Distributionally Robust Kalman Filtering over Finite and Infinite Horizon

Understand

This paper investigates the distributionally robust filtering of signals generated by state-space models driven by exogenous disturbances with noisy observations in finite and infinite horizon scenarios.

• The exact joint probability distribution of the disturbances and noise is unknown but assumed to reside within a Wasserstein-2 ambiguity ball centered around a given nominal distribution.
• We aim to derive a causal estimator that minimizes the worst-case mean squared estimation error among all possible distributions within this ambiguity set.
• We remove the iid restriction in prior works by permitting arbitrarily time-correlated disturbances and noises.