회 논문집 B
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• pp.443-445
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• 1998

In this paper, an alternate method for state-covariance assignment for SISO(single input single output) linear systems is proposed. This method is based on the inverse solution of the Lyapunov matrix equation and the resulting formulas are similar in structure to the formulas for pole placement. Further, the set of all assignable covariance matrices to a SISO linear system is also characterized.

• 한국멀티미디어학회논문지
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• 제18권7호
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• pp.886-894
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• 2015

In this paper, we conduct sensitivity analysis of parameters used for inverse modeling in order to estimate the PM₁₀ emissions from the 16 areas in East Asia accurately. Parameters used in sensitivity analysis are R, the observational error covariance matrix, and B, a priori (background) error covariance matrix. In previous studies, it was used with the predetermined parameter empirically. Such a method, however, has difficulties in estimating an accurate emissions. Therefore, an automatically determining method for the most suitable value of R and B with an error measurement criteria and posteriori emissions accuracy is required. We determined the parameters through a sensitivity analysis, and improved the accuracy of posteriori emissions estimation. Inverse modeling methods used in the emissions estimation are pseudo inverse, NNLS (Nonnegative Least Square), and BA(Bayesian Approach). Pseudo inverse has a small error, but has negative values of emissions. In order to resolve the problem, NNLS is used. It has a unrealistic emissions, too. The problems are resolved with BA(Bayesian Approach). We showed the effectiveness and the accuracy of three methods through case studies.

• Journal of the Korean Data and Information Science Society
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• 제26권6호
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• pp.1593-1600
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• 2015

A control chart is very useful in monitoring various production process. There are many situations in which the simultaneous control of two or more related quality variables is necessary. We construct bivariate Shewhart control charts based on the trace of the product of the estimated variance-covariance matrix and the inverse of the in-control matrix and investigate the properties of bivariate Shewart control charts with VSI procedure for monitoring covariance matrix in term of ATS (Average time to signal) and ANSW (Average number of switch) and probability of switch, ASI (Average sampling interval). Numerical results show that ATS is smaller than ARL. From examining the properties of switching in changing covariances and variances in ${\Sigma}$, ANSW values show that it does not switch frequently and does not matter to use VSI procedure.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.54.1-54
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• 2001

In this paper, an alternate method for state-covariance assignment for SISO(single input singe output) linear systems is proposed. This method is based on the inverse solution of the Lyapunov matrix equation and the resulting formulas are similar in structure to the formulas for pole placement. Further, the set of all assignable covariance matrices to a SISO linear system is also characterized.

• 대한전자공학회논문지SP
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• 제48권5호
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• pp.96-101
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• 2011

Capon 알고리듬은 지향방향에 대하여 일정한 이득을 유지하면서 배열의 출력을 최소화 시키므로 FM (Fourier method) 알고리듬에 비하여 우수한 분해능 (resolution)을 제공한다. 그러나 Capon 알고리듬의 DoA (Direction of Arrival) 추정 성능은 입사 신호의 SNR (signal-to-noise ratio)이 낮은 경우 급격히 저하되는 문제가 있어 신호원들의 입사각이 유사한 경우 각각의 신호원을 구분하지 못하는 문제가 있다. 본 논문에서는 Capon 알고리듬에서 사용되는 공분산 역행렬의 원소를 제거하는 기법을 이용하여 수신 신호의 SNR이 낮은 환경에서 보다 나은 분해능을 제공하는 개선 방안을 제안한다.

• 지질공학
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• 제6권2호
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• pp.83-93
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• 1996

최대우도법 (maximum likelihood method)을 이용하여 정류상태의 지하수위 자료로 부터 불균질성과 비등방성을 가지는 대수층의 수리상수를 추정하는 반전모델을 개발하였다. 반전모델을 이용하여 추정된 수리상수의 추정오차를 분석하기 위하여 Fisher information matrix 분석법을 도입하고, 수리상수의 추정을 위한 Parameterization의 방법으로 소유동영역화 방법 (zonation method)을 사용하였다. 개발된 반전모델을 이용하여 세가지 경우에 대해서 대구지역의 투수량계수를 추정하였다. 또한, 대구지역의 지하 수함양률을 각 소유동영역의 값으로 추정하였다. 각 추정에서 수반되는 추정오차의 특성을 Fisher information matrix를 구하여 사펴보았다.

• 한국지구과학회지
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• 제23권1호
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• pp.15-29
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• 2002

Bayesian inversion for gravity and resistivity data was performed to investigate the cavity structure appearing as a lava tunnel in Cheju Island, Korea. Dipole-dipole DC resistivity data were proposed for a prior information of gravity data and we applied the geostatistical techniques such as kriging and simulation algorithms to provide a prior model information and covariance matrix in data domain. The inverted resistivity section gave the indicator variogram modeling for each threshold and it provided spatial uncertainty to give a prior PDF by sequential indicator simulations. We also presented a more objective way to make data covariance matrix that reflects the state of the achieved field data by geostatistical technique, cross-validation. Then Gaussian approximation was adopted for the inference of characteristics of the marginal distributions of model parameters and Broyden update for simple calculation of sensitivity matrix and SVD was applied. Generally cavity investigation by geophysical exploration is difficult and success is hard to be achieved. However, this exotic multiple interpretations showed remarkable improvement and stability for interpretation when compared to data-fit alone results, and suggested the possibility of diverse application for Bayesian inversion in geophysical inverse problem.

• 한국전자파학회논문지
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• 제25권3호
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• pp.372-375
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• 2014

재밍 환경에서의 maximum likelihood(ML) 기반의 모노펄스 기법은 공분산 행렬의 역행렬을 이용하여 재머 신호를 억제시킨다. 재머 억제를 위해서는 재머 성분에 대한 충분한 횟수의 스냅샷(snapshot)이 필요하며, 높은 PRF 환경에서는 이것이 가능하지 않아 실시간 추적에 한계가 있다. 또한, JNR(Jammer to Noise Ratio)이 낮은 경우에는 재머의 스냅샷 수가 충분하더라도 정확한 재머 억제가 이루어지지 않아, 표적 방향 추정의 정확도가 감소한다. 본 논문에서는 재밍 환경에서 스냅샷이 적은 경우에도 ML 기반의 모노펄스 성능이 우수한 방법을 제안한다. 제안된 방법은 공분산 행렬의 잡음 부공간을 이용하는 모노펄스 방법으로, 이의 유도 과정을 보이고, 모의실험을 통해 기존의 방법에 비해 성능이 개선된 것을 보인다.