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Generalized cubature quadrature Kalman filters:derivations and extensions

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Journal of Systems Engineering and Electronics 2017年第3期28卷 556-562页

作者： Hongwei Wang Wei Zhang Junyi Zuo Heping Wang School of Aeronautics Northwestern Polytechnical UniversityXi’an 710072China Experimental Aircraft Design and Flight Testing Laboratory of Shaanxi Xi’an 710072China School of Electrical and Electronic Engineering Nanyang Technological UniversitySingapore 639798Singapore

A new Gaussian approximation nonlinear filter called generalized cubature quadrature Kalman filter (GCQKF) is introduced for nonlinear dynamic systems. Based on standard GCQKF, two extensions are developed, namely square root generalized cubature quadrature Kalman filter (SR-GCQKF) and iterated generalized cubature quadrature Kalman filter (I-GCQKF). In SR-GCQKF, the qr decomposition is exploited to alter the Cholesky decomposition and both predicted and filtered error covariances have been propagated in square root format to make sure the numerical stability. In I-GCQKF, the measurement update step is executed iteratively to make full use of the latest measurement and a new terminal criterion is adopted to guarantee the increase of likelihood. Detailed numerical experiments demonstrate the superior performance on both tracking stability and estimation accuracy of I-GCQKF and SR-GCQKF compared with GCQKF.

关键词： cubature rule quadrature rule Kalman filter iterated method qr decomposition nonlinear estimation target tracking

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The structured total least squares algorithm research for passive location based on angle information

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Science in China(Series F) 2009年第6期52卷 1043-1054页

作者： WANG Ding ZHANG Li WU Ying Institute of Information Engineering PLA Information Engineering University Zhengzhou 450002 China

Based on the constrained total least squares （CTLS） passive location algorithm with bearing-only measurements, in this paper, the same passive location problem is transformed into the structured total least squares （STLS） *** solution of the STLS problem for passive location can be obtained using the inverse iteration *** also expatiates that both the STLS algorithm and the CTLS algorithm have the same location mean squares error under certain ***, the article presents a kind of location and tracking algorithm for moving target by combining STLS location algorithm with Kalman filter （KF）.The efficiency and superiority of the proposed algorithms can be confirmed by computer simulation results.

关键词： passive location angle information least squares total least squares constrained total least squares structured total least squares Kalman filter singular value decomposition qr decomposition

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KERNEL NEIGHBORHOOD PRESERVING EMBEDDING FOR CLASSIFICATION

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Journal of Electronics(China) 2009年第3期26卷 374-379页

作者： Tao Xiaoyan Ji Hongbing Men Jian School of Electronic Engineering Xidian University Xi＇an 710071 China The Telecommunication Engineering Institute Air Force Engineering University Xi＇an 710077 China

The Neighborhood Preserving Embedding(NPE) algorithm is recently proposed as a new dimensionality reduction ***, it is confined to linear transforms in the data *** this, based on the NPE algorithm, a new nonlinear dimensionality reduction method is proposed, which can preserve the local structures of the data in the feature ***, combined with the Mercer kernel, the solution to the weight matrix in the feature space is gotten and then the corresponding eigenvalue problem of the Kernel NPE(KNPE) method is ***, the KNPE algorithm is resolved through a transformed optimization problem and qr *** experimental results on three real-world data sets show that the new method is better than NPE, Kernel PCA(KPCA) and Kernel LDA(KLDA) in performance.

关键词： Kernel Neighborhood Preserving Embedding (KNPE) Neighborhood structure Featureextraction qr decomposition

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Orthogonality Based Empirical Likelihood Inferences for Linear Mixed Effects Models

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Journal of Mathematical Research with Applications 2020年第2期40卷 209-220页

作者： Changqing LIU Peixin ZHAO Yiping YANG College of Mathematics and Statistics Baise University College of Mathematics and Statistics Chongqing Technology and Business University Chongqing Key Laboratory of Social Economy and Applied Statistics

Based on empirical likelihood method and qr decomposition technique, an orthogonality empirical likelihood based estimation method for the fixed effects in linear mixed effects models is proposed. Under some regularity conditions, the proposed empirical log-likelihood ratio is proved to be asymptotically chi-squared, and then the confidence intervals for the fixed effects are constructed. The proposed estimation procedure is not affected by the random effects,and then the resulting estimator is more effective. Some simulations and a real data application are conducted for further illustrating the performances of the proposed method.

