Bayesian Inference for Time Delay Systems with Application to Connected Automated Vehicles

In this paper, a Bayesian inference problem is set up to infer the time delay and the resistance models from the dynamics of a connected automated vehicle. The delayed rejection adaptive Metropolis Markov chain Monte Carlo method is applied to obtain the posterior distributions of time delay and resistance parameters simultaneously using experimental data. The estimations of the time delay are shown to be consistent among multiple datasets and different resistance models. The distribution of the posterior indicates that there exist multiple modes in time delay, corresponding to different behaviors in acceleration and deceleration.