Computationally efficient cholesky factorization of a covariance matrix with block toeplitz structure

1993 ◽  
Vol 45 (3-4) ◽  
pp. 203-218 ◽  
Author(s):  
C.R. Dietrich
Keyword(s):  
Covariance Matrix ◽  
Cholesky Factorization ◽  
Computationally Efficient ◽  
Block Toeplitz Structure ◽  
Toeplitz Structure

scholarly journals Computationally Efficient Direction-of-Arrival Estimation Algorithms for a Cubic Coprime Array

Sensors ◽  
2021 ◽  
Vol 22 (1) ◽  
pp. 136
Author(s):  
Pan Gong ◽  
Xixin Chen
Keyword(s):  
Covariance Matrix ◽  
Lower Boundary ◽  
Direction Of Arrival ◽  
Doa Estimation ◽  
Mimo Radar ◽  
Signal Classification ◽  
Computationally Efficient ◽  
Music Algorithm ◽  
Multiple Signal Classification ◽  
Multiple Signal

In this paper, we investigate the problem of direction-of-arrival (DOA) estimation for massive multi-input multi-output (MIMO) radar, and propose a total array-based multiple signals classification (TA-MUSIC) algorithm for two-dimensional direction-of-arrival (DOA) estimation with a coprime cubic array (CCA). Unlike the conventional multiple signal classification (MUSIC) algorithm, the TA-MUSIC algorithm employs not only the auto-covariance matrix but also the mutual covariance matrix by stacking the received signals of two sub cubic arrays so that full degrees of freedom (DOFs) can be utilized. We verified that the phase ambiguity problem can be eliminated by employing the coprime property. Moreover, to achieve lower complexity, we explored the estimation of signal parameters via the rotational invariance technique (ESPRIT)-based multiple signal classification (E-MUSIC) algorithm, which uses a successive scheme to be computationally efficient. The Cramer–Rao bound (CRB) was taken as a theoretical benchmark for the lower boundary of the unbiased estimate. Finally, numerical simulations were conducted in order to demonstrate the effectiveness and superiority of the proposed algorithms.

First order error-adapted eigen perturbation for real-time modal identification of vibrating structures

2020 ◽  
pp. 1-25
Author(s):  
Satyam Panda ◽  
Tapas Tripura ◽  
Budhaditya Hazra
Keyword(s):  
Real Time ◽  
Covariance Matrix ◽  
Passive Control ◽  
Perturbation Technique ◽  
Modal Identification ◽  
Eigenvalue Decomposition ◽  
Mode Shapes ◽  
Computationally Efficient ◽  
Order Error ◽  
First Order

Abstract A new computationally efficient error adaptive first-order eigen-perturbation technique for real-time modal identification of linear vibrating systems is proposed. The existence of error terms in the approximation of the eigenvalue problem of response covariance matrix, in a perturbative framework often hinders the convergence of response-only modal identification. In the proposed method, the error in first-order eigen-perturbation is incorporated using a feedback, formulated by exploiting the generalized eigenvalue decomposition of the real-time covariance matrix of streaming response data. Since the incorporation of the higher-order perturbation terms in the total perturbation is mathematically challenging, the proposed feedback approach provides a computationally efficient framework yet in a more elegant manner. A new criterion for the quality of updated eigenspace is proposed in the present work utilizing the concept of diagonal dominance. Numerical case studies and validation using a standard ASCE benchmark problem have shown applicability of the proposed approach in faster estimation of real-time modal properties and anomaly identification with minimal number of initially required batch data. The applicability of the proposed approach towards real-time under-determined modal identification problems is demonstrated using a real-time decentralized framework. The advantage of rapidly converging online mode-shapes is demonstrated using a passive vibration control problem, where a multi-tuned-mass-damper (MTMD) for a multi-degree of freedom system is tuned online. An extension for online retuning of the detuned MTMD system further demonstrates the fidelity of the proposed algorithm in online passive control.

