In this study, a GLSDC (Gaussian Least Squares Differential Correction) based parameter estimation algorithm is used to identify a PMSM (Permanent Magnet Synchronous Motor) model. In this method, a nonlinear model is assumed to be the correct representation of the underlying state dynamics and the output signals are assumed to be measured in a noisy environment. Using noisy input and output signals, parameters that constitute the coefficients of the nonlinear state and input signal terms are to be estimated using the state transition matrix which is computed by the numerical means that are detailed. Since a GLSDC algorithm requires correct initial state value, this term is also estimated in addition to the unknown coefficients whose bounds are assumed to be known, which is mostly the case in the industrial applications. The batch input and output signals are used to iteratively estimate the parameter set before and after the convergence, and to recover the filtered state trajectories. A couple of different scenarios are tested by means of numerical simulations and the results are addressed. Different methods are discussed to compute better initial estimate values, to shorten the convergence time.