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INITIALIZATION OF THE KALMAN FILTER WITH PARTIALLY DIFFUSE INITIAL CONDITIONS
Author(s) -
Snyder Ralph D.,
Saligari Grant R.
Publication year - 1996
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1996.tb00285.x
Subject(s) - cholesky decomposition , mathematics , initialization , kalman filter , ensemble kalman filter , filter (signal processing) , diagonal , incomplete cholesky factorization , matrix (chemical analysis) , control theory (sociology) , covariance matrix , diagonal matrix , alpha beta filter , extended kalman filter , invariant extended kalman filter , algorithm , statistics , computer science , eigenvalues and eigenvectors , moving horizon estimation , materials science , artificial intelligence , composite material , geometry , control (management) , quantum mechanics , computer vision , programming language , physics
. The problem of computing estimates of the state vector when the Kalman filter is seeded with an arbitrarily large variance is considered. To date the response in the literature has been the development of a number of relatively complex hybrid filters, usually involving additional quantities and equations over and above the conventional filter. We show, however, that a certain square root covariance filter is capable of handling the complete range of variances (zero, positive and infinite) without modification to the filtering equations themselves and without additional computation loads. Instead of the more conventional Cholesky factorization, our filter employs an alternative matrix factorization procedure based on a unit lower triangular matrix and a diagonal matrix. This permits the use of a modified form of fast Givens transformations, central to the development of an efficient algorithm.