Fractional-order Deep Neural Networks for Improved TDOA Localization in Wireless Sensor Networks

Accurate localization is critical for the effective operation of Wireless Sensor Networks (WSNs), yet traditional methods often struggle with noise and environmental variability. This research introduces a novel approach by incorporating fractional-order calculus into Deep Neural Networks (DNNs) to address two key technical challenges: (1) the sensitivity of Time-Difference-of-Arrival (TDOA) methods to noise and non-linearity in dynamic environments, and (2) the limitations of conventional gradient descent in DNN training, such as vanishing gradients and slow convergence. The proposed Fractional-Order (FODNNs) leverage the memory effects and non-local properties of fractional derivatives Grünwald–Letnikov definition) to enhance gradient computation and error propagation during backpropagation. Experimental results demonstrate that FODNNs reduce localization error by 50% (achieving a mean error of 0.21 ± 0.03 m vs. 0.42 ± 0.07 m for DNNs and converge 44.4% faster ($50\pm 3$ epochs vs. $90\pm 5$ epochs), while maintaining sub-0.25 m accuracy even in high-noise conditions (SNR $<$ 10 dB). The framework also shows superior robustness, with only 12.3% performance degradation under noise compared to 38.7% for DNNs.