Several heuristic procedures to estimate the rotor position of permanent magnet synchronous motors (PMSM) via signal injection have been reported in the literature. Using averaging theory, a framework to analyse such schemes has been recently proposed. However, to the best of our knowledge, no theoretical analysis of the performance of the conventional linear time invariant filtering methods, which are widely used as standard industrial practice, has been reported in the literature. The objective of this note is to propose a new method that, on one hand, is amenable to a rigorous theoretical analysis and, on the other hand, ensures an improved accuracy in the position estimation. An additional advantage of the new method is that it relies on the use of linear operators, implementable with simple computations. The effectiveness of the proposed scheme is assessed by experiments on an interior PMSM platform driven by a 521 V DC bus with 5-kHz PWM.