Optimal Sensor Placement for Hybrid Source Localization Using Fused TOA-RSS-AOA Measurements

Source localization techniques incorporating hybrid measurements improve the reliability and accuracy of the location estimate. Given a set of hybrid sensors that can collect combined time of arrival, received signal strength, and angle of arrival measurements, the localization accuracy can be enhanced further by optimally designing the placements of the hybrid sensors. In this article, we present an optimal sensor placement methodology, which is based on the principle of majorization-minimization (MM), for the hybrid localization technique. We first derive the Cramer-Rao lower bound of the hybrid measurement model, and formulate the design problem using the A-optimal criterion. Next, we introduce an auxiliary variable to reformulate the design problem into an equivalent saddle-point problem, and then, construct simple surrogate functions (having closed form solutions) over both primal and dual variables. The application of MM in this article is distinct from the conventional MM (that is usually developed only over the primal variable), and we believe that the MM framework developed in this article can be employed to solve many optimization problems. The main advantage of our method over most of the existing state-of-the-art algorithms (which are mostly analytical in nature) is its ability to work for both uncorrelated and correlated noise in the measurements. We also discuss the extension of the proposed algorithm for the optimal placement designs based on D and E optimal criteria. Finally, the performance of the proposed method is studied under different noise conditions and different design parameters.