The nonlinear nature of quadrotor dynamics requires high-fidelity reconstruction of vehicle position and attitude. In order to mitigate singularities associated with global three-parameter representations—such as Euler angles—the quadrotor attitude is conventionally parameterized via unit quaternions and reconstructed by integrating quaternion differential equations. However, the standard quaternion integration procedure is structure non-preserving. It is based on a set of linear differential equations that subsequently enforces the unitary norm of the quaternion through additional algebraic equations. To this end, the paper presents the utilization of the recently introduced structure-preserving attitude and position update algorithms, based on Lie groups, that overcome the drawbacks of the standard procedures. The numerical test cases involve UAV performing five different maneuvers. It is shown that conventional algorithms may suffer from instabilities and errors in kinematical update of position and attitude, which can be circumvented by using the geometric structure-preserving (Lie group-based) algorithms presented here.