In this paper, a current sensor fault estimation using the transformed currents in the Park synchronous rotating frame is proposed. We show that from an analytical model, the fault characteristics can be retrieved. From experimental raw data collected from a Permanent Magnet Synchronous Machine drive, the gain or offset fault characteristics (amplitude and frequency) have been estimated with an average error of 10%. For incipient fault, despite the analytical model, the estimation might be tedious because the fault is concealed by the noise. In this case the Kullback-Leibler Divergence between two Probability Density Functions can be computed and the fault estimated from the value of the divergence. If the distributions are Gaussian, the closed form of the divergence allows the fault estimation. However even if the data are not perfectly Gaussian-distributed, the closed form can still be used despite an overestimation of the fault characteristics that is preferable as it is a safety margin.