Statistical Methods in Surveying by Trilateration

Trilateration techniques use distance measurements to survey the spatial coordinates of unknown positions In practice distances are measured with error and statistical methods can quantify the uncertainty in the estimate of the unknown location Three methods for estimating the three dimensional position of a point via trilateration are presented a linear least squares estimator an iteratively reweighted least squares estimator and a nonlinear least squares technique In general the nonlinear least squares technique performs best but in some situations a linear estimator could in theory be constructed that would outperform it By eliminating the need to measure angles trilateration facilitates the implementation of fully automated real time positioning systems similar to the global positioning system GPS The methods presented in this paper are tested in the context of a realistic positioning problem that was posed by the Thunder Basin Coal Company in Wright Wyoming