Cooperative Direct Localization in Multipath Environments Using Binary Sparse Modeling and Cayley–Menger Determinant

This paper studies <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">direct localization</i> which is a technique used for positioning a source by directly searching within a planar grid. In this paper, we have developed an effective method involving sparse signal recovery using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{0}$ </tex-math></inline-formula>-pseudo-norm. Our novel contribution focuses on a cooperative direct localization technique that takes into account the ambiguity caused by reflections in the multipath environment. Specifically, we have factored in the distances between the source and the anchors using a mathematical relationship called the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Cayley-Menger</i> determinant. This determinant acts as a crucial component in deriving accurate range estimates. This relationship is added as an additional constraint to the sparse recovery problem which is NP-hard. To solve this NP-hard problem, we have employed a binary programming relaxation technique. Experiments reveal that our proposed approach significantly reduces localization errors when compared to traditional direct localization methods. This suggests that our cooperative direct localization method holds great potential for enhancing the accuracy and reliability of location estimation in challenging, multi-path scenarios.