**6. Conclusions**

This paper proposed a novel STSMFO for the active flux-based sensorless scheme. To demonstrate its effectiveness, a detailed mathematical analysis was given for comparing it with traditional observers, i.e., the pure integrator, the LPF, and the SMFO. It shows that the STSMFO can easily solve the problems caused by dc offset, unknown integral initial value, and saturation. Moreover, the robustness of STSMFO is much better than SMFO. Then, the precision of the stator flux estimation can be enhanced greatly without any amplitude and phase compensation. Furthermore, the rotor position can be observed accurately via the active flux over a wide speed domain. The numerical simulations and experimental tests have confirmed the capability of the steady state, the dynamic response, and the disturbance rejection.

**Author Contributions:** J.C. proposed the new scheme. J.C., S.C., and X.W. performed the simulations, experiments, and data analysis. J.C. wrote the first draft and S.C., X.W., G.T., and J.H. guided and revised the manuscript.

**Funding:** The project is supported by the National Natural Science Foundational of China (Grant number: U1610113) and National Key R&D Program of China (Grant number: 2016YFC0600804).

**Conflicts of Interest:** The authors declare no conflict of interest.
