  Humans make daily routine decisions based on their internal states in
intricate interaction scenarios. This paper presents a probabilistically
reconstructive learning approach to identify the internal states of
multi-vehicle sequential interactions when merging at highway on-ramps. We
treated the merging task's sequential decision as a dynamic, stochastic process
and then integrated the internal states into an HMM-GMR model, a probabilistic
combination of an extended Gaussian mixture regression (GMR) and hidden Markov
models (HMM). We also developed a variant expectation-maximum (EM) algorithm to
estimate the model parameters and verified it based on a real-world data set.
Experiment results reveal that three interpretable internal states can
semantically describe the interactive merge procedure at highway on-ramps. This
finding provides a basis to develop an efficient model-based decision-making
algorithm for autonomous vehicles (AVs) in a partially observable environment.
