Quaternion-based Kalman filtering on INS/GPS

In this paper, two quaternion-based nonlinear filtering methods are applied on the processing of measurements from the low-cost Micro-electromechanical Systems (MEMS) based Inertial Navigation system (INS) and Global Positioning System (GPS). One approach employs an Extended Kalman filter (EKF) propagating the quaternion vector using conventional vector addition operation. However, due to the fact that the unit sphere defined by the quaternion vector is not an Euclidean vector space, the vector addition and scaling should principally not be directly applied. Therefore, in the second approach, an Unscented Kalman filter (UKF) is used which propagates the quaternion vector based on the quaternion product chain rule, having a natural way of maintaining the normalization constraint. A field experiment based on the train ride is made for the comparison. The objective is to verify whether different handlings of nonlinearity in system models and different ways of propagating quaternion vector over time will practically yield differences in the estimation of attitude and sensor bias errors.