DocumentCode :
818993
Title :
A prefiltering version of the Kalman filter with new numerical integration formulas for Riccati equations
Author :
Womble, Edward M. ; Potter, James E.
Author_Institution :
Georgia Institute of Technology, Atlanta, USA
Volume :
20
Issue :
3
fYear :
1975
fDate :
6/1/1975 12:00:00 AM
Firstpage :
378
Lastpage :
381
Abstract :
A prefiltering version of the Kalman filter is derived for both discrete and continuous measurements. The derivation consists of determining a single discrete measurement that is equivalent to either a time segment of continuous measurements or a set of discrete measurements. This prefiltering version of the Kalman filter easily handles numerical problems associated with rapid transients and ill-conditioned Riccati matrices. Therefore, the derived technique for extrapolating the Riccati matrix from one time to the next constitutes a new set of integration formulas which alleviate ill-conditioning problems associated with continuous Riccati equations. Furthermore, since a time segment of continuous measurements is converted into a single discrete measurement, Potter´s square root formulas can be used to update the state estimate and its error covariance matrix. Therefore, if having the state estimate and its error covariance matrix at discrete times is acceptable, the prefilter extends square root filtering with all its advantages, to continuous measurement problems.
Keywords :
Differential Riccati equations; Kalman filtering; Linear systems, stochastic; Riccati equations, differential; State estimation; Stochastic systems, linear; Covariance matrix; Filtering; Gaussian noise; Kalman filters; Least squares methods; Matrix converters; Riccati equations; Space technology; State estimation; Time measurement;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1975.1100990
Filename :
1100990
Link To Document :
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