Because of the high photon flux, the Crab nebula pulsar is widely used as the observation target for X-ray pulsar-based navigation. The built profile of the Crab pulsar will change over time, however, which means that the pre-calibrated template cannot be used for the long term. In this paper, a novel pulsar-based template-independent navigation method is proposed. The detected phase propagation model is given as a term of position of the vehicle, taking the orbital motion into account. A different method of time-of-arrival process between the recovered profiles is introduced. With the aid of orbital transition matrix, a measurement model is derived to be a term of velocity error of the vehicle varying with time. The state errors of the vehicle are transformed into velocity errors by performing multi-segment observations to achieve the navigation system observability. The navigation equations of the system are then established and can be solved directly. Some simulations are performed to verify the method and suggest that the proposed method is feasible, effective and easy to implement. The precise orbit information of the vehicle can be determined. The state estimation accuracy is basically consistent with the traditional filtering algorithms, and the computational cost is still very low.