Pedestrian Attitude Estimation using a Multiplicative Extended Kalman Filter with Geometrically-Defined Innovation Covariance

This paper presents a multiplicative extended Kalman filter (MEKF) with a geometrically-defined innovation covariance as a robust attitude estimation algorithm within a pedestrian navigation framework. The MEKF avoids singularity issues due to it’s use of a quaternion as the nominal attitude representation. Though a quaternion is used for the nominal state, the error state will only utilize a three-component rotation vector to characterize the errors in order to avoid complex mappings of the states to their variances. The filter also utilizes a multiplicative correction step which mitigates the need for any additional uncertainty considerations that would be needed for a correction step that did not retain the unit quaternion. As an addition to the MEKF, the innovation covariance within the measurement update will use the geometric properties of covariance matrices, and their corresponding error ellipsoids, in attempts to geometrically bound the state and measurement covariances. This filter is tested on real inertial data collected with an iPhone 16 Pro and, compared with other methods, shows a decrease in both the average estimation error, as well as a decrease in the estimation error variance.