Optimal fusion of sensor data for Kalman filtering

Z. G. Feng; Kok Lay Teo; N. U. Ahmed; Yulin Zhao; W. Y. Yan

doi:10.3934/dcds.2006.14.483

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2006, Volume 14, Issue 3: 483-503. Doi: 10.3934/dcds.2006.14.483

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Optimal fusion of sensor data for Kalman filtering

1.
Department of Mathematics, Zhongshan University, Guangzhou 510275
2.
Department of Mathematics and Statistics, Curtin University, G.P.O. Box U1987, Perth, WA 6845
3.
School of Information Technology and Department of Mathematics, University of Ottawa, Ottawa K1N 6N5
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

Received: November 2004

Revised: September 2005

Published: July 2006

Abstract / Introduction Related Papers Cited by

Abstract

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:

Sensor,
optimal control,
control parametrization enhancing transform,
Kalman ﬁlter,
matrix Riccati differential equation.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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