This paper proposes an improved extended EMF (EEMF)-based sensorless control method for permanent magnet synchronous machine drive systems with a small dc-link capacitor, while considering the dc-link voltage measurement error. Due to fluctuating dc-link voltage, precise and stable dc-link voltage information is extremely important. It is demonstrated that the dc-link voltage measurement error will introduce a dc offset in the estimated position error under EEMF-based sensorless control. To address this issue, a dc-link voltage observer is proposed in this paper, which is immune to dc-link voltage measurement error and estimated position error. Specifically, the estimated position error caused by the dc-link voltage measurement error can be eliminated by using the estimated dc-link voltage. Meanwhile, to further improve the realism and practicality of the proposed observer, the magnetic saturation effect is analysed using finite element analysis. It is found that the parameter mismatch has only a minor effect on the proposed observer. In addition, this paper identifies the coupling issue introduced by using the estimated dc-link voltage in the EEMF-based sensorless control strategy and a back-EMF harmonic suppression method is proposed to suppress the harmonics in the estimated back-EMF, speed, position error, and dc-link voltage, thereby eliminating the coupling issue. A satisfactory system control performance can be achieved, which is validated by experiments.