Stand-Alone Satellite Based Global Positioning

Stand-alone positioning is the first crucial step in the different types of GPS positioning. It is normally adopted only for pseudo-range measurements, after an ionospheric and tropospheric correction, estimated through calculated models. This positioning approach allows estimation of the position of the rover receiver in the ECEF (Earth Centred Earth Fixed) reference system, with a variable level of accuracy which depends on the number of satellites used, but generally it has a metrical level. Stand-alone positioning using pseudo-range measurements will be analysed in this chapter, starting from the actual measurements of a rover receiver. In this chapter, pseudo-range equations will be written and the balance between measurement equations and unknowns (positions and clock offsets) will be analysed. Equations of observation will be linearized in order to be able to solve the problem with the least squares approach, beginning by writing the design matrix. In least squares, it is important to use an adequate stochastic model, in particular some solutions with different weight matrices will be considered. The relative motion defined during the time of signal propagation due to terrestrial rotation and satellite motion is also considered. The iterative procedure devoted to correct the rover position from these effects will also be considered. The least squares solution is followed by the definition of the precision positioning, by means of the estimation of the variance–covariance matrix. Following the theoretical section, a calculus example is proposed, with the purpose of leading the reader to understand the practical positioning problem and to realize an autonomous calculus, verifying the achieved results. Error estimation is not considered here, referring the reader to another chapter. The Dilution of Precision (DOP) is another related topic described in this chapter. This index represents the geometrical quality of satellite constellations. It allows us to foresee the precision of stand-alone positioning, in order to plan the measures. It is derived from the equations regarding stand-alone positioning, where satellite positions are known through the Keplerian elements of the almanac. An example of DOP estimation and visibility of the GPS satellite will be included in this chapter.