An Indoor Direct Localization Method Utilizing Structural Sparsity and Low-Rankness With Grid Refinement

Indoor positioning technologies are pivotal for achieving high-precision localization in GPS-denied environments. Wireless positioning methods based on angle of arrival (AOA) models leverage spatial diversity to mitigate indoor multipath challenges. Recent approaches combine the extended sparse reconstruction framework with direct positioning (DP) techniques to jointly extract location parameters at the raw signal level. However, the disadvantage is that they have limited utilization for structure information inherent in a sparse solution and overlook the low-rankness in array manifolds induced by redundant grid points. To overcome these problems, a novel structure-aware direct localization method namely SaDPD is proposed that incorporates comprehensive structural constraints of joint row plus element sparsity and low-rankness in the designed sparse framework. A new sparse reconstruction problem is formulated by decomposing the position weight matrix into two distinct feature matrices, in which they are optimized for correlated line-of-sight (LOS) and inconsistent non-line-of-sight (NLOS) components, respectively. In particular, it employs the Alternating Direction Method of Multipliers (ADMM) to effectively address the extended high-dimensional optimization and utilizes grid refinement to avoid quantization constraints. Finally, extensive simulations verify that SaDPD tremendously improves sparse reconstruction accuracy and localization performance. Experimental result further demonstrates its effectiveness and practical applicability against real-world interference. These advancements establish SaDPD as a robust solution for asset positioning and target tracking where localization accuracy beyond half-meter level under multipath interference is critical.