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Signal polynomial smoothing from correlated interrupted observations based on covariances
Author(s) -
Nakamori S.,
CaballeroÁguila R.,
HermosoCarazo A.,
JiménezLópez J. D.,
LinaresPérez J.
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.860
Subject(s) - smoothing , mathematics , estimator , polynomial , covariance , signal (programming language) , sampling (signal processing) , mathematical optimization , algorithm , least squares function approximation , statistics , computer science , mathematical analysis , filter (signal processing) , computer vision , programming language
The least‐squares polynomial smoothing problem of discrete‐time signals from uncertain observations is addressed, when the variables describing the uncertainty are correlated at consecutive sampling times. Defining suitable augmented signal and observation vectors, the polynomial estimation problem is reduced to the linear estimation problem of the augmented signal. By an innovationapproach, recursive algorithms are derived for the augmented linear estimators without requiring the knowledge of the state‐space model generating the signal, but only covariance information of the processes involved. Copyright © 2007 John Wiley & Sons, Ltd.