Lie Group Approach to Dynamic-Model-Aided Navigation of Multirotor Unmanned Aerial Vehicles

Abstract

In this study, the Lie group approach was used for state estimation of the dynamic-model-aided navigation (DMAN) of a small multirotor unmanned aerial vehicle. The unit quaternions constituting a Lie group called the three-sphere space (<i>S</i>&#x00B3;) were used to represent the attitude in the dynamic equations for the process and measurement models. The linearization of these models is presented in terms of Lie algebra corresponding to <i>S</i>&#x00B3;. The use of Lie algebra to describe the attitude increment conforms to the linearity assumption, on which the measurement update of the extended Kalman filter (EKF) is based. In this study, it was experimentally validated that the Lie group approach combined with DMAN performs better than the EKF that uses the conventional linearization of the process and measurement models under the assumption that the nonlinearity effect is negligible for a small attitude increment. It was demonstrated that the navigation states estimated using the proposed model are better than or comparable to those obtained using the current methods, and the proposed method significantly improves the internal properties.