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Integration of global positioning system (GPS) and inertial navigation system (INS) provides continuous positioning information of high accuracy due to the synergistic effect of both systems. While a Kalman filter is usually employed to fuse the GPS and INS measurements, this approach requires a priori knowledge on the stochastic and deterministic parameters of both systems. In practice, these unknown parameters are often determined by trial and error. We propose an expectation-maximization (EM) method here to estimate these unknowns in a maximum likelihood (ML) framework. In particular, we employ a delta operator model to approximate the continuous-time system instead of the conventional shift operator model. The proposed method achieves simultaneous positioning and unknown parameter estimation. To assess the performance of the proposed method, we derive the posterior Cramer-Rao bound (PCRB) of our model and compare the performance with adaptive Kalman filtering technique. Both real and simulated data arc used to validate the effectiveness of the proposed EM-based method.