Joint Estimation of Location and Transmit Power of Wireless Nodes Using Semidefinite Programming

Received signal strength (RSS)-based localization has been popular as it can achieve reasonable accuracy without the need for additional hardware. In this work, we consider RSS-based cooperative and non-cooperative localization when the transmit power of the nodes is unknown. The maximum likelihood (ML) formulation of the RSS-based localization is non-linear, non-convex, and discontinuous and cannot be solved using conventional techniques. Firstly, we linearize the relation between pairwise distance between nodes and received power using a least squares-based linearization technique. Next, we propose two RSS-based localization techniques, referred to as SDP-URSS and SDP-RSS, that convert the ML into a constrained convex optimization problem using the proposed linearization technique and semidefinite relaxation. SDP-URSS assumes the transmit powers are unknown and estimates them along with the location of the nodes, whereas SDP-RSS uses the transmit power information to improve the location estimates. Extensive performance evaluation of the proposed technique considering various performance metrics under non-cooperative and cooperative scenarios demonstrates the superiority of the proposed localization techniques over the existing methods.