Linear Observer Learning by Temporal Difference

This paper proposes a method for learning optimal state estimators from input/output data for linear discrete-time stochastic systems. We show that this problem can be expressed in the reinforcement learning framework, suitably adapted to the peculiar problem structure. In particular, we introduce the specific Bellman equation for the state estimation problem and use temporal differences to solve it. We show in simulations that the resulting data-driven method for state estimation converges to the optimal observer.