1. A method for determining a relative position of a remote receiving antenna with respect to a reference receiving antenna in a satellite-based positioning system under varying relative kinematic conditions between the remote and reference receiving antenna, the method comprising the steps of: making carrier phase measurements based on the reception of a dual frequency carrier signals L1 and L2 over one or more epochs of an initialization time period from each of a plurality of at least four satellites used to compute the relative position of the remote receiving antenna; deriving from the carrier phase measurements an initial set of potential solutions that are grid points for the relative position, wherein the initial set of potential solution grid points all are within a region of uncertainty defined by a search volume, and wherein multiple potential solution grid points arise because of whole cycle ambiguity of the carrier signals L1 and L2; eliminating a first set of false solutions from the initial set of potential solutions leaving a reduced number of potential solution; determining a final unique solution from the reduced number of potential solutions, by using a triple difference evaluation technique, the triple difference techniques is defined as: iteratively evaluating the reduced number of potential solutions using a runout triple difference trajectory starting position of a grid point final candidate position using a least squares technique, converting a resulting runout triple difference trajectory position to computed ranges of each final candidate position, scoring the difference between the computed ranges of each final candidate position and carrier ranges with module one cycle, determining the final solution by applying error statistics to each final candidate that i) reflects a degree of coincidence of that final candidate's yield ambiguities to integer values and ii) a smallness of residuals for an ionospherically-free linear combination of carrier ranges.