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Sensors 2012, 12(7), 8877-8894; doi:10.3390/s120708877

Observability Analysis of a Matrix Kalman Filter-Based Navigation System Using Visual/Inertial/Magnetic Sensors

1
The College of Mechatronics and Automation, National University of Defense Technology, Changsha 410073, Hunan, China
2
School of Surveying and Spatial Information Systems, University of New South Wales, Sydney, NSW 2052, Australia
*
Author to whom correspondence should be addressed.
Received: 14 May 2012 / Revised: 14 June 2012 / Accepted: 18 June 2012 / Published: 27 June 2012
(This article belongs to the Special Issue New Trends towards Automatic Vehicle Control and Perception Systems)
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Abstract

A matrix Kalman filter (MKF) has been implemented for an integrated navigation system using visual/inertial/magnetic sensors. The MKF rearranges the original nonlinear process model in a pseudo-linear process model. We employ the observability rank criterion based on Lie derivatives to verify the conditions under which the nonlinear system is observable. It has been proved that such observability conditions are: (a) at least one degree of rotational freedom is excited, and (b) at least two linearly independent horizontal lines and one vertical line are observed. Experimental results have validated the correctness of these observability conditions.
Keywords: matrix Kalman filter; Lie derivatives; observability of nonlinear systems; navigation; vision; inertial measurement unit matrix Kalman filter; Lie derivatives; observability of nonlinear systems; navigation; vision; inertial measurement unit
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Feng, G.; Wu, W.; Wang, J. Observability Analysis of a Matrix Kalman Filter-Based Navigation System Using Visual/Inertial/Magnetic Sensors. Sensors 2012, 12, 8877-8894.

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