The Kalman filter for linear systems on time scales

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:406

Article

Bohner, Martin¹  Wintz, Nick² 

[1] Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA

[2] Lindenwood Univ, Dept Math, St Charles, MO 63301 USA

关键词: Kalman filter;    Time scale;    Dynamic equation;    Optimal estimation;    Mean square error;    Riccati equation;   

DOI  :  10.1016/j.jmaa.2013.04.075

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free