On relative positioning

The problem of relative positioning is introduced and some solutions are proposed. The topic is studied as applied to the Global Positioning System (GPS). Unlike usual GPS positioning, in relative positioning, the navigator's location in some Earth-bound coordinates is not the desired result, but instead, the position of one GPS user relative to another. The relative position is given in user-centered coordinates. Rather than determining the relative position vector through explicit calculation of both navigator locations, alternative methods are developed to serve specifically relative positioning. The purpose is to reduce the needed amount of computations in this particular problem and to enhance accuracy. The former objective is met by algebraic manipulations of the positioning equations and the latter one is achieved by making use of the typical properties of GPS measurement errors.