A Behavioral Approach to Estimation in the Presence of Disturbances

In this article, we study the problem of estimation in the presence of disturbances within the context of the behavioral approach developed by J.C. Willems. For this purpose, we use the behavioral theory of observers introduced by Valcher, Willems, Trentelman, and Trumpf, combined with the notions of behavioral invariance, conditioned invariance, and behavioral detectability subspaces. With these tools, we provide necessary and sufficient conditions for the solvability of the aforementioned problem together with the construction of an estimator.