Enhancing and Generalizing Position-Velocity Tracking in Imperfect <i>mm</i>Wave Systems Using a Low-Complexity Neural Network

This work aims to enhance and generalize the joint position-velocity tracking process in millimeter wave (mmWave) systems that suffer from hardware impairments (HWIs), all while considering computational complexity. Initially, we investigate the performance of two widely used traditional trackers: the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). Through this investigation, we identify the strengths and limitations of these trackers. Besides, we evaluate the gap between traditional tracking performance and the theoretical optimum by deriving the Bayesian Cramér-Rao Bound (BCRB) as a benchmark. Our findings reveal a significant disparity between the performance of traditional trackers and the benchmark, with performance being influenced by noise characteristics, initial conditions, and the accuracy of prior knowledge about the transition model. To address these challenges, we propose a neural network (NN)-based approach to achieve accurate and generalized tracking without relying on prior knowledge of the transition model, initial conditions, or noise characteristics. Specifically, our method trains a NN that performs effectively under any noise conditions, without needing to recognize the transition model or initial state. To manage the computational demands of the training phase, we employ a low-complexity algorithm, the Extreme Learning Machine (ELM), which calculates weights and biases through closed-form solution, avoiding complex optimization processes. Finally, we validate the accuracy and generality of the ELM tracker through computer simulations, testing it under various scenarios, including Gaussian and non-Gaussian HWI distortions, as well as systems with known transition models and those involving uncharacterized inputs.