关键词： Linear mixed effects model orthogonality empirical likelihood qr decomposition random effects

On Linear Algebra for Non Mathematics Majors

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Journal of Applied Mathematics and Physics 2016年第4期4卷 595-601页

作者： Huaichen Chen Shuping Gao Wei Yang Department of Electronic Engineering Xidian University Xi’an China Department of Science Xidian University Xi’an China Department of Technical Physics Xidian University Xi’an China

To find out what knowledge in linear algebra is essential to non-mathematics students, a reverse tracking method was used. Based on practical problems likely to encountered by students in subsequent engineering courses, the minimum contents required has been determined. Rules are proposed to meet the background of most freshman students. An application oriented, easy to understand, computer based text book “Applied Popular Linear Algebra with MATLAB” [1] was published.

关键词： Linear Algebra Determinant Matrix Operation Vector Space Visualizing Teaching Gaussian Elimination Rank Singular Value decomposition qr decomposition Computerized Solution MATLAB

Effective Methods of qr-decompositions of Square Complex Matrices by Fast Discrete Signal-Induced Heap Transforms

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Advances in Linear Algebra & Matrix Theory 2022年第4期12卷 87-110页

作者： Artyom M. Grigoryan Department of Electrical and Computer Engineering The University of Texas at San Antonio San Antonio USA

The purpose of this work is to present an effective tool for computing different qr-decompositions of a complex nonsingular square matrix. The concept of the discrete signal-induced heap transform (DsiHT, Grigoryan 2006) is used. This transform is fast, has a unique algorithm for any length of the input vector/signal and can be used with different complex basic 2 × 2 transforms. The DsiHT is zeroing all components of the input signal while moving or heaping the energy of the signal to one component, for instance the first one. We describe three different types of qr-decompositions that use the basic transforms with the T, G, and M-type complex matrices we introduce, as well as without matrices but using analytical formulas. We also present the mixed qr-decomposition, when different type DsiHTs are used in different stages of the algorithm. The number of such decompositions is greater than 3(N-1), for an N × N complex matrix. Examples of the qr-decomposition are described in detail for the 4 × 4 and 6 × 6 complex matrices and compared with the known method of Householder transforms. The precision of the qr-decompositions of N × N matrices, when N are 6, 13, 17, 19, 21, 40, 64, 100, 128, 201, 256, and 400 is also compared. The MATLAB-based scripts of the codes for qr-decompositions by the described DsiHTs are given.

关键词： qr decomposition Signal-Induced Heap Transform Householder Transform Givens Rotations

Modified Gram-Schmidt Orthogonalization and qr Decompositon Extraction for Digital Predistorter

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Modified Gram-Schmidt Orthogonalization and QR Decompositon ...

Realization and Comparison of qrD Algorithms for STAP

2011 Chinese Control and Decision Conference（CCDC）

作者： Zhao xia is with the Department of Control Science and Engineering,School of Electronics and Information Engineering,Tongji University,Shanghai,China 200092.He yabo,was with Huawei Technologies Co.,Ltd.,Shanghai,China.He is now with the Shanghai JunTong Electronic Science and Technology Co.Ltd,Shanghai,200090,China

Digital baseband predistorter modeled by a memory polynomial and implemented by an indirect learning architecture is among the most cost effective method for linearizing power *** to high correlation between each element of polynomial,general parameter extraction algorithms,*** decomposition combined with linear least square method,have worse numerical stability when higher order terms are *** polynomials are good substitutes,but finding closed-form expressions for orthogonal polynomials for an arbitrary distribution is generally a difficult problem,and the derivations are not easily *** on modified Gram-Schmidt （MGS） orthogonalization method,the article put forward an easy,novel method to find orthogonal basis for random input signal with distribution function of uniformly distributed between 0 and *** same time,we use qr decomposition not linear least squares to obtain coefficients of *** method guarantees good numerical stability from above two aspects,and can be easily realized in real *** exhibits the effective of the methods.

关键词： Power amplifiers(PAs) Digital predistorter Modified Gram-Schmidt orthogonalization qr decomposition

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Realization and Comparison of QRD Algorithms for STAP

A New Noise Variance and Post Detection SNR Estimation Method for MIMO OFDM Systems

2009 2nd Asian-Pacific Conference on Synthetic Aperture Radar（APSAR2009）

作者： Shang Bin Li Shaohong Ren Yi Li Jingsheng (BeiHang University Beijing 100191 China Aviation Industry Corporation I Beijing 100022)

For space time adaptive processing of airborne multi-channel array radar,the computation load of calculating weighting vector is the *** sample matrix inversion（SMI）algorithm,qr decomposition usually is used to calculate weighting *** types of qr decomposition algorithm,Gram-Schmidt,modified Gram-Schmidt,Householder transform and Givens rotation,were studied in this *** realization with ADSP-TS201,the computation efficiency and numerical stability of these four algorithms were *** realization results were validated with simulated multi-channel echo data.

关键词： Multi-Channel Array Radar STAP qr decomposition

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A New Noise Variance and Post Detection SNR Estimation Metho...