A Deep Dictionary Learning Framework for Device-Free Localization Based on Nonconvex Sparse Regularization and DC Programming

Received signal strength (RSS) based device-free localization (DFL) is commonly used in the Internet of Things (IoT) field. However, the current DFL algorithms have limitations in terms of stability and accuracy, which hinders the widespread application of DFL. Current research on DFL predominantly revolves around sparse representation and deep learning. The sparse representation method requires building a suitable dictionary to achieve higher accuracy, while the deep learning method is affected by data volume and computational complexity. In contrast to traditional localization methods that rely on raw data features, this paper suggests using the deep dictionary learning (DDL) framework to extract depth features. Then, the extracted low-level and high-level features are not only used to construct a dictionary but also to reconstruct the testing data for DFL using sparse representation classification. This approach leverages the advantages of sparse representation and deep learning to achieve highly accurate localization. The proposed deep dictionary learning model involves learning multiple dictionaries with varying descriptive capabilities to extract deep features from the observed signal through a layer-by-layer deep dictionary learning process. For better dictionary learning, we introduce the minimax-concave penalty (MCP) for each layer of dictionary learning. Utilizing the difference of convex (DC) programming, the formulated nonconvex problems are efficiently optimized. Furthermore, to enhance localization accuracy, the data is expanded to reinforce the essential features of deep dictionary learning. The performance of the DC deep dictionary learning (DCDDL) algorithm was assessed using collected laboratory datasets and public datasets, demonstrating its superiority over existing localization algorithms.