Abstract: On the basis of analysis of the principle of positioning and speed measuring in satellite navigation and inertial navigation, fundamental issues of the theory of space and time are discussed in this paper. A perfect form of observation equations for satellite navigation, including physical effects of inertial system and non\|inertial system, is provided. The first order effect of the Lorentz transformation is discussed emphatically. The evolution from Galileo transformation into Lorentz transformation leads naturally to the relativity of ‘simultaneity’. The puzzles caused by Einstein’s definition based on ‘to\|and\|fro’two way signal are analysed from the point of view of the one way electromagnetic signal specific for satellite navigation. It is pointed out that the Hubble’s red shift is a verification of a kind of first order effect of Lorentz transformation. The theoretical foundation of inertial navigation is discussed on the basis of Einstein’s principle of equivalence of inertial mass and gravitational mass. A measurement mechanism of speed more than 3×10 8m/s is discussed.

Key words: Satellite navigation, Inertial navigation, Space and time, Lorentz first order effect, Hubble’s red shift