Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2011;11(10):9182-206.
doi: 10.3390/s111009182. Epub 2011 Sep 27.

Kalman-filter-based orientation determination using inertial/magnetic sensors: observability analysis and performance evaluation

Angelo Maria Sabatini  1
Affiliations

Kalman-filter-based orientation determination using inertial/magnetic sensors: observability analysis and performance evaluation

Angelo Maria Sabatini. Sensors (Basel). 2011.

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.

Keywords: Extended Kalman filter; Lie derivatives; ambulatory human motion tracking; inertial measurement unit; observability of nonlinear systems; orientation determination.

PubMed Disclaimer

Figures

Figure 1.
Figure 1.
(a)–(e) State errors from the EKF. (f) Heading estimation error. (a)–(c) Quaternion components q1, q2, q3. (d) Magnetic variation Y-component. (e) Gyro bias Z-component. The black lines show the 3 standard deviation bounds estimated by the filter.
Figure 2.
Figure 2.
Orientation RMSE vs. magnetic dip angle.
Figure 3.
Figure 3.
The time function of the X-component of the magnetic field, estimated by the EKF-MA. In blue the time function of the measured X-component of the magnetic field (see text).
Figure 4.
Figure 4.
Heading angle time function estimated by the EKF-MA and by the Xsens-EKF (bσh = 0.01 a.u./s)
Figure 5.
Figure 5.
Euler angles time functions (truth reference and EKF-MA estimation errors).
Figure 5.
Figure 5.
Euler angles time functions (truth reference and EKF-MA estimation errors).
See this image and copyright information in PMC

References

    1. Welch GF, Foxlin E. Motion tracking: No silver bullet, but a respectable arsenal. IEEE Comput. Graph. Appl. 2002;22:24–38.
    1. Sabatini AM. Quaternion-based extended Kalman filter for determining orientation by inertial and magnetic sensing. IEEE Trans. Biomed. Eng. 2006;53:1346–1356. - PubMed
    1. Yun X, Bachmann ER, McGhee RB. A simplified quaternion-based algorithm for orientation estimation from earth gravity and magnetic field measurements. IEEE Trans. Instrum. Meas. 2008;57:638–650.
    1. Lee JK, Park EJ. A fast quaternion-based orientation optimizer via virtual rotation for human motion tracking. IEEE Trans. Biomed. Eng. 2009;56:1574–1582. - PubMed
    1. Veltink PH, Bussmann HBJ, de Vries WHK, Martens WLJ, Van Lummel RC. Detection of static and dynamic activities using uniaxial accelerometers. IEEE Trans. Rehabil. Eng. 1996;4:375–385. - PubMed

Publication types

LinkOut - more resources