A nonlinear measurement model is used in pseudolite (PL) positioning
systems to precisely determine a rover’s position as in conventional global navigation satellite system (GNSS), such as GPS, GLONASS, or Galileo.Linearization is a necessary step of most positioning algorithms for the nonlinear model. Because distances between pseudolites and rovers are shorter than those in conventional GPS positioning scenario, effects of linearization on positioning algorithm cannot be ignored under some
conditions. In this paper, effects of linearization in pseudolite positioning system are presented. Firstly, through geometrical analysis, bounds of linearization bias in pseudolite systems are given exactly. Then, the effects of linearization bias on accuracy of positioning algorithms are discussed in different noise environments. Furthermore, based on differential geometry theory, a simplified criterion is proposed to evaluate the convergence of Gauss-Newton method for nonlinear least squares (NLLS) in pseudolite positioning systems. With the criterion, it is possible to make a prediction about convergence from the system model. Finally, comparative simulation results based on realistic indoor positioning environments are studied,which demonstrate the efficiency of the convergence criterion.