Outlier Suppression via Non-Convex Robust PCA for Efficient Localization in Wireless Sensor Networks

Due to the fact that outliers can degrade localization accuracy significantly in wireless sensor networks, we propose an outlier suppression approach via non-convex robust principal component analysis (Robust PCA). By introducing several non-convex penalty functions to approximate both the rank function and the sparse penalty function in the original Robust PCA problem, we establish a non-convex objective function and solve it efficiently by the augmented Lagrangian multiplier method and difference of convex programming technique. This framework creates the opportunity to safely perform localization with dimension reduction by standard PCA, which has well-known fragile characteristics in the presence of outliers. Thus, the localization algorithms obtained by sparse coding provide the benefits of computational efficiency in low-dimension. The device-free localization (DFL) experiment on a real-world data set shows the improvement in localization accuracy after standard PCA in the presence of outliers. A statistical distance, called the Wasserstein distance, is introduced to evaluate the processed result of outlier suppression, illustrating that the proposed approach can identify and eliminate outliers in DFL problems.