In this study, first, it is shown that the least-squares (LS) algorithm outperforms well known methods such as extended Kalman filter and unscented Kalman filter for synchronous generator (SG) parameters estimation using phasor measurement unit (PMU) data. However, as the LS algorithm may estimate the SG parameters inaccurately if the initial values of SG model state variables are not valid, a modified LS (MLS) algorithm, which estimates the initial values of SG model state variables alongside SG parameters, is proposed. In addition to parameters estimation of an SG classical model, the performance of this algorithm in the estimation of whole electromagnetic parameters and rotor inertia constant of an SG full-order model is evaluated. Note that conventionally, measurements of generators rotor angles were used to estimate SGs full-order model parameters; nevertheless, in the proposed MLS algorithm, online SG parameters estimation is accomplished using PMU data without relying on rotor angle measurement that is difficult to be obtained in practise. Simulation results demonstrate the effectiveness of the proposed algorithm in SG parameters estimation for various disturbances and noisy measurements. Furthermore, the effect of mechanical torque signal unavailability on the proposed algorithm capability is studied, where the efficacy of this algorithm is proven.