DOA Estimation Method Using Sparse Representation with Orthogonal Projection

In order to reduce the effect of noises on DOA estimation,this paper proposes a direc-tion-of-arrival(DOA)estimation method using sparse representation with orthogonal projection(OPSR).The OPSR method obtains a new covariance matrix by projecting the covariance matrix of the array data to the signal subspace,leading to the elimination of the noise subspace.After-wards,based on the new covariance matrix after the orthogonal projection,a new sparse representa-tion model is established and employed for DOA estimation.Simulation results demonstrate that compared to other methods,the OPSR method has higher angle resolution and better DOA estima-tion performance in the cases of few snapshots and low SNRs.

Orthogonal projection based subspace identification against colored noise

In this paper, a bias-eliminated subspace identification method is proposed for industrial applications subject to colored noise. Based on double orthogonal projections, an identification algorithm is developed to eliminate the influence of colored noise for consistent estimation of the extended observability matrix of the plant state-space model. A shift-invariant approach is then given to retrieve the system matrices from the estimated extended observability matrix. The persistent excitation condition for consistent estimation of the extended observability matrix is analyzed. Moreover, a numerical algorithm is given to compute the estimation error of the estimated extended observability matrix. Two illustrative examples are given to demonstrate the effectiveness and merit of the proposed method.

Development of a Circuit-theory Based Transmission Cost Allocation Method by Orthogonal Projection and Equal-sharing Principle

This paper presents a new solution to the problem of transmission cost allocation to its users.The proposed technique utilizes modified Z-bus theory,equivalent current injection and impedance of the generators and loads,and is developed by the equal-sharing as well as the orthogonal projection principle.The procedure is performed in three steps.First,the modified Z-bus theory is used to calculate the contribution of the users into the network bus voltages as well as the branch currents.Then,the equal sharing principle is confirmed by the game theory solutions and is subsequently applied to identify the users’contributions into the branch power flows.After that,the orthogonal projections of the contributions are calculated and the concept of effective contributions is suggested.The proposed methodology provides the percentage shares of the users on the network complex variables,which help to better assess the contributions.A 2-bus and the IEEE 30-bus test system are used to validate the proposed technique.Finally,the proposed methodology is applied to the polish 2383-bus system to emphasize its applicability to large practical systems.

Fault Diagnosis Model Based on Feature Compression with Orthogonal Locality Preserving Projection

Based on feature compression with orthogonal locality preserving projection（OLPP）,a novel fault diagnosis model is proposed in this paper to achieve automation and high-precision of fault diagnosis of rotating machinery.With this model,the original vibration signals of training and test samples are first decomposed through the empirical mode decomposition（EMD）,and Shannon entropy is constructed to achieve high-dimensional eigenvectors.In order to replace the traditional feature extraction way which does the selection manually,OLPP is introduced to automatically compress the high-dimensional eigenvectors of training and test samples into the low-dimensional eigenvectors which have better discrimination.After that,the low-dimensional eigenvectors of training samples are input into Morlet wavelet support vector machine（MWSVM） and a trained MWSVM is obtained.Finally,the low-dimensional eigenvectors of test samples are input into the trained MWSVM to carry out fault diagnosis.To evaluate our proposed model,the experiment of fault diagnosis of deep groove ball bearings is made,and the experiment results indicate that the recognition accuracy rate of the proposed diagnosis model for outer race crack、inner race crack and ball crack is more than 90%.Compared to the existing approaches,the proposed diagnosis model combines the strengths of EMD in fault feature extraction,OLPP in feature compression and MWSVM in pattern recognition,and realizes the automation and high-precision of fault diagnosis.

AN IMPLICIT SOLUTION OF BI-PENALTY APPROXIMATION WITH ORTHOGONALITY PROJECTION FOR THE NUMERICAL SIMULATION OF BINGHAM FLUID FLOW

An implicit algorithm of Bi-penalty approximation with orthogonality projection for the numerical simulation of Bingham fluid flow problems is proposed in this paper. A Newton fluid flow with two kinds of artificial viscosity subjected to the inequality constraint is introduced to approximate the Bingham fluid flow. This approach can effectively simulate the Bingham fluid flow with floating rigid cores or fixing rigid cores.

