A method for estimating a location of a terminal device of a non-terrestrial cellular data communication network is disclosed. The non-terrestrial cellular data communication network includes at least one airborne or spaceborne base station moving along a flight trajectory. The terminal device and a location service node store information describing the flight trajectory of the at least one airborne or spaceborne base station. The method further includes: at the at least one airborne or spaceborne base station, transmitting a reference timing signal; at the terminal device, accumulating over time the respective arrival times of the reference timing signal received from at least three different positions taken by the at least one airborne or spaceborne base station; and at the terminal device, computing, from said arrival times, at least two arrival time differences with respect to one reference arrival time.