New constrained least squares approach for range-based positioning

The problem of finding the location of a target based on range measurements from an array of receivers is addressed. In the linear least squares (LLS) approach for range-based positioning, an extra range variable is usually introduced. In this paper, we derive a LLS algorithm with exploiting the known relation between the source position and range variable, which results in a simple constrained optimization problem. The optimality of the proposed algorithm at sufficiently small noise conditions is demonstrated by the theoretical analysis as well as computer simulations.