In order to accurately describe the system noise of permanent magnet synchronous motor (PMSM) under different operating conditions, the variable matrix was used to estimate the system noise based on the innovation sequence and state residual. An adaptive extended Kalman filter (AEKF) algorithm based on the variable matrix was adopted to estimate the speed. At the same time, the research on the stability of AEKF was conducted. The simulation proves that compared with the traditional extended Kalman filter algorithm, the AEKF is better in convergence speed and convergence precision and has better robustness.