Deep Learning Based Low-Rank Matrix Completion for IoT Network Localization

Sunwoo Kim, Luong Trung Nguyen, Junhan Kim, Byonghyo Shim

Abstract: In this letter, we propose a deep learning-based technique to recover a Euclidean distance matrix <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</b> in IoT network localization. In contrast to conventional localization algorithms that search <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</b> over a whole set of matrices, the proposed technique, called multiple deep neural networks for localization (MDNL), estimates <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</b> over the set of Euclidean distance matrices. Other than the low-rank constraint, a Euclidean distance matrix is symmetric, and its diagonal and non-diagonal entries are zero and positive, respectively. To exploit these properties in recovering <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</b> , we express <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</b> as a function of the sensor coordinate matrix that ensures the symmetry and zero diagonal and positive non-diagonal entries of <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</b> , and then jointly recover <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</b> and the sensor coordinate matrix by employing deep neural network. Numerical results demonstrate that the proposed MDNL technique not only brings significant performance gain over conventional localization approaches in the noiseless scenario, but it also shows competitive recovery performance in the presence of noise.