Indoor Localization Based on Least Squares Fuzzy Support Tensor Machine

Channel State Information (CSI), encompassing both spatial richness and temporal dynamics, can be effectively represented as a three-dimensional tensor to retain its inherent structural characteristics. However, effectively processing such tensors while maintaining their structural integrity remains a significant challenge. Moreover, CSI data is highly susceptible to noise, which can severely degrade localization performance. To address these issue, this study proposes a novel indoor positioning method named LSFSTM based on CSI tensor. Specifically, first, a Variational Autoencoder-Convolutional Neural Network (VAE-CNN) model is developed to denoise tensor data samples, solving the problem of noise in CSI data that can affect the accuracy of positioning. Second, the Fuzzy Support Tensor Machine (FSTM) is proposed based on the traditional STM where a sigmoid fuzzy membership function is defined to handle the internal noise, to better capture the fuzzy relationships in the data, thus further improving robustness. Moreover, the binary FSTM model is then extended to a multi-class framework through the integration of Lagrange multipliers and Tensor-Tucker decomposition, resolving the challenge of tensor data vectorization, which can disrupt the structural integrity of the data. Finally, a Least Squares is integrated into the FSTM to reduce the computational complexity associated with solving the optimization problem, making the model more efficient and scalable for large datasets. Experimental results demonstrate that the proposed method significantly improves positioning accuracy.