A closed-loop subspace identification method is proposed for the system identification of quadrotors, focusing on improving innovation estimation. Firstly, the innovation form of the state-space model for the quadrotor is established, and the innovation sequence is recursively estimated row by row using the least squares, making it suitable for closed-loop systems. Subsequently, an auxiliary matrix containing innovation sequence is constructed, and principal component analysis is performed to determine the observability subspace of the system, addressing the interference issue caused by acceleration information in quadrotor systems identification. Finally, the static gain of the quadrotor as prior knowledge is transformed into an equation related to the impulse response coefficients, and the least squares with equality constraints are employed to obtain the system matrix, thereby enhancing identification accuracy. Model simulation verification is conducted using flight data of the quadrotor, and the proposed method is compared with other subspace identification methods. The simulation results suggest that the approach introduced in this research provides enhanced accuracy and superiority.