High-fidelity Digital Twins (DTs) are standard tools for offline tasks such as virtual prototyping and validation, yet their deployment in real-time control applications remains limited. The Twin-in-the-Loop (TiL) observer architecture addresses this by leveraging a DT as an embedded prediction model to simultaneously estimate the full state of a complex system. However, the use of a black-box DT precludes analytic gradients, turning observer tuning into a challenging high-dimensional, zeroth-order optimization problem. This study addresses this challenge by applying and extending Gradient Information with Bayesian Optimization ( GIBO ), an algorithm designed for high-dimensional black-box local optimization. We introduce GIBO+LS , a novel variant augmented with a one-dimensional line search, which significantly reduces convergence variability and computational time. Furthermore, we integrate a pseudo-random warm-start strategy and an average-cost optimization across multiple datasets to enhance global search capabilities and empirical robustness. Case studies in a vehicular application using real-world data demonstrate that the proposed method reduces median velocity estimation error by 34% over previous TiL tuning methods and by up to 46% over established Kalman-filter benchmarks.
Delcaro et al. (Sat,) studied this question.