In this paper, a generalized differentiation–integration observer is presented based on sensors selection. The proposed differentiation–integration observer can estimate the multiple integrals and high-order derivatives of a signal, synchronously. The parameters selection rules are presented for the differentiation–integration observer. The theoretical results are confirmed by the frequency–domain analysis. The effectiveness of the proposed observer is verified through the numerical simulations on a quadrotor aircraft: i) through the differentiation–integration observer, the attitude angle and the uncertainties in attitude dynamics are estimated synchronously from the measurements of angular velocity; ii) a control law is designed based on the observers to drive the aircraft to track a reference trajectory.