Theory of Blind Navigation by Dynamical Measurements

摘要

This paper discusses the theory of blind navigation by means of dynamical measurements (measurements of forces or accelerations) made on a proof body in a reference frame internal to a vehicle. Instrumentally, such measurements are made by an accelerometer in a reference frame provided by gyroscopic or other means. The differential equation is considered which determines the position of a vehicle from dynamical measurements of the non-gravitational acceleration b made internally. Three linear approximations to the gravitational field g(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.