• Journal of Institute of Control, Robotics and Systems
• /
• v.16 no.8
• /
• pp.766-770
• /
• 2010

In this paper, we present an effective covariance tracking algorithm based on adaptive size changing of tracking window. Recent researches have advocated the use of a covariance matrix of object image features for tracking objects instead of the conventional histogram object models used in popular algorithms. But, according to the general covariance tracking algorithm, it can not deal with the scale changes of the moving objects. The scale of the moving object often changes in various tracking environment and the tracking window(or object kernel) has to be adapted accordingly. In addition, the covariance matrix of moving objects should be adaptively updated considering of the tracking window size. We provide a solution to this problem by segmenting the moving object from the background pixels of the tracking window. Therefore, we can improve the tracking performance of the covariance tracking method. Our several simulations prove the effectiveness of the proposed method.

• 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.

• Atmosphere
• /
• v.23 no.1
• /
• pp.33-37
• /
• 2013

In meteorology, exploitation of Kalman filter as a data assimilation system is virtually impossible due to simultaneous requirements of adjoint model and large computer resource. The other substitute of utilizing ensemble Kalman filter is only affordable by compensating an enormous usage of computing resource. Furthermore, the latter employs ensemble integration sets for evolving the background error covariance matrix by compensating the dynamical feature of the temporal evolution of weather conditions. We propose a new implementation method that works without the adjoint model by utilizing the explicit expression of the background error covariance matrix in backward evolution. It will also break a barrier in the evolution of the covariance matrix. The method may be applied with a slight modification to the real time assimilation or the retrospective analysis.

• Journal of the Korean Data and Information Science Society
• /
• v.23 no.4
• /
• pp.807-814
• /
• 2012

We know that the exponentially weighted moving average (EWMA) control charts are sensitive to detecting relatively small shifts. Multivariate EWMA control charts are considered for monitoring of variance-covariance matrix when the distribution of process variables is multivariate normal. The performances of the proposed EWMA control charts are evaluated in term of average run length (ARL). The performance is investigated in three types of shifts in the variance-covariance matrix, that is, the variances, covariances, and variances and covariances are changed respectively. Numerical results show that all multivariate EWMA control charts considered in this paper are effective in detecting several kinds of shifts in the variance-covariance matrix.

• Journal of the Korean Data and Information Science Society
• /
• v.28 no.4
• /
• pp.937-945
• /
• 2017

The purpose of using a control chart is to detect any change that occurs in the process. When control charts are used to monitor processes, we want to identify this changes as quickly as possible. Many problems in quality control involve a vector of observations of several characteristics rather than a single characteristic. Multivariate CUSUM or EWMA charts have been developed to address the problem of monitoring covariance matrix or the joint monitoring of mean vector and covariance matrix. However, control charts tend to work poorly when we use the highly correlatted variables. In order to overcome it, Hawkins (1991) proposed the use of regression adjustment variables. In this paper, to monitor covariance matrix, we investigate the performance of MEWMA-type control charts with and without the use of regression adjusted variables.

• Communications for Statistical Applications and Methods
• /
• v.27 no.2
• /
• pp.201-210
• /
• 2020

Baseline-category logit random effects models have been used to analyze longitudinal nominal data. The models account for subject-specific variations using random effects. However, the random effects covariance matrix in the models needs to explain subject-specific variations as well as serial correlations for nominal outcomes. In order to satisfy them, the covariance matrix must be heterogeneous and high-dimensional. However, it is difficult to estimate the random effects covariance matrix due to its high dimensionality and positive-definiteness. In this paper, we exploit the modified Cholesky decomposition to estimate the high-dimensional heterogeneous random effects covariance matrix. Bayesian methodology is proposed to estimate parameters of interest. The proposed methods are illustrated with real data from the McKinney Homeless Research Project.

• Journal of Broadcast Engineering
• /
• v.21 no.1
• /
• pp.60-65
• /
• 2016

This paper introduces the non-local means (NLM) algorithm for image denoising, and also introduces an improved algorithm which is based on the principal component analysis (PCA). To do the PCA, a covariance matrix of a given image should be evaluated first. If we let the size of neighborhood patches of the NLM S × S², and let the number of pixels Q, a matrix multiplication of the size S² × Q is required to compute a covariance matrix. According to the characteristic of images, such computation is inefficient. Therefore, this paper proposes an efficient method to compute the covariance matrix by sampling the pixels. After sampling, the covariance matrix can be computed with matrices of the size S² × floor (Width/l) × (Height/l).

• Journal of Korean Society for Quality Management
• /
• v.29 no.1
• /
• pp.1-10
• /
• 2001

We consider the problem of detecting special variations in multivariate $T^2$-control chart when two or more multivariate outliers are present. Since a multivariate outlier may reflect slippage in mean, variance, or correlation, it can distort the sample mean vector and sample covariance matrix. Damaged sample mean vector and sample covariance matrix have difficulty in examining special variations clearly, An alternative to detection outliers or special variations is to use robust estimators of mean vector and covariance matrix that are less sensitive to extreme observations than are the standard estimators $\bar{x}$ and $\textbf{S}$. We applied popular minimum volume ellipsoid(MVE) and minimum covariance determinant(MCD) method to estimate mean vector and covariance matrix and compared its results with standard $T^2$-control chart using simulated multivariate data with outliers. We found that the modified $T^2$-control chart based on the above robust methods were more effective in detecting special variations clearly than the standard $T^2$-control chart.

• Communications for Statistical Applications and Methods
• /
• v.7 no.1
• /
• pp.285-290
• /
• 2000

We noted a property of a stationary distribution on the matrix C, which is the covariance matrix of order statistics of standard normal distribution That is the sup norm of th powers of C is ee' divided by its dimension. The matrix C can be taken as a transition probability matrix in an acyclic Markov chain.

• Journal of the Korea Society of Computer and Information
• /
• v.15 no.5
• /
• pp.13-21
• /
• 2010

The Optimal results of Kalman Filtering on the Inverted Pendulum System requires an effective factor such as the noise covariance matrix Q, the measurement noise covariance matrix R and the initial error covariance matrix $P_0$. We present a special case where the optimality of the filter is not destroyed and not sensitive to scaling of these covariance matrix because these factors are unknown or are known only approximately in the practical situation. Moreover, the error covariance matrices issued by this method predict errors in the state estimate consistent with the scaled covariance matrices and not the issued state estimates. Various results using the scalar gain $\delta$ are derived to described the relations among the three covariance matrices, Kalman Gain and the error covariance matrices. This paper is described as follows: Section III a brief overview of the Inverted Pendulum system. Section IV deals with the mathematical dynamic model of the system used for the computer simulation. Section V presents a various simulation results using the scalar gain.