Mobile location estimation in urban areas using mixed Manhattan/Euclidean norm and convex optimization

In this study, we propose a combined scheme for mobile location estimation in urban areas. First, the proposed scheme employs particle filters to estimate the unobstructed distances traveled by light between base stations (BSs) and the mobile station (MS). Next, according to those estimations of unobstructed distances, which are usually non-Euclidean due to Non-Line of Sight (NLOS) radio propagations, the locating problem is formulated as a non-convex and unconstrained optimization problem with the proposed mixed Manhattan/Euclidean norm. The solution to such a non-convex and unconstrained optimization problem serves as a more accurate estimation of the location of MS. The advantage of the proposed mobile location estimation method is that this method can be applied to both LOS and NLOS propagations and there is no need to reconstruct the Euclidean distances between BSs and the MS from mostly non-Euclidean distances so that the reconstruction error can be avoided and a more accurate mobile location estimation can be achieved. Finally, a convex and constrained optimization problem is introduced to approximate the non-convex and unconstrained optimization problem since the convex optimization problems can be solved very efficiently nowadays.