The present invention provides methods and systems that enable a mobile navigation receiver to accurately determine its trajectory with non-current ephemeris in stand-alone mode. In an embodiment, the receiver computes the position for the same location using non-current ephemeris and current ephemeris at different time instances. The receiver then determines a position correction by finding the difference between these two computed positions, and applies this correction to the trajectory generated with non-current ephemeris to obtain a more accurate trajectory. In another embodiment, the receiver computes an initial position of the receiver using non-current ephemeris and finds the difference between the computed initial position and an accurate approximation of the initial position. The receiver then shifts the subsequent receiver trajectory computed using non-current ephemeris by the difference to obtain a more accurate trajectory.