A method for estimating the position of a rotor of a synchronous electrical machine, includes a rotor and a stator coupled to an inverted synchronous electrical machine via a rectifier comprising the following steps: measurement of a current iabc circulating in the stator of the synchronous electrical machine; determination of two signals in quadrature iα; iβ according to a stationary reference frame from the current iabc and isolation of two filtered signals iαh; iβh from the two signals in quadrature iα; iβ; demodulation of the two filtered signals iαh; iβh in order to obtain two demodulated signals iαobs, iβobs; obtaining of an estimated position {circumflex over (θ)} of the rotor from the two demodulated signals iαobs, iβobs.