In the last few years, Motor Current Signature Analysis (MCSA) has proven to be an effective method for electrical machines condition monitoring. Indeed, compared to vibration and temperature analysis, current measurement proves to be a convenient and non-invasive alternative. Moreover, it has proven to be a reliable method since many mechanical and electrical faults manifest as side-band spectral components generated around the fundamental frequency component of the motor’s current. These components are called interharmonics and they are a major focus of fault detection using MCSA. However, the main drawback of this approach is that the interference of other more prevalent components such as the fundamental and noise components can obstruct the effect of interharmonics in the spectrum and may therefore affect fault detection accuracy. Thus, we propose in this paper an alternative approach that aims to decompose the different current components using a model based on a Vandermonde matrix, in order to monitor each component independently. Then, the tracking of each distinct component in time and spectral domains is implemented. This is achieved by estimating their respective relevant parameters using the Gradient Descent algorithm. This method has been favorably compared to an existing estimation algorithm (MUSIC) and its efficiency has been validated. The results of this work prove to be promising and establish the parametric tracking of the electrical current components using the Gradient Descent algorithm as a reliable monitoring approach.