This paper evaluates a dynamic state estimation algorithm for power transmission systems, which operates without knowledge of the underlying system model. It relies purely on measurement data from phasor measurement units (PMUs) along with input data to the system (such as loads, field voltages). The algorithm uses Gaussian processes (GPs) to approximate the measurement and process functions. The hyperparameters of the GP are learned from past measurements and corresponding state estimates. The learned GP, in conjunction with the unscented Kalman filter (UKF), facilitates sequential state estimation. The algorithm, when evaluated on IEEE 14-bus test case, gives an accuracy rate of over 94%.