Square Root Modified Bryson-Frazier Smoother

We derive here an algorithm for a complete square root implementation of the modified Bryson-Frazier (MBF) smoother. The MBF algorithm computes the smoothed covariance as the difference of two symmetric matrices. Numerical errors in this differencing can result in the covariance matrix not being pos...

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Vydáno v:	IEEE transactions on automatic control Ročník 56; číslo 2; s. 452 - 456
Hlavní autor:	Gibbs, R G
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.02.2011 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algorithms Applied sciences Automatic control Computation Computer science; control theory; systems Control theory. Systems Covariance Covariance matrix Equations Estimation Exact sciences and technology Kalman filtering Kalman filters Mathematical analysis Mathematical model Matrices Matrix decomposition Matrix methods Modelling and identification Roots Smoothing methods Symmetric matrices Covariance Symmetric matrix Kalman filter Estimation Positive definite matrix Householder transformation Kalman filtering Covariance matrix
ISSN:	0018-9286, 1558-2523
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Abstract	We derive here an algorithm for a complete square root implementation of the modified Bryson-Frazier (MBF) smoother. The MBF algorithm computes the smoothed covariance as the difference of two symmetric matrices. Numerical errors in this differencing can result in the covariance matrix not being positive semi-definite. Earlier algorithms implemented the computation of intermediate quantities in square root form but still computed the smoothed covariance as the difference of two matrices. We show how to compute the square root of the smoothed covariance by solving an equation in the form CCT = AAT - BBT using QR decomposition with hyperbolic Householder transformations.
AbstractList	We derive here an algorithm for a complete square root implementation of the modified Bryson-Frazier (MBF) smoother. The MBF algorithm computes the smoothed covariance as the difference of two symmetric matrices. Numerical errors in this differencing can result in the covariance matrix not being positive semi-definite. Earlier algorithms implemented the computation of intermediate quantities in square root form but still computed the smoothed covariance as the difference of two matrices. We show how to compute the square root of the smoothed covariance by solving an equation in the form CC T = AA T - BB T using QR decomposition with hyperbolic Householder transformations. We derive here an algorithm for a complete square root implementation of the modified Bryson-Frazier (MBF) smoother. The MBF algorithm computes the smoothed covariance as the difference of two symmetric matrices. Numerical errors in this differencing can result in the covariance matrix not being positive semi-definite. Earlier algorithms implemented the computation of intermediate quantities in square root form but still computed the smoothed covariance as the difference of two matrices. We show how to compute the square root of the smoothed covariance by solving an equation in the form using QR decomposition with hyperbolic Householder transformations. We derive here an algorithm for a complete square root implementation of the modified Bryson-Frazier (MBF) smoother. The MBF algorithm computes the smoothed covariance as the difference of two symmetric matrices. Numerical errors in this differencing can result in the covariance matrix not being positive semi-definite. Earlier algorithms implemented the computation of intermediate quantities in square root form but still computed the smoothed covariance as the difference of two matrices. We show how to compute the square root of the smoothed covariance by solving an equation in the form CCT = AAT - BBT using QR decomposition with hyperbolic Householder transformations.
Author	Gibbs, R G
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Cites_doi	10.1109/TASSP.1986.1164998 10.1109/9.376092 10.1080/00207179508921582 10.2514/6.1972-877 10.1109/9.489212 10.1080/00207177308932487 10.1007/BF00929358 10.2514/3.3166
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SubjectTerms	Algorithms Applied sciences Automatic control Computation Computer science; control theory; systems Control theory. Systems Covariance Covariance matrix Equations Estimation Exact sciences and technology Kalman filtering Kalman filters Mathematical analysis Mathematical model Matrices Matrix decomposition Matrix methods Modelling and identification Roots Smoothing methods Symmetric matrices
Title	Square Root Modified Bryson-Frazier Smoother
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