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Journal of Mathematical Analysis and Applications


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.


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Martin Bohner is a Professor of Mathematics at Missouri S&T. His research interests center around differential, difference, and dynamic equations as well as their applications to economics, finance, biology, physics, and engineering.

Nick Wintz is an Assistant Professor in Mathematics at Lindenwood University. His research interests include differential and difference equations, dynamic equations on time scales, optimal control and estimation, and game theory.

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Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

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