American Institute of Mathematical Sciences

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July  2006, 14(3): 483-503. doi: 10.3934/dcds.2006.14.483

Optimal fusion of sensor data for Kalman filtering

Z. G. Feng 1, , Kok Lay Teo 2, , N. U. Ahmed 3, , Yulin Zhao 4, and  W. Y. Yan 5,

1. 

Department of Mathematics, Zhongshan University, Guangzhou 510275, China
2. 

Department of Mathematics and Statistics, Curtin University, G.P.O. Box U1987, Perth, WA 6845, Australia
3. 

School of Information Technology and Department of Mathematics, University of Ottawa, Ottawa K1N 6N5, Canada
4. 

Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275
5. 

Department of Electrical and Computer Engineering, Curtin University of Technology, Perth W.A. 6845, Australia

Received  November 2004 Revised  September 2005 Published  December 2005

In this paper we consider the question of optimal fusion of sensor data for Kalman filtering. The basic problem is to design a linear filter whose output provides an unbiased minimum variance estimate of a signal process whose noisy measurements from multiple sensors are available for input to the filter. The problem is to assign weights to each of the sources (sensor data) dynamically so as to minimize estimation errors. We formulate the problem as an optimal control problem where the weight given to each of the sensor data is considered as one of the control variables satisfying certain constraints. There are as many controls as there are sensors. Using the control parametrization enhancing transform technique (CPET), we develop an efficient method for determining the optimal fusion strategy. Some numerical results are presented for illustration.
Keywords: control parametrization enhancing transform, optimal control, Kalman filter, Sensor, matrix Riccati differential equation..
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Z. G. Feng, Kok Lay Teo, N. U. Ahmed, Yulin Zhao, W. Y. Yan. Optimal fusion of sensor data for Kalman filtering. Discrete and Continuous Dynamical Systems, 2006, 14 (3) : 483-503. doi: 10.3934/dcds.2006.14.483
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