Adaptive detection based on orthogonal partition of the primary and secondary data

A novel adaptive detection scheme both for point-like and distributed targets in the presence of Gaussian disturbance in the partial y homogeneous environment （PHE） is proposed. The novel detection scheme is based on the orthogonal projection technique. Both the case of known covariance matrix structure and the case of unknown covariance matrix structure are con-sidered. For the former case, the closed-form statistical pro-perty of the novel detectors is derived. When the covariance matrix is unknown, the corresponding detectors have higher probabilities of detection （PDs） than their natural competitors. Moreover, they ensure constant false alarm rate （CFAR） property.

Arnoldi Projection Fractional Tikhonov for Large Scale Ill-Posed Problems

It is well known that Tikhonov regularization in standard form may determine approximate solutions that are too smooth for ill-posed problems,so fractional Tikhonov methods have been introduced to remedy this shortcoming.And Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented by determining apartial Arnoldi decomposition of the given matrix.In this paper,we propose a new method to compute an approximate solution of large scale linear discrete ill-posed problems which applies projection fractional Tikhonov regularization in Krylov subspace via Arnoldi process.The projection fractional Tikhonov regularization combines the fractional matrices and orthogonal projection operators.A suitable value of the regularization parameter is determined by the discrepancy principle.Numerical examples with application to image restoration are carried out to examine that the performance of the method.

A REPLACEMENT SCHEME ON THE CONSTRUCTION OF ORTHOGONAL ARRAYS

A method of constructing orthogonal arrays is presented by Zhang, Lu and Pang in 1999.In this paper,the method is developed by introducing a replacement scheme on the construction of orthogonal arrays ,and some new mixed-level orthogonal arrays of run size 36 are constructed.

New direction of arrival estimation method for wideband coherent signals

To estimate the direction-of-arrival （DOA） of wideband coherent signals, a new method by modifying the orthogonality of the projected suhspaces method is proposed. And it can deal with randomly position perturbed arrays by using the Toeplitz method. This method needn＇t the primary information of DOA for focusing matrix and the sector dividing of interpolated method, which improving the precision of estimation and reducing the computational complexity. Simulations illustrate the effectiveness of this method.

HOLDITCH THEOREM FOR THE CLOSED SPACE CURVES IN LORENTZIAN 3-SPACE

In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking into account the Lorentzian matrix multiplication for the closed space curves by using their othogonal projections onto the Euclidean plane in the fixed Lorentzian space. Moreover, we generalize this Holditch Theorem for noncollinear three fixed points of the moving Lorentzian space and any other fixed point on the plane which is determined by these three fixed points.

Optimum Presentation Featuring the 3D-View of a Composite Solid Model

A 3D-view is helpful to instantly grasp what is presented in a drawing. There exist a variety of ways to present the same part with 3D-views. To facilitate the choice of an optimum one among them, the work divides composite solid models into three categories, so as to convey the originality of design concisely and accurately by using the least ＂ engineering language＂.

Evaluations of Novel Waveform Coding Signals Based on Finite Projective Plane

The most popular and representative classic waveform codes are referred to as orthogonal,bi-orthogonal,simplex,and etc,but the choice of waveform codes is essentially identical in error performance and cross correlation characteristic.Though bi-orthogonal coding requires half the bandwidth of the others,such coding scheme is attractive only when large bandwidth is available.In this paper,a novel finite projective plane（FPP） based waveform coding scheme is proposed,which is with similar error performance and cross correlation.Nevertheless,the bandwidth requirement will grow in a quadratic way,but not in an exponential way with the values of message bit numbers（k）.The proposed scheme takes obvious advantages over the bi-orthogonal scheme when k ≥ 6.

A new result on recovery sparse signals using orthogonal matching pursuit

Orthogonal matching pursuit(OMP)algorithm is a classical greedy algorithm widely used in compressed sensing.In this paper,by exploiting the Wielandt inequality and some properties of orthogonal projection matrix,we obtained a new number of iterations required for the OMP algorithm to perform exact recovery of sparse signals,which improves significantly upon the latest results as we know.

