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, 12 (7), 8491-506

Variable-State-Dimension Kalman-based Filter for Orientation Determination Using Inertial and Magnetic Sensors

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Variable-State-Dimension Kalman-based Filter for Orientation Determination Using Inertial and Magnetic Sensors

Angelo Maria Sabatini. Sensors (Basel).

Abstract

In this paper a quaternion-based Variable-State-Dimension Extended Kalman Filter (VSD-EKF) is developed for estimating the three-dimensional orientation of a rigid body using the measurements from an Inertial Measurement Unit (IMU) integrated with a triaxial magnetic sensor. Gyro bias and magnetic disturbances are modeled and compensated by including them in the filter state vector. The VSD-EKF switches between a quiescent EKF, where the magnetic disturbance is modeled as a first-order Gauss-Markov stochastic process (GM-1), and a higher-order EKF where extra state components are introduced to model the time-rate of change of the magnetic field as a GM-1 stochastic process, namely the magnetic disturbance is modeled as a second-order Gauss-Markov stochastic process (GM-2). Experimental validation tests show the effectiveness of the VSD-EKF, as compared to either the quiescent EKF or the higher-order EKF when they run separately.

Keywords: Kalman filters; inertial/magnetic sensing; orientation determination; sensor fusion.

Figures

Figure 1.
Figure 1.
Static test. (a) The ground-truth magnetic field; (b) The magnetic field estimated by the VSD-EKF; (c) the magnetic field estimated by the higher-order EKF; (d) the magnetic field estimated by the quiescent EKF.
Figure 2.
Figure 2.
Fading memory average used for switching from the quiescent state model to the higher-order state model in the VSD-EKF (static test).
Figure 3.
Figure 3.
Estimated yaw angle for the three different filters (static test).
Figure 4.
Figure 4.
Components of the ground-truth reference magnetic field. The horizontal bars at the top of the plot show the time intervals of sojourns in the higher-order state model (dynamic test).
Figure 5.
Figure 5.
Ground-truth Euler angles and estimation errors incurred by the VSD-EKF (dynamic test).
Figure 5.
Figure 5.
Ground-truth Euler angles and estimation errors incurred by the VSD-EKF (dynamic test).

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