  Robots deployed to the real world must be able to interact with other agents
in their environment. Dynamic game theory provides a powerful mathematical
framework for modeling scenarios in which agents have individual objectives and
interactions evolve over time. However, a key limitation of such techniques is
that they require a-priori knowledge of all players' objectives. In this work,
we address this issue by proposing a novel method for learning players'
objectives in continuous dynamic games from noise-corrupted, partial state
observations. Our approach learns objectives by coupling the estimation of
unknown cost parameters of each player with inference of unobserved states and
inputs through Nash equilibrium constraints. By coupling past state estimates
with future state predictions, our approach is amenable to simultaneous online
learning and prediction in receding horizon fashion. We demonstrate our method
in several simulated traffic scenarios in which we recover players' preferences
for, e.g., desired travel speed and collision-avoidance behavior. Results show
that our method reliably estimates game-theoretic models from noise-corrupted
data that closely matches ground-truth objectives, consistently outperforming
state-of-the-art approaches.
