Validating car-following behaviors of autonomous vehicles by structural assessment with empirical data

Many researchers argue that the modular perception–planning–control design of autonomous vehicles (AVs) inevitably introduces delays, yet how such delays influence car-following behaviors and what their magnitudes are remain uncertain due to limited empirical data and ineffective calibration methods. Using large-scale naturalistic autonomous vehicle trajectory data, we develop an optimization-based calibration framework that jointly estimates feedback delay in perception/decision and parasitic lag in actuation, and accommodates both linear constant-time-headway and nonlinear intelligent-driver-model controllers. The method combines Bayesian optimization (BO) for globally searching delay parameters with simultaneous perturbation stochastic approximation (SPSA) for efficiently tuning controller parameters. Results show that incorporating both delays substantially improves model accuracy, reducing the root mean square error (RMSE) by up to an order of magnitude compared with models without delays, while linear controllers reproduce AV trajectories more faithfully and local calibration proves more accurate for short horizons whereas global calibration is more reliable for long horizons.