Recursive updating the eigenvalue decomposition of a covariance matrix

1991 ◽  
Vol 39 (5) ◽  
pp. 1136-1145 ◽  
Author(s):  
K.-B. Yu
Keyword(s):  
Covariance Matrix ◽  
Eigenvalue Decomposition ◽  
Recursive Updating

Study on the Improvement of MUSIC Algorithm Fire Wireless Communication

2014 ◽  
Vol 1049-1050 ◽  
pp. 1880-1884
Author(s):  
Bin Ni
Keyword(s):  
Covariance Matrix ◽  
Time Domain ◽  
Analytical Signal ◽  
Time Domain Analysis ◽  
Observation Time ◽  
Eigenvalue Decomposition ◽  
Target Range ◽  
Radio Communication ◽  
Music Algorithm ◽  
Good Spatial Resolution

Music algorithm has good spatial resolution, provides the possibility to further improve the performance of fire radio communication system, but the algorithm in the target range rapidly changing circumstances poor stability. Aiming at this problem, this paper proposes a MUSIC algorithm based on time domain analytical signals (TAMUSIC, Time-domain Analysis MUSIC). The TAMUISC algorithm first constructs analytical time-domain signal; then the time domain analytical signal covariance matrix; finally the covariance matrix eigenvalue decomposition, the noise subspace estimation results of spatial spectrum. The simulation results show that, TAMUSIC algorithm in target azimuth change quickly, compared with the conventional MUSIC algorithm, need a short observation time, observation has smaller variance.

2D DOA Estimation Using Sparse Representation of Higher-Order Power of Covariance Matrix

2014 ◽  
Vol 998-999 ◽  
pp. 779-783
Author(s):  
Zheng Luo ◽  
Fei Yu ◽  
Lin Wu ◽  
Yuan Liu
Keyword(s):  
Covariance Matrix ◽  
Estimation Algorithm ◽  
Doa Estimation ◽  
Higher Order ◽  
Eigenvalue Decomposition ◽  
Coherent Signals ◽  
Sparse Decomposition ◽  
Sparse Signal Representation ◽  
2D Doa Estimation ◽  
Source Signals

A novel two-dimensional (2D) direction-of-arrival (DOA) estimation algorithm utilizing a sparse signal representation of higher-order power of covariance matrix is proposed. Through applying the higher-order power of covariance matrix to construct a new sparse decomposition vector, this algorithm avoids the estimation of incident signal number and eigenvalue decomposition. And the hierarchical granularity-dictionary is studied, which forms the over-complete dictionary adaptively in the light of source signals’ distribution. Compared with MUSIC and L1-SVD, this algorithm not only provides a better 2D DOA performance but also possesses the capability of coherent signals estimation. Theoretical analysis and simulation results demonstrate the validity and robust of the proposed algorithm.

RECURSIVE UPDATING OF ERROR COVARIANCE MATRIX IN SUBSPACE METHODS

2006 ◽  
Vol 39 (1) ◽  
pp. 285-290 ◽  
Author(s):  
Yoshinori Takei ◽  
Hidehito Nanto ◽  
Shunshoku Kanae ◽  
Zi-Jiang Yang ◽  
Kiyoshi Wada
Keyword(s):  
Covariance Matrix ◽  
Subspace Methods ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Recursive Updating

Approximation of Spatio-Temporal Random Processes Using Tensor Decomposition

2014 ◽  
Vol 16 (1) ◽  
pp. 75-95 ◽  
Author(s):  
Debraj Ghosh ◽  
Anup Suryawanshi
Keyword(s):  
Covariance Matrix ◽  
Covariance Function ◽  
Heat Conduction Problem ◽  
Random Processes ◽  
Single Parameter ◽  
Eigenvalue Decomposition ◽  
Spatial Covariance ◽  
Practical Applications ◽  
Temporal Process ◽  
Spatio Temporal

AbstractA new representation of spatio-temporal random processes is proposed in this work. In practical applications, such processes are used to model velocity fields, temperature distributions, response of vibrating systems, to name a few. Finding an efficient representation for any random process leads to encapsulation of information which makes it more convenient for a practical implementations, for instance, in a computational mechanics problem. For a single-parameter process such as spatial or temporal process, the eigenvalue decomposition of the covariance matrix leads to the well-known Karhunen-Loève (KL) decomposition. However, for multiparameter processes such as a spatio-temporal process, the covariance function itself can be defined in multiple ways. Here the process is assumed to be measured at a finite set of spatial locations and a finite number of time instants. Then the spatial covariance matrix at different time instants are considered to define the covariance of the process. This set of square, symmetric, positive semi-definite matrices is then represented as a third-order tensor. A suitable decomposition of this tensor can identify the dominant components of the process, and these components are then used to define a closed-form representation of the process. The procedure is analogous to the KL decomposition for a single-parameter process, however, the decompositions and interpretations vary significantly. The tensor decompositions are successfully applied on (i) a heat conduction problem, (ii) a vibration problem, and (iii) a covariance function taken from the literature that was fitted to model a measured wind velocity data. It is observed that the proposed representation provides an efficient approximation to some processes. Furthermore, a comparison with KL decomposition showed that the proposed method is computationally cheaper than the KL, both in terms of computer memory and execution time.

