Accurate parameters are critical to permanent magnet synchronous machine (PMSM) drive. This paper investigates accurate flux linkages, inductances and PM flux linkage estimation for PMSM with core loss compensation. With conventional model, core loss will induce the flux linkage error especially in the deep saturation region. Hence, this paper firstly proposes a novel differential modeling technique to compensate core loss, in which differential measurement is defined as the incremental value calculated from the actual measurements under two different speed conditions. With multiple differential measurements, the flux linkage error due to core loss can be compensated to improve the accuracy of flux linkage estimation. Then, the polynomial based flux linkage model is employed to derive the PM flux linkage and cross-saturation inductances. Self-inductances are estimated from the flux linkage model using least squares method. The proposed approach can accurately estimate parameters without the need of core loss data and can improve the estimation accuracy especially in deep saturation region, which is validated on a laboratory interior PMSM and compared with existing methods under various operating conditions.