A near-optimal least squares solution to received signal strength difference based geolocation

A simple geometric interpretation for received signal strength (RSS) difference based geolocation can be illustrated by considering a plane containing a single pair of receivers and a transmitter. If the path loss follows a simple inverse power law, the RSS difference (in decibels) between the two receivers can be shown to define a circle on which the transmitter must lie. With additional receivers, the position of the transmitter can be solved by finding the common intersection of the circles corresponding to the different pairs of receivers. In practice, the solution of this problem is complicated by the errors contributed by environmental noise, measurement errors and the deviation of the actual path losses from the model. The optimal nonlinear least squares solution can be obtained by performing a search on a planar grid. However, the computational cost becomes an issue when the number of receivers is large. This paper presents an efficient least squares solution whose performance approaches that of the optimal nonlinear least squares solution.