Robust Smoothing of Wireless Ranging Errors Using Tensor Fibered Rank in IoT-Enabled Positioning

Wireless sensor networks (WSNs) that can provide essential location information have become the key driver for various industrial Internet of Things (IoT) applications. Time-varying and open wireless channels are susceptible to noise and non-line of sight interferences, which can cause the wireless ranging errors and even measurement outliers. Since similar sampling locations can generate similar wireless ranging, this paper proposes a tensor fibered rank based on the weighted total variation (TFR-WTV) method for smoothing wireless ranging errors. Considering the local correlation characteristics of wireless ranging, the sparsely measured wireless ranging data is mapped into a wireless ranging tensor, which can be further decomposed into a low-rank target tensor and a sparse noise tensor using the robust principal component analysis. Based on the multidimensional low-rank property, the tensor singular value decomposition (t-SVD) is extended to modek-t-SVD, and a fibered nuclear norm of nonconvex logarithmic operators is used as the low-rank smooth approximation to enhance wireless global correlation. Meanwhile, a weighted total variation serves as the joint constraint term for capturing wireless local continuity and structural details. Finally, the proposed TFR-WTV algorithm is efficiently solved by the alternating direction method of multipliers (ADMM), which can obtain the smoothed low-rank target tensor. Simulation experiments are conducted to evaluate the smoothing performance of wireless ranging error with different noises and different outlier rates. With use of the networked measurement platform and publicly available data with obstacle interferences, the wireless ranging smoothing are evaluated using seven baseline algorithms, which can provide reliable location-based services for industrial IoT applications.