Optimization of Device-Free Localization with Springback Dual Models: A Synthetic and Analytical Framework

In complex environments, traditional device-free localization (DFL) methods based on received signal strength (RSS) encounter difficulties in simultaneously achieving high accuracy and efficiency due to multipath effects and noise interference. These methods typically depend on convex sparsity regularization, which, despite its computational convenience, is insufficient in capturing the sparsity of signals. In contrast, non-convex sparsity regularization methods, while theoretically more capable of approximating ideal sparsity, are associated with higher computational complexity and a greater likelihood of getting stuck in local optima. To address these issues, this study proposes a synthetic model based on a novel weakly convex penalty function called Springback. This model combines a compression term (ℓ1) that promotes sparsity and a rebound term (ℓ2) that preserves signal amplitude, adjusting parameters to balance sparsity and computational complexity. Furthermore, to tackle the low efficiency of traditional synthetic models when dealing with large-scale data, we introduce a Springback-transform model based on an analytical transform learning framework. This model can directly extract sparse features from signals, avoiding the complex computational processes inherent in traditional synthetic models. Both models are solved using a difference of convex algorithm (DCA), significantly improving positioning accuracy and computational efficiency. Experimental results demonstrate that the proposed models exhibit high accuracy, low positioning error, and a short computation time across various environments, outperforming other state-of-the-art models. These achievements offer a new solution to the problem of DFL in complex environments, with high practical value and application prospects.