Abstract
We introduce the Kalman filter for linear systems on time scales, which includes the discrete and continuous versions as special cases. When the system is also stochastic, we show that the Kalman filter is an observer that estimates the system when the state is corrupted by noisy measurements. Finally, we show that the duality of the Kalman filter and the Linear Quadratic Regulator (LQR) is preserved in their unification on time scales. A numerical example is provided. © 2013 Elsevier Ltd.
Recommended Citation
M. Bohner and N. Wintz, "The Kalman Filter for Linear Systems on Time Scales," Journal of Mathematical Analysis and Applications, vol. 406, no. 2, pp. 419 - 436, Elsevier, Oct 2013.
The definitive version is available at https://doi.org/10.1016/j.jmaa.2013.04.075
Department(s)
Mathematics and Statistics
Keywords and Phrases
Dynamic equation; Kalman filter; Mean square error; Optimal estimation; Riccati equation; Time scale
International Standard Serial Number (ISSN)
1096-0813; 0022-247X
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Elsevier, All rights reserved.
Publication Date
15 Oct 2013
