  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 are
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.