Algorithms for least‐squares linear prediction and maximum entropy spectral analysis—Part I: Theory

Geophysics ◽  
1980 ◽  
Vol 45 (3) ◽  
pp. 420-432 ◽  
Author(s):  
I. Barrodale ◽  
R. E. Erickson
Keyword(s):  
Spectral Analysis ◽  
Least Squares ◽  
Maximum Entropy ◽  
Linear Prediction ◽  
Fortran Program ◽  
Computationally Efficient ◽  
Rounding Errors ◽  
Maximum Entropy Spectral Analysis ◽  
Short Sample ◽  
Toeplitz Structure

Experience with the maximum entropy spectral analysis (MESA) method suggests that (1) it can produce inaccurate frequency estimates of short sample sinusoidal data, and (2) it sometimes produces calculated values for the filter coefficients that are unduly contaminated by rounding errors. Consequently, in this report we develop an algorithm for solving the underlying least‐squares linear prediction (LSLP) problem directly, without forcing a Toeplitz structure on the model. This approach leads to more accurate frequency determination for short sample harmonic processes, and our algorithm is computationally efficient and numerically stable. The algorithm can also be applied to two other versions of the linear prediction problem. A Fortran program is given in Part II.

Some properties of periodic B-spline collocation matrices

1983 ◽  
Vol 94 (3-4) ◽  
pp. 235-246 ◽  
Author(s):  
S. L. Lee ◽  
C. A. Micchelli ◽  
A. Sharma ◽  
P. W. Smith
Keyword(s):  
Null Space ◽  
Spline Interpolation ◽  
Total Positivity ◽  
Spline Collocation ◽  
Positive Elements ◽  
Interpolation Problems ◽  
Totally Positive ◽  
Positive Matrices ◽  
Block Toeplitz Structure ◽  
Toeplitz Structure

SynopsisIn three recent papers by Cavaretta et al., progress has been made in understanding the structure of bi-infinite totally positive matrices which have a block Toeplitz structure. The motivation for these papers came from certain problems of infinite spline interpolation where total positivity played an important role.In this paper, we re-examine a class of infinite spline interpolation problems. We derive new results concerning the associated infinite matrices (periodic B-spline collocation matrices) which go beyond consequences of the general theory. Among other things, we identify the dimension of the null space of these matrices as the width of the largest band of strictly positive elements.

Computationally Efficient Multisensor Fusion Estimation Algorithms

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Seokhyoung Lee ◽  
Vladimir Shin
Keyword(s):  
Computational Complexity ◽  
Computational Analysis ◽  
Approximation Scheme ◽  
Estimation Algorithm ◽  
Block Matrix ◽  
Cholesky Factorization ◽  
Computationally Efficient ◽  
Estimation Algorithms ◽  
Matrix Weights ◽  
Cross Covariance

This paper provides two computationally effective fusion estimation algorithms. The first algorithm is based on Cholesky factorization of a cross-covariance block matrix. This algorithm has low computational complexity and is equivalent to the standard composite fusion estimation algorithm as well. The second algorithm is based on a special approximation scheme for local cross-covariances. Such approximation is useful to compute matrix weights for fusion estimation in a multidimensional-multisensor environment. Subsequent computational analysis of the proposed fusion algorithms is presented with corresponding examples showing the low computational complexities of the new fusion estimation algorithms.

Improving Minimum-Variance Portfolios by Alleviating Overdispersion of Eigenvalues

2019 ◽  
Vol 55 (8) ◽  
pp. 2700-2731
Author(s):  
Fangquan Shi ◽  
Lianjie Shu ◽  
Aijun Yang ◽  
Fangyi He
Keyword(s):  
Covariance Matrix ◽  
General Framework ◽  
Minimum Variance ◽  
Risk Minimization ◽  
Portfolio Risk ◽  
Computationally Efficient ◽  
Estimation Errors ◽  
Inverse Covariance Matrix ◽  
Sample Covariance ◽  
Out Of Sample

In portfolio risk minimization, the inverse covariance matrix of returns is often unknown and has to be estimated in practice. Yet the eigenvalues of the sample covariance matrix are often overdispersed, leading to severe estimation errors in the inverse covariance matrix. To deal with this problem, we propose a general framework by shrinking the sample eigenvalues based on the Schatten norm. The proposed framework has the advantage of being computationally efficient as well as structure-free. The comparative studies show that our approach behaves reasonably well in terms of reducing out-of-sample portfolio risk and turnover.

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