Method and device for determining the relative position of two points

A method of determining the relative position of a mobile in relation to the known position of a reference station, each using an antenna for receiving radio signals originating from an arrangement of positioning satellites transmitting on at least two frequencies L1 and L2, this method comprising the periodic determination, for each of said frequencies, of a set of 2p pseudo-ranges, i.e. p pseudo-ranges between the mobile and the p satellites and p pseudo-ranges between the reference station and the p satellites, the supply of the pseudo-ranges to a position-calculating unit, and the calculation by this unit of a relative position of the mobile in relation to the reference station based, on the one hand, on the pseudo-ranges and, on the other hand, on an estimated position Pe of the mobile in relation to the reference station, this method being mainly characterized in that, for a given set of 4p pseudo-ranges received by the calculating unit, the calculation of the relative position, comprising the following steps:

• a) choosing a linear combination aL1+bL2 of said frequencies L1 and L2 from a predetermined list having two linear combinations of frequencies,
• b) calculating the linear combinations of pseudo-ranges corresponding to the linear combination, and, on the basis of these linear combinations of pseudo-ranges and the estimated position Pe, calculating a precise relative position Pp of the mobile in relation to the reference station,
• c) choosing from the list the following linear combination, if it exists, and, in this case, reiterating step b), considering the estimated position to be said precise position Pp, and using the same set of 4p pseudo-ranges to obtain an even more precise relative position,
• d) reiterating step c) for all the linear combinations in the list.