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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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 56; no. 2; pp. 452 - 456
Main Author: Gibbs, R G
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.02.2011
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2010.2089753