• Journal of the Korean Data and Information Science Society
• /
• v.14 no.4
• /
• pp.1007-1012
• /
• 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
• /
• v.28 no.3_4
• /
• pp.913-921
• /
• 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.

• Proceedings of the KIEE Conference
• /
• 1998.07b
• /
• pp.443-445
• /
• 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.

• Journal of Korea Multimedia Society
• /
• v.18 no.7
• /
• pp.886-894
• /
• 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
• /
• v.26 no.6
• /
• pp.1593-1600
• /
• 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
• /
• 2001.10a
• /
• pp.54.1-54
• /
• 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.

• Journal of the Institute of Electronics Engineers of Korea SP
• /
• v.48 no.5
• /
• pp.96-101
• /
• 2011

It is well known that the Capon algorithm offers better resolution compared to that of the FM (Fourier method) algorithm by minimizing the total output power while maintaining a constant gain in the look direction. Unfortunately, the DoA (Direction of Arrival) estimation performance of the Capon algorithm is drastically degraded when the SNR of received signal is low and thus, it cannot distinguish among signal sources which have similar incidence angles. In this paper, we propose a novel scheme enhancing the resolution of the Capon algorithm by ing all rows except the first row of an inverse covariance matrix.

• The Journal of Engineering Geology
• /
• v.6 no.2
• /
• pp.83-93
• /
• 1996

A method is proposed to estimate aquifer parameters in a heterogeneous and anisotropic aquifer under steady-state groundwater flow conditions on the basis of maximum likelihood concept. Zonation method is adopted for parameterization, and estimation errors are analyzed by examining the estimation error covariance matrix in the eigenspace. This study demonstrates the ability of the proposed model to estimate parameters and helps to understand the characteristics of the inverse problem. This study also explores various features of the inverse methodology by applying it to a set of field data of the Taegu area. In the field example, transmissivities were estimated under three different zonation patterns. Recharge rates in the Taegu area were also estimated using MODINV which is an inverse model compatible with MODFLOW.The estimation results indicate that anisotropy of aquifer parameters should be considered for the crystalline rock aquifer which is the dominant aquifer system in Korea.

• Journal of the Korean earth science society
• /
• v.23 no.1
• /
• pp.15-29
• /
• 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.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.25 no.3
• /
• pp.372-375
• /
• 2014

A monopulse based on maximum likelihood(ML) in jamming scenario can suppress jamming signal using an inverse matrix of a covariance matrix. In order to achieve adequate suppression of jamming signal, the sufficient number of snapshots is required. However, this is not possible in high PRF scenario, which hinders a real-time tracking. Moreover, even with the large number of snapshots, the estimation accuracy of the target direction is decreased in low JNR(Jammer to Noise Ratio) due to insufficient jammer suppression. In this paper, we propose a monopulse algorithm that doesn't degrade performance significantly with a small number of snapshots and in low JNR. We show its derivation that exploits noise-jammer subspace of a covariance matrix, along with its performance through simulation.