Outlier Detection of Space Trilateration Localization Based on Geometric Inequalities

The three-dimensional positioning problem remains as a challenge in modern commercial communication networks. Yet conventional algorithms, such as the trilateration localization algorithm, are vulnerable to abnormal distance input values which are common in praxis. To address this problem, we introduced an outlier detection approach based on geometric reasoning prior to localization. This process detects and discards abnormal distance values and thus increase the robustness of conventional localization algorithms. Our main concern is the validity of geometry, for example, whether triangle or tetrahedron can be formed is valued in the spatial trilateration localization algorithm. This method is generally used to locate target on the ground, and the problem of ambiguity can be avoided. To this end, geometric reasoning based algorithms such as the triangle inequality and tetrahedral inequality are applied for detection. In this paper, we have mathematically validated the correctness of the proposed method. We have also demonstrated that the proposed method outperforms conventional methods using in silico simulation.