Probabilistic modeling for positioning applications using inertial sensors

In this thesis, we consider the problem of estimating position and orientation (6D pose) using inertial sensors (accelerometers and gyroscopes). Inertial sensors provide information about the change in position and orientation at high sampling rates. However, they suffer from integration drift and hence need to be supplemented with additional sensors. To combine information from the inertial sensors with information from other sensors we use probabilistic models, both for sensor fusion and for sensor calibration. Inertial sensors can be supplemented with magnetometers, which are typically used to provide heading information. This relies on the assumption that the measured magnetic field is equal to a constant local magnetic field and that the magnetometer is properly calibrated. However, the presence of metallic objects in the vicinity of the sensor will make the first assumption invalid. If the metallic object is rigidly attached to the sensor, the magnetometer can be calibrated for the presence of this magnetic disturbance. Afterwards, the measurements can be used for heading estimation as if the disturbance was not present. We present a practical magnetometer calibration algorithm that is experimentally shown to lead to improved heading estimates. An alternative approach is to exploit the presence of magnetic disturbances in indoor environments by using them as a source of position information. We show that in the vicinity of a magnetic coil it is possible to obtain accurate position estimates using inertial sensors, magnetometers and knowledge of the magnetic field induced by the coil. We also consider the problem of estimating a human body’s 6D pose. For this, multiple inertial sensors are placed on the body. Information from the inertial sensors is combined using a biomechanical model which represents the human body as consisting of connected body segments. We solve this problem using an optimization-based approach and show that accurate 6D pose estimates are obtained. These estimates accurately represent the relative position and orientation of the human body, i.e. the shape of the body is accurately represented but the absolute position can not be determined. To estimate absolute position of the body, we consider the problem of indoor positioning using time of arrival measurements from an ultra-wideband (uwb) system in combination with inertial measurements. Our algorithm uses a tightlycoupled sensor fusion approach and is shown to lead to accurate position and orientation estimates. To be able to obtain position information from the uwb measurements, it is imperative that accurate estimates of the receivers’ positions and clock offsets are known. Hence, we also present an easy-to-use algorithm to calibrate the uwb system. It is based on a maximum likelihood formulation and represents the uwbmeasurements assuming a heavy-tailed asymmetric noise distribution to account for measurement outliers.