On state-estimation in weakly-observable scenarios and implicitly regularized observers

This work proposes a framework to design observers for systems that present low observability. It is shown that, in these scenarios, the estimation problem becomes ill-posed, which drastically limits the performance of standard observers, specially in the presence of noise. Consequently, this paper presents a method to design an observer that optimizes some potential function to be defined by the designer. This allows to implicitly regularize the estimation and recover a well-posed problem. The proposed technique is validated in a set of weakly-observable systems and the performance is compared with a common Kalman filter-like observer.