In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm ineq...In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.展开更多
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 co...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.展开更多
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 shortcom...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.展开更多
We propose a method to improve positioning accuracy while reducing energy consumption in an indoor Wireless Local Area Network(WLAN) environment.First,we intelligently and jointly select the subset of Access Points(AP...We propose a method to improve positioning accuracy while reducing energy consumption in an indoor Wireless Local Area Network(WLAN) environment.First,we intelligently and jointly select the subset of Access Points(APs) used in positioning via Maximum Mutual Information(MMI) criterion.Second,we propose Orthogonal Locality Preserving Projection(OLPP) to reduce the redundancy among selected APs.OLPP effectively extracts the intrinsic location features in situations where previous linear signal projection techniques failed to do,while maintaining computational efficiency.Third,we show that the combination of AP selection and OLPP simultaneously exploits their complementary advantages while avoiding the drawbacks.Experimental results indicate that,compared with the widely used weighted K-nearest neighbor and maximum likelihood estimation method,the proposed method leads to 21.8%(0.49 m) positioning accuracy improvement,while decreasing the computation cost by 65.4%.展开更多
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 ...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.展开更多
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 correlati...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.展开更多
文摘In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.
基金the National Natural Science Foundation of China(No.61701133)the Fundamental Research Funds for the Central Universities(No.D5000210641).
文摘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.
基金supported by the National Natural Science Foundations of China(Nos.11571171and 61473148)
文摘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.
基金the High-Tech Research and Development Program of China，the National Seience Foundation for Young Scientists of China，the China Postdoctoral Science Foundation funded project
文摘We propose a method to improve positioning accuracy while reducing energy consumption in an indoor Wireless Local Area Network(WLAN) environment.First,we intelligently and jointly select the subset of Access Points(APs) used in positioning via Maximum Mutual Information(MMI) criterion.Second,we propose Orthogonal Locality Preserving Projection(OLPP) to reduce the redundancy among selected APs.OLPP effectively extracts the intrinsic location features in situations where previous linear signal projection techniques failed to do,while maintaining computational efficiency.Third,we show that the combination of AP selection and OLPP simultaneously exploits their complementary advantages while avoiding the drawbacks.Experimental results indicate that,compared with the widely used weighted K-nearest neighbor and maximum likelihood estimation method,the proposed method leads to 21.8%(0.49 m) positioning accuracy improvement,while decreasing the computation cost by 65.4%.
文摘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.
基金supported by MOST under Grant MOST 103-2633-E-242-002
文摘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.
