This paper develops a robust generalized maximum-likelihood Koopman operator-based Kalman filter (GM-KKF) to estimate the rotor angle of synchronous generators. The approach is data-driven and model independent. The design phase is carried out offline and requires estimates of the synchronous generators' rotor angle and active and reactive power; in real-time operation, only measurements of active and reactive power at the terminal of the synchronous generators are assumed. We first investigate the probability distribution of the dynamic states by means of Q-Q plots and verify that the states of the GM-KKF approximately follow a Student's t-distribution with 20 degrees of freedom when the initial state vector is normally distributed. Under this assumption, our filter presents high statistical efficiency. Then, we carry out numerical simulations on the IEEE 39-bus test system. They reveal that the GM-KKF has a faster convergence rate than the non-robust Koopman operator-based Kalman filter. They also show that the computing time of the GM-KKF is roughly reduced by one-third as compared to the one taken by our previously developed robust GM-extended Kalman filter.