Position and Speed Estimation Using Deep Learning-Based KKL Observer in Mixed Autonomy Traffic Systems

This paper proposes a deep learning-based Kazantzis–Kravaris–Luenberger (KKL) observer design to estimate position and speed in mixed-autonomy traffic environments. The approach relies on position measurements of vehicles surrounding the autonomous vehicle (AV), obtained through remote sensing, resulting in a subsequent time delay due to communication latency. The proposed deep learning KKL observer is designed to compensate for this delay and to ensure global asymptotic convergence of the estimation of position and speed by using a chain of sub-observers. We employ an unsupervised learning-based approach to identify the nonlinear injective map involved in the KKL observer design, as well as its left inverse. Based on the obtained mappings, a chain of observers is designed in the latent space, ensuring global asymptotic convergence in both coordinates. The performance of the proposed deep learning-based KKL chain of observer estimation approach is evaluated through numerical simulations and validated using experimental data. Our findings underscore the importance of the KKL-based chain of observers in compensating for output-delayed measurements, thereby establishing a relationship between delay bounds and the number of sub-observers while ensuring stable performance in mixed-autonomy traffic environments.