Using Inertial Sensors for Position and Orientation Estimation

1 Using Inertial Sensors for Positionand Orientation EstimationManon Kok?, Jeroen D. Hol and Thomas B. Sch on ?Delft Center for Systems and Control, Delft University of Technology, the Netherlands1E-mail: Xsens Technologies , Enschede, the NetherlandsE-mail: Department of Information Technology, Uppsala University, SwedenE-mail: Please cite this version:Manon Kok, Jeroen D. Hol and Thomas B. Sch on (2017), Using Inertial Sensors for Position andOrientation Estimation , Foundations and Trends in Signal Processing: Vol. 11: No. 1-2, pp recent years, microelectromechanical system (MEMS) Inertial Sensors (3D accelerometers and3D gyroscopes) have become widely available due to their small size and low cost.

2 Inertial sensormeasurements are obtained at high sampling rates and can be integrated to obtain Position andorientation information. These estimates are accurate on a short time scale, but suffer from inte-gration drift over longer time scales. To overcome this issue, Inertial Sensors are typically combinedwith additional Sensors and models. In this tutorial we focus on the signal processing aspects ofposition and Orientation Estimation Using Inertial Sensors . We discuss different modeling choices anda selected number of important algorithms.

3 The algorithms include optimization-based smoothingand filtering as well as computationally cheaper extended Kalman filter and complementary filterimplementations. The quality of their estimates is illustrated Using both experimental and the moment of publication Manon Kok worked as a Research Associate at the University of Cambridge, UK. Amajor part of the work has been done while she was a PhD student at Link oping University, [ ] 10 Jun 2018 Contents1 Background and motivation .. Using Inertial Sensors for Position and Orientation Estimation .

4 Tutorial content and its outline ..72 Inertial Coordinate frames .. Angular velocity .. Specific force .. sensor errors .. 113 Probabilistic Introduction .. Parametrizing Orientation .. matrices .. vector .. angles .. quaternions .. Probabilistic Orientation modeling .. methods .. Measurement models .. measurement models .. measurement models .. additional information .. Choosing the state and modeling its dynamics .. Models for the prior.

5 Resulting probabilistic models .. Estimation .. Estimation .. 304 Estimating Position and Smoothing in an optimization framework .. optimization .. estimates of the Orientation Using optimization .. the uncertainty .. Filtering Estimation in an optimization framework .. estimates of the Orientation Using optimization .. Extended Kalman filtering .. Orientation Using quaternions as states .. Orientation Using Orientation deviations as states .. Complementary filtering.

6 Evaluation based on experimental and simulated data .. characteristics .. uncertainty .. the different algorithms .. Extending to pose Estimation .. 5615 Maximum a posteriori calibration .. Maximum likelihood calibration .. Orientation Estimation with an unknown gyroscope bias .. Identifiability .. 626 sensor Fusion Involving Inertial Non-Gaussian noise distributions: time of arrival measurements .. Using more complex sensor information: Inertial and vision .. Including non-sensory information: Inertial motion capture.

7 Beyond pose Estimation : activity recognition .. 697 Concluding Remarks708 Notation and Acronyms72A Orientation Quaternion algebra .. Conversions between different parametrizations .. 76B Pose Smoothing in an optimization framework .. Filtering in an optimization framework .. Extended Kalman filter with quaternion states .. Extended Kalman filter with Orientation deviation states .. 79C Gyroscope Bias Smoothing in an optimization framework .. Filtering in an optimization framework.

8 Extended Kalman filter with quaternion states .. Extended Kalman filter with Orientation deviation states .. 812 Chapter 1 IntroductionIn this tutorial, we discuss the topic of Position and Orientation Estimation Using Inertial Sensors . Weconsider two separate problem formulations. The first is Estimation of Orientation only, while the other isthe combined Estimation of both Position and Orientation . The latter is sometimes calledpose start by providing a brief background and motivation in and explain what Inertial Sensors areand give a few concrete examples of relevant application areas of pose Estimation Using Inertial , we subsequently discuss how Inertial Sensors can be used to provide Position and orientationinformation.

9 Finally, in we provide an overview of the contents of this tutorial as well as an outlineof subsequent Background and motivationThe terminertial sensoris used to denote the combination of a three-axis accelerometer and a three-axis gyroscope. Devices containing these Sensors are commonly referred to as Inertial measurement units(IMUs). Inertial Sensors are nowadays also present in most modern smartphone, and in devices such asWii controllers and virtual reality (VR) headsets, as shown in Figure gyroscope measures the sensor sangular velocity, rate of change of the sensor s accelerometer measures theexternal specific forceacting on the sensor .

10 The specific force consists ofboth thesensor s accelerationand theearth s gravity. Nowadays, many gyroscopes and accelerometersare based on microelectromechanical system (MEMS) technology. MEMS components are small, light,inexpensive, have low power consumption and short start-up times. Their accuracy has significantlyincreased over the is a large and ever-growing number of application areas for Inertial Sensors , [7, 59,109, 156]. Generally speaking, Inertial Sensors can be used to provide information about the pose of anyobject that they are rigidly attached to.