Robust heading estimation indoors using convex optimization

The problem of estimating heading is central in the indoor positioning problem based on measurements from inertial measurement and magnetic units. Integrating rate of turn angular rate gives the heading with unknown initial condition and a linear drift over time, while the magnetometer gives absolute heading, but where long segments of data are useless in practice because of magnetic disturbances. A basic Kalman filter approach with outlier rejection has turned out to be difficult to use with high integrity. Here, we propose an approach based on convex optimization, where segments of good magnetometer data are separated from disturbed data and jointly fused with the yaw rate measurements. The optimization framework is flexible with many degrees of freedom in the modeling phase, and we outline one design. A recursive solution to the optimization is derived, which has a computational complexity comparable to the simplest possible Kalman filter. The performance is evaluated using data from a handheld smartphone for a large amount of indoor trajectories, and the result demonstrates that the method effectively resolves the magnetic disturbances.