Scalable Cooperative Localization using Augmented Lagrangian Method with Experimental Validation

Received signal strength (RSS)-based localization techniques rely on the transmit power of nodes, with many existing approaches assuming full knowledge of this parameter. However, transmit power depends on various factors like battery levels, antenna orientation, and component aging. To address this issue, existing techniques typically employ semidefinite programming (SDP), which exhibits significantly high computational complexity. In this paper, we present a cooperative RSS-based localization technique named CR-CA (Convex Relaxation with Centralized Armijo optimization), which jointly estimates nodes’ locations and transmit power. CR-CA transforms the unconstrained maximum likelihood (ML) of the RSS-based localization problem into a constrained optimization problem using a convex approximation of the non-convex and discontinuous objective function. We demonstrate that the relaxed ML objective function possesses a Lipschitz continuous gradient. We solve the relaxed ML problem using the augmented Lagrange multiplier method and provide the theoretical proof of its convergence. Additionally, we derive the Cramer-Rao Lower Bound (CRLB) for RSS-based cooperative localization under scenarios where transmit power is unknown. We conduct extensive simulations and real-world experiments to verify the effectiveness of CR-CA, showcasing its superior accuracy in estimating nodes’ locations and transmit power. Simulations and experiments further validate that CR-CA exhibits linear computational complexity with the number of wireless links, thus making it suitable for large-scale networks.