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Sensitivity of discrete‐time Kalman filter to statistical modeling errors
Author(s) -
Saab Samer S.,
Nasr George E.
Publication year - 1999
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/(sici)1099-1514(199909/10)20:5<249::aid-oca659>3.0.co;2-2
Subject(s) - kalman filter , covariance , covariance matrix , fast kalman filter , covariance intersection , ensemble kalman filter , invariant extended kalman filter , mathematics , control theory (sociology) , extended kalman filter , sensitivity (control systems) , noise (video) , matrix (chemical analysis) , computer science , algorithm , statistics , artificial intelligence , engineering , materials science , control (management) , composite material , electronic engineering , image (mathematics)
The optimum filtering results of Kalman filtering for linear dynamic systems require an exact knowledge of the process noise covariance matrix Q k , the measurement noise covariance matrix R k and the initial error covariance matrix P 0 . In a number of practical solutions, Q k , R k and P 0 , are either unknown or are known only approximately. In this paper the sensitivity due to a class of errors in statistical modelling employing a Kalman Filter is discussed. In particular, we present a special case where it is shown that Kalman filter gains can be insensitive to scaling of covariance matrices. Some basic results are derived to describe the mutual relations among the three covariance matrices (actual and perturbed covariance matrices), their respective Kalman gain K k and the error covariance matrices P k . It is also shown that system modelling errors, particularly scaling errors of the input matrix, do not perturb the Kalman gain. A numerical example is presented to illustrate the theoretical results, and also to show the Kalman gain insensitivity to less restrictive statistical uncertainties in an approximate sense. Copyright © 1999 John Wiley & Sons, Ltd.