An Adaptive Sampling Scheme via Approximate Volume Sampling for Fingerprint-Based Indoor Localization

In recent years Wi-Fi fingerprinting has attracted much attention in indoor localization because of the availability of high-quality signal and pervasive deployment of wireless LANs. For fingerprint-based localization, however, offline site survey is usually time-consuming and labor-intensive. Therefore, reducing the burden of offline site survey becomes an important issue for fingerprint-based indoor localization. In this paper, using a low-tubal-rank tensor to model Wi-Fi fingerprints of all reference points (RPs), we propose an adaptive sampling scheme via approximate volume sampling to improve reconstruction accuracy of radio map with reduced expenditure. We propose a rank-increasing strategy to effectively estimate the rank of the underlying fingerprint tensor to alleviate the computation burden for tensor completion. We provide a theoretical foundation to analyze the proposed scheme and derive the performance bounds in terms of sample complexity and reconstruction error. We prove that the proposed scheme can achieve a relative error guarantee. Finally, we validate the effectiveness of the proposed scheme through extensive simulations using both synthetic and real datasets. The simulation results demonstrate that the proposed scheme is able to not only reduce reconstruction error and improve localization accuracy but also reduce running time compared to the state-of-the-art schemes.