The differential equation is considered which determines the position of a vehicle from dynamical measurements of the non‐gravitational accelerationbmade internally. Three linear approximations to the gravitational fieldg(r) of the earth, which lead to explicit solutions of this equation, are considered and their limitations are discussed. An interval‐wise solution (linear continuation) for trajectories of extended range is described, which is based on such linear approximations and has definite advantages in this application. The theory is applied to the trajectory of the German A10 vehicle.