Patent ID: 7259717

Claim:
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 L 1 and L 2 , this method comprising the steps of: periodically determining, for each of said frequencies, of a set of 2p pseudo-ranges, for p pseudo-ranges between the mobile and the p satellites and p pseudo-ranges between the reference station and the p satellites, supplying of the pseudo-ranges to a position-calculating unit, and calculating by the position-calculating unit of a relative position of the mobile in relation to the reference station based on the pseudo-ranges and on an estimated position Pe of the mobile in relation to the reference station, and, for a given set of 4p pseudo-ranges received by the position-calculating unit, calculating the relative position, comprising the following steps: a) choosing a linear combination equation aL 1 +bL 2 of said frequencies L 1 and L 2 from a predetermined list having at least two linear combination equations of frequencies, b) calculating linear combinations of pseudo-ranges corresponding to the chosen linear combination equation, 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 equation, setting the estimated position Pe to be a new estimated position Pe equal to said precise position Pp, and reiterating steps b) by calculating new linear combination equation using the same set of 4p pseudo-ranges and, on the basis of the new linear combination of pseudo-ranges and the new estimated position Pe, obtaining an even more precise relative position, d) reiterating step c) for all the remaining linear combination equations in the list.