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The Received Signal Strength (RSS) fingerprint-based indoor localization method in Wireless Local Area Network (WLAN) environment has been widely used due to its low hardware requirements and high positioning accuracy. However, the positioning system requires enormous effort to collect fingerprint at each reference point in positioning area, which is time-consuming and laborious. For the practicability of the method, it is essential to reduce the workload of fingerprint collection in the offline phase and construct a fingerprint database efficiently and accurately. Utilizing the high spatial correlation of RSS, in this paper, an efficient fingerprint database construction method is proposed based on low-rank matrix completion. In the meanwhile, different from the traditional matrix completion model, we propose an improved optimization model by converting to the weighted nuclear norm and introducing <inline-formula> <tex-math notation="LaTeX">${\ell _{1}}$ </tex-math></inline-formula>-norm and Frobenius norm to recover unknown data accurately and reduce the influence of outliers and Gaussian noise simultaneously. Furthermore, we combine the K-Nearest Neighbor (KNN) method to solve the problem that matrix completion cannot deal with all unknown rows or columns in the matrix. The experiment results indicate that the proposed algorithm can recover the fingerprint database completely through a few RSS information and has higher accuracy than other algorithms in various scenarios.

An Efficient Fingerprint Database Construction Approach Based on Matrix Completion for Indoor Localization