Characterization of planar-intensity based heading likelihood functions in magnetically disturbed indoor environments

Heading information is a critical input to pedestrian dead reckoning. Unlike in most outdoor environments, the magnetic field inside of buildings is often strongly perturbed and inhomogeneous. Hence, straightforward approaches to use measurements of two-axis and three-axis magnetometers perform poorly. In recent measurements we have observed statistical properties of the magnetic field indicating that knowledge of the measured horizontal magnetic intensity is informative about the expected deviation of the measured magnetic heading. This statistical dependence has been quantified based on indoor measurements that have been collected in several offices and corridors in 3 buildings having different building orientations. A decrease in the spread of the horizonal angle is exhibited for larger horizontal intensities suggesting that measurements with large horizontal intensities are more reliable. We provide an approach to determine a likelihood function for the measured magnetic heading as a function of the local magnetic intensity in indoor environments. We show how the Expectation Maximization (EM) algorithm is used to construct a parametric two dimensional distribution of heading and planar-intensity, which can serve as a heading likelihood function in Bayesian positioning estimators, based upon which, greater weight is given to the less disturbed (strong-intensity) heading measurements and lower weight to the more erroneous ones (low-intensity). Drawing on our empirical data we show the performance improvement achieved with this new likelihood function.