In recent years, inertial sensors have undergone major developments. The quality of their measurements has improved while their cost has decreased, leading to an increase in availability. They can be found in stand-alone sensor units, so-called inertial measurement units, but are nowadays also present in for instance any modern smartphone, in Wii controllers and in virtual reality headsets.

The term inertial sensor refers to the combination of accelerometers and gyroscopes. These measure the external specific force and the angular velocity, respectively. Integration of their measurements provides information about the sensor's position and orientation. However, the position and orientation estimates obtained by simple integration suffer from drift and are therefore only accurate on a short time scale. In order to improve these estimates, we combine the inertial sensors with additional sensors and models. To combine these different sources of information, also called sensor fusion, we make use of probabilistic models to take the uncertainty of the different sources of information into account. The first contribution of this thesis is a tutorial paper that describes the signal processing foundations underlying position and orientation estimation using inertial sensors.

In a second contribution, we use data from multiple inertial sensors placed on the human body to estimate the body's pose. A biomechanical model encodes the knowledge about how the different body segments are connected to each other. We also show how the structure inherent to this problem can be exploited. This opens up for processing long data sets and for solving the problem in a distributed manner.

Inertial sensors can also be combined with time of arrival measurements from an ultrawideband (UWB) system. We focus both on calibration of the UWB setup and on sensor fusion of the inertial and UWB measurements. The UWB measurements are modeled by a tailored heavy-tailed asymmetric distribution. This distribution naturally handles the possibility of measurement delays due to multipath and non-line-of-sight conditions while not allowing for the possibility of measurements arriving early, i.e. traveling faster than the speed of light.

Finally, inertial sensors can be combined with magnetometers. We derive an algorithm that can calibrate a magnetometer for the presence of metallic objects attached to the sensor. Furthermore, the presence of metallic objects in the environment can be exploited by using them as a source of position information. We present a method to build maps of the indoor magnetic field and experimentally show that if a map of the magnetic field is available, accurate position estimates can be obtained by combining inertial and magnetometer measurements.