On Consistency of EKF for Pedestrian Dead Reckoning with Foot Mounted IMU

We investigate dead reckoning with foot-mounted inertial measurement unit (IMU). To improve accuracy of navigation the zero velocity update (ZUPT) technic is commonly used, aiding the IMU with information on zero foot velocity during the stance phase of a step. This information is fed to a extended Kalman-type filter. We write the ZUPT condition in two ways and show that the one most commonly used yields inconsistent results. We suggest a consistent ZUPT algorithm based on coordinate transformation in the error equations to the so-called dynamic errors. We proceed with analysis of two feet mounted IMU fusion by using the feet distance upper bound. Here we show again how inconsistency of EKF can arise and can be avoided by employing the dynamic errors. All results are based on purely analytical observability and covariance analysis under certain simplifying assumptions.