[Objective] To address the issue of demodulation coefficient mismatch caused by variations in d-axis and q-axis inductances due to changing operating conditions, which degrades position observation accuracy in zero- and low-speed interior permanent magnet synchronous motor drives using high-frequency square-wave signal injection, an adaptive demodulation coefficient compensation method based on online inductance identification is proposed. [Methods] Firstly, a high-frequency square-wave injection demodulation model was established. The difference method was used to extract the high-frequency current, and the transfer mechanism of how inductance variation affects the demodulation coefficient and position observation error was derived. On this basis, a fuzzy logic cascade model reference adaptive system (FLC-MRAS) was employed to identify Ld and Lq online. The identification results were then used to reconstruct the demodulation coefficients in real time, compensating the two-phase demodulation signals. Finally, the phase error signal was fed into a phase-locked loop to achieve closed-loop estimation of rotor position and speed, thereby mitigating the impact of parameter variations on the system. [Results] Simulations were conducted on the Matlab/Simulink platform. The results indicated that under the speed step condition, the maximum identification errors of Ld and Lq using FLC-MRAS were reduced by 94.1% and 97.1%, respectively, compared to the traditional MRAS. Compared with conventional high-frequency square-wave injection, the negative peak and positive overshoot of the speed error were decreased by 43.9% and 42.4% after compensation, and the peak position error was reduced by 30.6%. Under the load step condition, the maximum identification errors of Ld and Lq were lowered by 85.7% and 95.7%, respectively; the speed drop amplitude and error peak were decreased by 70.8% and 64.8%; and the amplitude of the angular error was reduced by 60.0%. [Conclusion] The proposed method is based on FLC-MRAS online inductance identification to correct the high-frequency demodulation model in real time, which mitigates coefficient mismatch caused by inductance variations, improves the observation accuracy of speed and rotor position, and enhances system robustness under different operating conditions.