Unscented Kalman filter and Magnetic Angular Rate Update (MARU) for an improved Pedestrian Dead-Reckoning

The Extended Kalman Filter (EKF) has been the state of the art in Pedestrian Dead-Reckoning for foot-mounted Inertial Measurements Units. However due to the non-linearity in the propagation of the orientation the EKF is not the optimal Bayesian filter. We propose the usage of the Unscented Kalman Filter (UKF) as the integration algorithm for the inertial measurements. The UKF improves the mean and covariance propagation needed for the Kalman filter. Although the UKF provides a better estimate of the orientation, with Zero velocity UPdaTes (ZUPT) measurements, the yaw and the bias in the gyroscope associated with it becomes unobserved and might generate errors in the positioning. We studied the changes in the magnetic field during the stance phase and their relationship with the turn rates to propose three measurements using the magnetometer signal that will be called Magnetic Angular Rate Updates (MARUs). The first measurement uses the change in the angle of the magnetic field in the horizontal plane to measure the change in the yaw and provides a simple measurement for the UKF implementation. The second measurement relates the change in the magnetic field vector to the turn rate and provides information on the bias of the gyroscope for an UKF. The last measurement uses a first order approximation to generate a linear relationship with the gyroscope bias and therefore it can be used in an EKF. Finally we proposed a metric for the reliability of the stance as a way to use the pre and post stance information but adjusting the covariance of the measurements gradually from swing to stance. These methods were tested on real and simulated signals and they have shown improvements over the original PDR algorithms.