In recent years, microelectromechanical system (MEMS) inertial sensors (3D accelerometers and 3D gyroscopes) have become widely available due to their small size and low cost. Inertial sensor measurements are obtained at high sampling rates and can be integrated to obtain position and orientation information. These estimates are accurate on a short time scale, but suffer from integration drift over longer time scales. To overcome this issue, inertial sensors are typically combined with additional sensors and models. In this tutorial we focus on the signal processing aspects of position and orientation estimation using inertial sensors. We discuss different modeling choices and a selected number of important algorithms. The algorithms include optimization-based smoothing and filtering as well as computationally cheaper extended Kalman filter and complementary filter implementations. The quality of their estimates is illustrated using both experimental and simulated data.

An optimization-based approach to human body motion capture using inertial sensors, 2014, In Proceedings of the 19th IFAC World Congress, 2014, 79-85. ISBN: 978-3-902823-62- Abstract: In inertial human motion capture, a multitude of body segments are equipped with inertial measurement units, consisting of 3D accelerometers, 3D gyroscopes and 3D magnetometers. Relative position and orientation estimates can be obtained using the inertial data together with a biomechanical model. In this work we present an optimization-based solution to magnetometer-free inertial motion capture. It allows for natural inclusion of biomechanical constraints, for handling of nonlinearities and for using all data in obtaining an estimate. As a proof-of-concept we apply our algorithm to a lower body configuration, illustrating that the estimates are drift-free and match the joint angles from an optical reference system.

Abstract-In this work we present an approach to combine measurements from inertial sensors (accelerometers and gyroscopes) with time of arrival measurements from an ultrawideband system for indoor positioning. Our algorithm uses a tightlycoupled sensor fusion approach, where we formulate the problem as a maximum a posteriori problem that is solved using an optimization approach. It is shown to lead to accurate 6D position and orientation estimates when compared to reference data from an independent optical tracking system. To be able to obtain position information from the ultrawideband measurements, it is imperative that accurate estimates of the ultrawideband receivers' positions and their clock offsets are available. Hence, we also present an easy-to-use algorithm to calibrate the ultrawideband system using a maximum likelihood formulation. Throughout this work, the ultrawideband measurements are modeled by a tailored heavy-tailed asymmetric distribution to account for measurement outliers. The heavy-tailed asymmetric distribution works well on experimental data, as shown by analyzing the position estimates obtained using the ultrawideband measurements via a novel multilateration approach.

The use of inertial measurement units (IMUs) has gained popularity for the estimation of lower limb kinematics. However, implementations in clinical practice are still lacking. The aim of this review is twofold—to evaluate the methodological requirements for IMU-based joint kinematic estimation to be applicable in a clinical setting, and to suggest future research directions. Studies within the PubMed, Web Of Science and EMBASE databases were screened for eligibility, based on the following inclusion criteria: (1) studies must include a methodological description of how kinematic variables were obtained for the lower limb, (2) kinematic data must have been acquired by means of IMUs, (3) studies must have validated the implemented method against a golden standard reference system. Information on study characteristics, signal processing characteristics and study results was assessed and discussed. This review shows that methods for lower limb joint kinematics are inherently application dependent. Sensor restrictions are generally compensated with biomechanically inspired assumptions and prior information. Awareness of the possible adaptations in the IMU-based kinematic estimates by incorporating such prior information and assumptions is necessary, before drawing clinical decisions. Future research should focus on alternative validation methods, subject-specific IMU-based biomechanical joint models and disturbed movement patterns in real-world settings.

We present a method for scalable and fully 3D magnetic field simultaneous localisation and mapping (SLAM) using local anomalies in the magnetic field as a source of position information. These anomalies are due to the presence of ferromagnetic material in the structure of buildings and in objects such as furniture. We represent the magnetic field map using a Gaussian process model and take well-known physical properties of the magnetic field into account. We build local maps using three-dimensional hexagonal block tiling. To make our approach computationally tractable we use reduced-rank Gaussian process regression in combination with a Rao-Blackwellised particle filter. We show that it is possible to obtain accurate position and orientation estimates using measurements from a smartphone, and that our approach provides a scalable magnetic field SLAM algorithm in terms of both computational complexity and map storage.

Abstract-In this work we present a practical algorithm for calibrating a magnetometer for the presence of magnetic disturbances and for magnetometer sensor errors. To allow for combining the magnetometer measurements with inertial measurements for orientation estimation, the algorithm also corrects for misalignment between the magnetometer and the inertial sensor axes. The calibration algorithm is formulated as the solution to a maximum likelihood problem and the computations are performed offline. The algorithm is shown to give good results using data from two different commercially available sensor units. Using the calibrated magnetometer measurements in combination with the inertial sensors to determine the sensor's orientation is shown to lead to significantly improved heading estimates.

Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell's equations, we derive and present a Bayesian nonparametric probabilistic modeling approach for interpolation and extrapolation of the magnetic field. We model the magnetic field components jointly by imposing a Gaussian process (GP) prior on the latent scalar potential of the magnetic field. By rewriting the GP model in terms of a Hilbert space representation, we circumvent the computational pitfalls associated with GP modeling and provide a computationally efficient and physically justified modeling tool for the ambient magnetic field. The model allows for sequential updating of the estimate and time-dependent changes in the magnetic field. The model is shown to work well in practice in different applications: we demonstrate mapping of the magnetic field both with an inexpensive Raspberry Pi powered robot and on foot using a standard smartphone.

Starting from the electromagnetic theory, we derive a Bayesian nonparametric model allowing for joint estimation of the magnetic field and the magnetic sources in complex environments. The model is a Gaussian process which exploits the divergence-and curl-free properties of the magnetic field by combining well-known model components in a novel manner. The model is estimated using magnetometer measurements and spatial information implicitly provided by the sensor. The model and the associated estimator are validated on both simulated and real world experimental data producing Bayesian nonparametric maps of magnetized objects.