Abstract
In this paper we present a quaternion-based Extended Kalman Filter (EKF) for estimating the three-dimensional orientation of a rigid body. The EKF exploits the measurements from an Inertial Measurement Unit (IMU) that is integrated with a tri-axial magnetic sensor. Magnetic disturbances and gyro bias errors are modeled and compensated by including them in the filter state vector. We employ the observability rank criterion based on Lie derivatives to verify the conditions under which the nonlinear system that describes the process of motion tracking by the IMU is observable, namely it may provide sufficient information for performing the estimation task with bounded estimation errors. The observability conditions are that the magnetic field, perturbed by first-order Gauss-Markov magnetic variations, and the gravity vector are not collinear and that the IMU is subject to some angular motions. Computer simulations and experimental testing are presented to evaluate the algorithm performance, including when the observability conditions are critical.
Highlights
IntroductionAccurate tracking of the orientation of rigid bodies moving in a three-dimensional (3D) space is important in several applications, including navigation of man-made vehicles, robotics, machine
Accurate tracking of the orientation of rigid bodies moving in a three-dimensional (3D) space is important in several applications, including navigation of man-made vehicles, robotics, machineSensors 2011, 11 interaction and, of main interest to us in this paper, ambulatory human motion analysis
The observability conditions are that the magnetic field vector, perturbed by first-order Gauss-Markov magnetic variations, and the gravity vector are not collinear, and that the Inertial Measurement Unit (IMU) is subject to some angular motions
Summary
Accurate tracking of the orientation of rigid bodies moving in a three-dimensional (3D) space is important in several applications, including navigation of man-made vehicles, robotics, machine. Sensors 2011, 11 interaction and, of main interest to us in this paper, ambulatory human motion analysis. Several approaches are available to create trackers that determine orientation based on measurements from, e.g., acoustic, mechanical, optical, inertial and magnetic sensors [1]. One popular approach is based on the principles behind inertial/magnetic sensing. A state-of-the-art Inertial Measurement Unit (IMU) consists of a tri-axial accelerometer, a tri-axial gyro, and a tri-axial magnetic sensor, referred to as an integrated IMU. The 3D orientation can be computed by time-integrating the gyro output from known initial conditions. Due to low-frequency gyro bias drift this operation is subject to errors that tend to grow unbounded over time
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