The purpose of this paper is to investigate the idea that by implementing decoupling control algorithms in Permanent Magnet Synchronous Machine (PMSM) controllers, observers like extended Kalman filters (EKFs) can achieve an advantage in computational load. In particular, the KF is designed as a combined state and parameter estimator. The approach is based on the possibility to consider individual electrical current dynamics, together with key system parameters influencing their dynamics, i.e. their inductances Ld, Lq, which is enabled by a decoupling control. Even though the decoupled dynamics are linear, the resulting augmented subsystems, including the inductances as estimation variables, are nonlinear. Furthermore, the paper shows that high-frequency inputs, caused, for example, by control chattering, can enable the EKF-based estimation of the inductances by providing for a never-ending transient phase in the case of the decoupled variant. The computational advantage is ultimately achieved by reducing the complexity of the Kalman filters by around 75%. The results are validated using computer simulations of coupled as well as decoupled control systems, also demonstrating the benefits of chattery input voltages.