N4SID and MOESP Algorithms to Highlight the Ill-conditioning into Subspace Identification

In this paper,an analysis for ill conditioning problem in subspace identifcation method is provided.The subspace identifcation technique presents a satisfactory robustness in the parameter estimation of process model which performs control.As a frst step,the main geometric and mathematical tools used in subspace identifcation are briefly presented.In the second step,the problem of analyzing ill-conditioning matrices in the subspace identifcation method is considered.To illustrate this situation,a simulation study of an example is introduced to show the ill-conditioning in subspace identifcation.Algorithms numerical subspace state space system identifcation(N4SID)and multivariable output error state space model identifcation(MOESP)are considered to study,the parameters estimation while using the induction motor model,in simulation(Matlab environment).Finally,we show the inadequacy of the oblique projection and validate the efectiveness of the orthogonal projection approach which is needed in ill-conditioning;a real application dealing with induction motor parameters estimation has been experimented.The obtained results proved that the algorithm based on orthogonal projection MOESP,overcomes the situation of ill-conditioning in the Hankel s block,and thereby improving the estimation of parameters.

On the Index of Fredholm Pairs of Idempotents

Using the technique of block-operators, in this note, we prove that if P and Q are idempotents and （P - Q）^2n＋1 is in the trace class, then （P - Q）^2m＋1 is also in the trace class and tr（P - Q）^2m＋1 = dim（k（P） ∩ k（Q）^⊥） -dim（k（P）^⊥ N k（Q））, for all m ≥ n. Moreover, we prove that dim（k（P）∩ k（Q）^⊥） = dim（k（P）^⊥ ∩k（Q）） if and only if there exists a unitary U such that UP = QU and PU = UQ, where k（T） denotes the range of T. Keywords Fredholm, orthogonal projection, positive operator

The Bifurcation of the Equatorial Periodic Orbit of the Planar Polynomial Vector Fields

In this paper,we have obtained the necessary and sufficient condition for the set of points at infinity on the plane R^2 to be a periodic orbit which is called an equatorial periodic orbit of a planar vector field X(x),and the formulae about the multiplicity of the equatorial periodic orbit of X(x).We have also proved that the main result of [9] is erroneous with regard to the formlae.

Conjugate Decomposition and Its Applications

The conjugate decomposition(CD),which was given for symmetric and positive definite matrices implicitly based on the conjugate gradient method,is gen-eralized to every m×n matrix.The conjugate decomposition keeps some S VD prop-erties,but loses uniqueness and part of orthogonal projection property.From the com-putational point of view,the conjugate decomposition is much cheaper than the SVD.To illustrate the feasibility of the CD,some application examples are given.Finally,the application of the conjugate decomposition in frequency estimate is given with comparison of the SVD and FFT.The numerical results are promising.

On Scientific Data and Image Compression Based on Adaptive Higher-Order FEM

We present a novel compression algorithm for 2D scientific data and images based on exponentially-convergent adaptive higher-order finite element methods(FEM).So far,FEM has been used mainly for the solution of partial differential equations(PDE),but we show that it can be applied to data and image compression easily.The adaptive compression algorithm is trivial compared to adaptive FEM algorithms for PDE since the error estimation step is not present.The method attains extremely high compression rates and is able to compress a data set or an image with any prescribed error tolerance.Compressed data and images are stored in the standard FEM format,which makes it possible to analyze them using standard PDE visualization software.Numerical examples are shown.The method is presented in such a way that it can be understood by readers who may not be experts of the finite element method.

A novel suboptimal algorithm for state estimation of Markov jump linear systems

This paper is concerned with state estimation problem for Markov jump linear systems where the disturbances involved in the systems equations and measurement equations are assumed to be Gaussian noise sequences.Based on two properties of conditional expectation,orthogonal projective theorem is applied to the state estimation problem of the considered systems so that a novel suboptimal algorithm is obtained.The novelty of the algorithm lies in using orthogonal projective theorem instead of Kalman filters to estimate the state.A numerical comparison of the algorithm with the interacting multiple model algorithm is given to illustrate the effectiveness of the proposed algorithm.