The Spectral Decomposition of Covariance Matrices for the Variance Components Models

2006 ◽  
Vol 97 (10) ◽  
pp. 2190-2205 ◽  
Author(s):  
Shi Jian-Hong ◽  
Wang Song-Gui
Keyword(s):  
Spectral Decomposition ◽  
Variance Components ◽  
Covariance Matrices

An Adaptive Kalman Filter Based on Sage Windowing Weights and Variance Components

2003 ◽  
Vol 56 (2) ◽  
pp. 231-240 ◽  
Author(s):  
Yuanxi Yang ◽  
Tianhe Xu
Keyword(s):  
Kalman Filter ◽  
Adaptive Filtering ◽  
Variance Components ◽  
Covariance Matrices ◽  
Adaptive Kalman Filter ◽  
Dynamic States

In this paper a brief review of Sage adaptive filtering is followed by an analysis of the shortcomings of covariance matrices formed by windowing residual vectors, innovation vectors and correction vectors of the dynamic states. A new adaptive Kalman filter is developed by combining the Sage filter and the variance components and its use tested against various other schemes.

Quadratic Discriminant Analysis of Spatially Correlated Data

2001 ◽  
Vol 6 (2) ◽  
pp. 15-28 ◽  
Author(s):  
K. Dučinskas ◽  
J. Šaltytė
Keyword(s):  
Discriminant Function ◽  
Error Rate ◽  
Gaussian Random Field ◽  
Correlated Data ◽  
Covariance Matrices ◽  
Classification Rule ◽  
Spatial Correlations ◽  
Linear Quadratic ◽  
Spatial Correlation Function ◽  
Spatially Correlated

The problem of classification of the realisation of the stationary univariate Gaussian random field into one of two populations with different means and different factorised covariance matrices is considered. In such a case optimal classification rule in the sense of minimum probability of misclassification is associated with non-linear (quadratic) discriminant function. Unknown means and the covariance matrices of the feature vector components are estimated from spatially correlated training samples using the maximum likelihood approach and assuming spatial correlations to be known. Explicit formula of Bayes error rate and the first-order asymptotic expansion of the expected error rate associated with quadratic plug-in discriminant function are presented. A set of numerical calculations for the spherical spatial correlation function is performed and two different spatial sampling designs are compared.

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