Manon Kok

Modeling magnetic fields using Gaussian processes

Starting from the electromagnetic theory, we derive a Bayesian non-parametric 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.

An optimization-based approach to human body motion capture using inertial sensors

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.

Magnetometer Calibration Using Inertial Sensors

In this paper, 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.

Maximum likelihood calibration of a magnetometer using inertial sensors

Magnetometers and inertial sensors (accelerometers and gyroscopes) are widely used to estimate 3D orientation. For the orientation estimates to be accurate, the sensor axes need to be aligned and the magnetometer needs to be calibrated for sensor errors and for the presence of magnetic disturbances. In this work we use a grey-box system identification approach to compute maximum likelihood estimates of the calibration parameters. An experiment where the magnetometer data is highly disturbed shows that the algorithm works well on real data, providing good calibration results and improved heading estimates. We also provide an identifiability analysis to understand how much rotation is needed to be able to solve the calibration problem.

Modeling and Interpolation of the Ambient Magnetic Field by Gaussian Processes

Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwells 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 to 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.

MEMS-based inertial navigation based on a magnetic field map

This paper presents an approach for 6D pose estimation where MEMS inertial measurements are complemented with magnetometer measurements assuming that a model (map) of the magnetic field is known. The resulting estimation problem is solved using a Rao-Blackwellized particle filter. In our experimental study the magnetic field is generated by a magnetic coil giving rise to a magnetic field that we can model using analytical expressions. The experimental results show that accurate position estimates can be obtained in the vicinity of the coil, where the magnetic field is strong.

Accelerometer calibration using sensor fusion with a gyroscope

In this paper, a calibration method for a triaxial accelerometer using a triaxial gyroscope is presented. The method uses a sensor fusion approach, combining the information from the accelerometers and gyroscopes to find an optimal calibration using Maximum likelihood. The method has been tested by using real sensors in smart-phones to perform orientation estimation and verified through Monte Carlo simulations. In both cases, the method is shown to provide a proper calibration, reducing the effect of sensor errors and improving orientation estimates.

Newton-based maximum likelihood estimation in nonlinear state space models

Maximum likelihood (ML) estimation using Newton’s method in nonlinear state space models (SSMs) is a challenging problem due to the analytical intractability of the log- likelihood and its gradient ...

On orientation estimation using iterative methods in Euclidean space

This paper presents three iterative methods for orientation estimation. The first two are based on iterated Extended Kalman filter (IEKF) formulations with different state representations. The first is using the well-known unit quaternion as state (q-IEKF) while the other is using orientation deviation which we call IMEKF. The third method is based on nonlinear least squares (NLS) estimation of the angular velocity which is used to parametrise the orientation. The results are obtained using Monte Carlo simulations and the comparison is done with the non-iterative EKF and multiplicative EKF (MEKF) as baseline. The result clearly shows that the IMEKF and the NLS-based method are superior to q-IEKF and all three outperform the non-iterative methods.

Using inertial sensors for position and orientation estimation

In recent years, micro-machined electromechanical system (MEMS) inertial sensors (3D accelerometers and 3D gyroscopes) have become widely available due to their small size and low cost. Inertial se ...