Synthesis of Robust State Estimation Algorithms Under Unknown Sensor Inputs

The problem of estimating the state of a dynamical system using sensor measurements becomes challenging when some of the measurements are modified by unknown inputs, which can arise due to sensor faults, modeling errors, or adversarial data injection attacks. To solve this problem, several authors have developed robust state estimation algorithms by assuming that the unknown input follows a known dynamical or probabilistic model. However, to the best of our knowledge, the stability of the existing algorithms under arbitrary unknown input sequences (which may violate the assumed dynamical or probabilistic model) has not been studied in the literature. In this paper, we address this limitation by proposing and analyzing a class of robust state estimation algorithms which unifies the existing algorithms. We derive stability guarantees that are applicable to a wider range of unknown input sequences, including (but not limited to) the ones considered in the literature. Through a numerical example, it is demonstrated that the proposed robust state estimation method achieves better state estimation performance than the existing algorithms in the presence of unknown inputs.