Closed-Form DRSS Localization Based on Projection for Sensor Networks

Energy-based localization techniques, such as received signal strength (RSS) and differential RSS (DRSS), have gained widespread use in both indoor and outdoor environments due to their high accuracy and low cost. Recently, a new model for DRSS has been introduced, accompanied by a suboptimal solution that fails to attain the Cramér–Rao bound (CRB). However, a comprehensive solution that achieves the CRB and the corresponding analysis is still lacking. To address this gap, this letter proposes a novel formulation for DRSS localization that takes into account sensor position errors from the perspective of nullspace projection. A closed-form coarse estimate is obtained and subsequently refined by the constraint. In addition, we enhance the accuracy of our approach in the presence of large noise and errors by utilizing the Taylor expansion. We provide a theoretical performance analysis that establishes the achievement of the proposed solution to the CRB, which is verified through simulation. Our results demonstrate that the proposed solution outperforms existing algorithms in both mean square error and bias.