• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.249-258
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• 1993

It is well known that design matrix X for any factorial design can be represented by a product $X = TX_o$ where T is replication matrix and $X_o$ is the corresponding balanced design matrix. Since $X_o$ consists of regular arrangement of 0's and 1's, we can easily find the spectral decomposition of $X_o',X_o$. Also using this we propose an efficient algorithm for computing the orthogonal projection matrix for a balanced factorial design.

• Transactions of the Korean Society of Automotive Engineers
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• v.5 no.1
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• pp.154-161
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• 1997

This paper presents the method to eliminate the constraint reaction in the Lagrange multiplier form equation of motion by using a generalized coordinate driveder from the velocity constraint equation. This method introduces a matrix method by considering the m dimensional space spanned by the rows of the constraint jacobian matrix. The orthogonal vectors defining the constraint manifold are projected to null vectors by the tangential vectors defined on the constraint manifold. Therefore the orthogonal projection matrix is defined by the tangential vectors. For correcting the generalized position coordinate, the optimization problem is formulated. And this correction process is analyzed by the quasi Newton method. Finally this method is verified through 3 dimensional vehicle model.

• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.523-533
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• 2020

This paper suggests three available methods for finding nonnegative estimates of variance components of the random effects in mixed models. The three proposed methods based on the concepts of projections are called projection method I, II, and III. Each method derives sums of squares uniquely based on its own method of projections. All the sums of squares in quadratic forms are calculated as the squared lengths of projections of an observation vector; therefore, there is discussion on the decomposition of the observation vector into the sum of orthogonal projections for establishing a projection model. The projection model in matrix form is constructed by ascertaining the orthogonal projections defined on vector subspaces. Nonnegative estimates are then obtained by the projection model where all the coefficient matrices of the effects in the model are orthogonal to each other. Each method provides its own system of linear equations in a different way for the estimation of variance components; however, the estimates are given as the same regardless of the methods, whichever is used. Hartley's synthesis is used as a method for finding the coefficients of variance components.

• Journal of Electrical Engineering and Technology
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• v.13 no.2
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• pp.868-874
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• 2018

In this paper, we propose a new jammer suppression algorithm that uses orthogonal waveform space projection (OWSP) processing for a multiple input multiple output (MIMO) radar system exposed to a jamming signal. Generally, a conventional suppression algorithm based on adaptive beamforming (ABF) needs a covariance matrix composed of the jammer and noise only. By exploiting the orthogonality of the transmitting waveforms of MIMO, we can construct a transmitting waveform space (TWS). Then, using the OWSP processing, we can build a space orthogonal to the TWS that contains no SOI. By excluding the SOI from the received signal, even in the case that contains the SOI and jamming signal, the proposed algorithm makes it possible to evaluate the covariance matrix for ABF. We applied the proposed OWSP processing to suppressing the jamming signal in bistatic MIMO radar. We verified the performance of the proposed algorithm by comparing the SINR loss to that of the ideal covariance matrix composed of the jammer and noise only. We also derived the computational complexity of the proposed algorithm and compared the estimation of the DOD and DOA using the SOI with those using the generalized likelihood ratio test (GLRT) algorithm.

• Current Optics and Photonics
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• v.5 no.6
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• pp.686-698
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• 2021

A camouflaged encryption scheme based on Hadamard matrix and ghost imaging is proposed. In the process of the encryption, an orthogonal matrix is used as the projection pattern of ghost imaging to improve the definition of the reconstructed images. The ciphertext of the secret image is constrained to the camouflaged image. The key of the camouflaged image is obtained by the method of sparse decomposition by principal component orthogonal basis and the constrained ciphertext. The information of the secret image is hidden into the information of the camouflaged image which can improve the security of the system. In the decryption process, the authorized user needs to extract the key of the secret image according to the obtained random sequences. The real encrypted information can be obtained. Otherwise, the obtained image is the camouflaged image. In order to verify the feasibility, security and robustness of the encryption system, binary images and gray-scale images are selected for simulation and experiment. The results show that the proposed encryption system simplifies the calculation process, and also improves the definition of the reconstructed images and the security of the encryption system.

• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.423-429
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• 2014

This paper discusses a method for getting Type I sums of squares by projections under a two-way fixed-effects model when variances of errors are not equal. The method of weighted least squares is used to estimate the parameters of the assumed model. The model is fitted to the data in a sequential manner by using the model comparison technique. The vector space generated by the model matrix can be composed of orthogonal vector subspaces spanned by submatrices consisting of column vectors related to the parameters. It is discussed how to get the Type I sums of squares by using the projections into the orthogonal vector subspaces.

• Journal of the Korea Society of Computer and Information
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• v.27 no.5
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• pp.77-84
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• 2022

In this paper, we propose a novel unsupervised feature selection method. Conventional unsupervised feature selection method defines virtual label and uses a regression analysis that projects the given data to this label. However, since virtual labels are generated from data, they can be formed similarly in the space. Thus, in the conventional method, the features can be selected in only restricted space. To solve this problem, in this paper, features are selected using orthogonal projections and low-rank approximations. To solve this problem, in this paper, a virtual label is projected to orthogonal space and the given data set is also projected to this space. Through this process, effective features can be selected. In addition, projection matrix is restricted low-rank to allow more effective features to be selected in low-dimensional space. To achieve these objectives, a cost function is designed and an efficient optimization method is proposed. Experimental results for six data sets demonstrate that the proposed method outperforms existing conventional unsupervised feature selection methods in most cases.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.14 no.5
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• pp.506-512
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• 2003

An output multiplexer of manifold type is widely used in a recent satellite transponder f3r its mass and volume reduction. For correct operation, the filter of such a multiplexer must be singly terminated. In this paper, a simple synthesis method of a 6-pole dual-mode singly terminated filter is described. From the transfer function of the filter, network parameters such as in/output terminations and coupling matrix are obtained with the aid of orthogonal projection and plane rotation. The rotation order, pivot, and rotation angle of the plane rotation process are given for easy filter synthesis. Two different-structure filters are taken into consideration and the network parameters of each filter have been obtained from the same transfer function. The method described in this paper can be applied to the other degree singly terminated filter.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.4A
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• pp.399-406
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• 2011

Adaptive beamformers, which utilize a priori information on the arrival angle of the desired signal. suppress interferences while maximizing their gains in the desired signal direction. However, if there exist errors in the direction information, they can suffer from severe performance degradation since the desired signal is treated as an interference. A robust adaptive beamforming method is presented which exploits the signal-blocking structure of the Duvall beamformer. The proposed method finds an interference signal space directly from correlations of received signals and then obtains a weight vector such that it is orthogonal to the space. Applying the weight vector to two sub arrays which consist of one less sensors than the original uniform lineal array (ULA), the beamformer efficiently estimates the arrival angle of the desired signal. Its computational complexity is lower than existing methods, which require matrix inversion or eigendecomposition.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.1-6
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• 1992

A principle of "orthogonalization" is proposed as an extended notion of hybrid (force and position) control for robot manipulators under geometric endpoint constraints. The principle realizes the hybrid control in a strict sense by letting position and velocity feedback signals be orthogonal in joint space to the contact force vector whose components are exerted at corresponding joints. This orthogonalization is executed via a projection matrix computed in real-time from a gradient of the equation of the surface in joint coordinates and hence both projected position and velocity feedback signals become perpendicular to the force vector that is normal to the surface at the contact point in joint space. To show the important role of the principle in control of robot manipulators, three basic problems are analyzed, the first is a hybrid trajectory tracking problem by means of a "modified hybrid computed torque method", the second is a model-based adaptive control problem for robot manipulators under geometric endpoint constraints, and the third is an iterative learning control problem. It is shown that the passivity of residual error dynamics of robots follows from the orthogonalization principle and it plays a crucial role in convergence properties of both positional and force error signals.force error signals.