Average performance analysis of circular and hyperbolic geolocation

A comparative performance analysis of four geolocation methods in terms of their theoretical root mean square positioning errors is provided. Comparison is established in two different ways: strict and average. In the strict type, methods are examined for a particular geometric configuration of base stations (BSs) with respect to mobile position, which determines a given noise profile affecting the respective time-of-arrival (TOA) or time-difference-of-arrival (TDOA) estimates. In the average type, methods are evaluated in terms of the expected covariance matrix of the position error over an ensemble of random geometries, so that comparison is geometry independent. Exact semianalytical equations and associated lower bounds (depending solely on the noise profile) are obtained for the average covariance matrix of the position error in terms of the so-called information matrix specific to each geolocation method. Statistical channel models inferred from field trials are used to define realistic prior probabilities for the random geometries. A final evaluation provides extensive results relating the expected position error to channel model parameters and the number of base stations.