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.

Prestack seismic data reconstruction and denoising by orientation-dependent tensor decomposition

Geophysics ◽  
2020 ◽  
pp. 1-66
Author(s):  
Quézia Cavalcante ◽  
Milton J. Porsani
Keyword(s):  
Covariance Matrix ◽  
Seismic Data ◽  
Missing Values ◽  
Tensor Decomposition ◽  
Low Rank ◽  
Eigenvalue Decomposition ◽  
Data Reconstruction ◽  
Frequency Space ◽  
Multidimensional Signals ◽  
Seismic Data Reconstruction

Multidimensional seismic data reconstruction and denoising can be achieved by assuming noiseless and complete data as low-rank matrices or tensors in the frequency-space domain. We propose a simple and effective approach to interpolate prestack seismic data that explores the low-rank property of multidimensional signals. The orientation-dependent tensor decomposition represents an alternative to multilinear algebraic schemes. Our method does not need to perform any explicit matricization, only requiring to calculate the so-called covariance matrix for one of the spatial dimensions. The elements of such a matrix are the inner products between the lower-dimensional tensors in a convenient direction. The eigenvalue decomposition of the covariance matrix provides the eigenvectors for the reduced-rank approximation of the data tensor. This approximation is used for recovery and denoising, iteratively replacing the missing values. We present synthetic and field data examples to illustrate the method's effectiveness for denoising and interpolating 4D and 5D seismic data with randomly missing traces.

scholarly journals Signal Denoise Method Based on the Higher Order Cumulant and Local Tangent Space Mean Reconstruction

2011 ◽  
Vol 2-3 ◽  
pp. 188-192
Author(s):  
Guang Bin Wang ◽  
Xue Jun Li ◽  
Ke Wang
Keyword(s):  
Covariance Matrix ◽  
Tangent Space ◽  
Higher Order ◽  
Second Order ◽  
High Order ◽  
Eigenvalue Decomposition ◽  
Order Moment ◽  
Dimensional Manifold ◽  
Intrinsic Dimension ◽  
Local Tangent

In signal denoise method to nonlinear time series based on principle manifold learning, reduction target dimension is chosen at random, which cause low efficiency. Local low dimensional manifold is obtained by the eigenvalue decomposition to the covariance matrix, but covariance belongs to the second order statistics and cannot reflect the nonlinear essential structure of signal, these reduce denoise efficiency and effect. In order to solve these problem, a new denoise algorithm based on the higher order cumulant and local tangent space mean reconstruction is proposed in this reserch. First, the signal's intrinsic dimension is obtained as dimension of reduction targets by maximum likelihood estimation. And then making use of restraining character to colored noise of high order cumulan,covariance matrix is constructed by high order cumulant function instead of second order moment function. The data outside intrinsic dimension space will be regarded as noise signal to be eliminated. Finanly the process of global array by affine transformation will be replaced by mean reconstruction,the data after denoise may be obtained in the inverse process of the phase space reconstruction. The effectiveness of the algorithm is verified through the denoise experiment in fan vibration signal with noise.

scholarly journals Subspace Based Adaptive Beamforming Algorithm with Interference Plus Noise Covariance Matrix Reconstruction

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yuxi Du ◽  
Weijia Cui ◽  
Yinsheng Wang ◽  
Bin Ba ◽  
Fengtong Mei
Keyword(s):  
Covariance Matrix ◽  
Reconstruction Algorithm ◽  
Doa Estimation ◽  
Adaptive Beamforming ◽  
Training Data ◽  
Eigenvalue Decomposition ◽  
Noise Covariance Matrix ◽  
Subspace Algorithm ◽  
Noise Covariance ◽  
Beamforming Algorithm

As we all know, the model mismatch, primarily when the desired signal exists in the training data, or when the sample data is used for training, will seriously affect algorithm performance. This paper combines the subspace algorithm based on direction of arrival (DOA) estimation with the adaptive beamforming. It proposes a reconstruction algorithm based on the interference plus noise covariance matrix (INCM). Firstly, the eigenvector of the desired signal is obtained according to the eigenvalue decomposition of the subspace algorithm, and the eigenvector is used as the estimated value of the desired signal steering vector (SV). Then the INCM is reconstructed according to the estimated parameters to remove the adverse effect of the desired signal component on the beamformer. Finally, the estimated desired signal SV and the reconstructed INCM are used to calculate the weight. Compared with the previous work, the proposed algorithm not only improves the performance of the adaptive beamformer but also dramatically reduces the complexity. Simulation experiment results show the effectiveness and robustness of the proposed beamforming algorithm.

Sign in / Sign up

Export Citation Format

Share Document