Denoising-Autoencoder-Aided Euclidean Distance Matrix Reconstruction for Connectivity-Based Localization: A Low-Rank Perspective

Abstract

In contrast to conventional localization methods, connectivity-based localization is a promising approach that leverages wireless links among network nodes. Here, the Euclidean distance matrix (EDM) plays a pivotal role in implementing the multidimensional scaling technique for the localization of wireless nodes based on pairwise distance measurements. This is based on the representation of complex datasets in lower-dimensional spaces, resulting from the mathematical property of an EDM being a low-rank matrix. However, EDM data are inevitably susceptible to contamination due to errors such as measurement imperfections, channel dynamics, and clock asynchronization. Motivated by the low-rank property of the EDM, we introduce a new pre-processor for connectivity-based localization, namely denoising-autoencoder-aided EDM reconstruction (DAE-EDMR). The proposed method is based on optimizing the neural network by inputting and outputting vectors of the eigenvalues of the noisy EDM and the original EDM, respectively. The optimized NN denoises the contaminated EDM, leading to an exceptional performance in connectivity-based localization. Additionally, we introduce a relaxed version of DAE-EDMR, i.e., truncated DAE-EDMR (T-DAE-EDMR), which remains operational regardless of variations in the number of nodes between the training and test phases in NN operations. The proposed algorithms show a superior performance in both EDM denoising and localization accuracy. Moreover, the method of T-DAE-EDMR notably requires a minimal number of training datasets compared to that in conventional approaches such as deep learning algorithms. Overall, our proposed algorithms reduce the required training dataset's size by approximately one-tenth while achieving more than twice the effectiveness in EDM denoising, as demonstrated through our experiments.