Modeling and State Estimation for Dynamic Systems With Linear Equality Constraints

• Published in: IEEE transactions on signal processing Vol. 61; no. 11; pp. 2927 - 2939
• Main Authors: Linfeng Xu, Li, X. R., Zhansheng Duan, Jian Lan
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2013; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; constrained estimation; Detection, estimation, filtering, equalization, prediction; Dynamics modeling; Exact sciences and technology; Information, signal and communications theory; linear equality constraint; linear minimum mean squared error (LMMSE) estimate; Signal and communications theory; Signal, noise; Telecommunications and information theory; Performance evaluation; constrained estimation; Prior information; Parameter estimation; Kalman filter; Theoretical study; linear equality constraint; Dynamical system; Non linear system; Modeling; Mean square error; Projection method; Sufficient condition; Linear system; linear minimum mean squared error (LMMSE) estimate; Signal processing; Dynamics modeling; Dynamic model; State estimation
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2013.2255045

The problem of modeling and estimation for linear equality constrained (LEC) systems is considered. The exact constrained dynamic model usually is not readily available or is too complicated, and hence in many studies an auxiliary dynamic model is employed in which the state does not necessarily obey the constraint strictly. Based on the understanding that the constraints, as prior information about the state, should be incorporated into the dynamics modeling, an LEC dynamic model (LECDM) is constructed first. The model optimally fuses the linear equality constraint (LEC) and the auxiliary dynamics. Some of its superior properties are presented. Next, the linear minimum mean squared error (LMMSE) estimate of the LEC state is proved to satisfy the constraint. The LMMSE estimator for linear systems, called the LEC Kalman filter (LECKF), and two approximate LMMSE estimators for nonlinear systems are presented. The LECKF is compared with other constrained estimators, and a sufficient condition is also provided under which the estimate projection method mathematically equals the LECKF. Furthermore, extensions of the LECDM for the LEC systems with uncertain or unknown constraint parameters are discussed. Finally, illustrative examples are provided to show the effectiveness and efficiency of the LECKF and to verify the theoretical results given in the paper.