A Binary Structured Sparsity Approach for Multi-Anchor Direct Localization

Structured sparsity improves on traditional sparse modeling by suggesting that only a limited number of input variables is needed to describe the output variable. These methods go a step further by incorporating structured patterns in variable selection, such as groups or networks of input variables. This paper introduces a novel binary approximation method leveraging structured sparsity to enhance multi-anchor direct localization performance. By reformulating the sparse recovery as a quadratic unconstrained binary optimization (QUBO) problem, we address the significant computational complexity inherent in NP-hard problems. Employing compressed sensing and binary programming, our method reduces approximation errors and ensures that the line-of-sight component is consistently identified from a coherent grid point among anchors, thus enhancing localization accuracy. Our findings demonstrate a significant improvement in the accuracy of direct localization methods, underscoring the potential of structured sparsity and QUBO formulation to advance localization technologies in multipath environments.