Uncertainties in the environment and behavior model inaccuracies compromise the state estimation of a dynamic obstacle and its trajectory predictions, introducing biases in estimation and shifts in predictive distributions. Addressing these challenges is crucial to safely control an autonomous system. In this paper, we propose a novel algorithm SIED-MPC, which synergistically integrates Simultaneous State and Input Estimation (SSIE) and Distributionally Robust Model Predictive Control (DR-MPC) using model confidence evaluation. The SSIE process produces unbiased state estimates and optimal input gap estimates to assess the confidence of the behavior model, defining the ambiguity radius for DR-MPC to handle predictive distribution shifts. This systematic confidence evaluation leads to producing safe inputs with an adequate level of conservatism. Our algorithm demonstrated a reduced collision rate in autonomous driving simulations through improved state estimation, with a 54% shorter average computation time.

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