Receding Horizon Estimation of Arbitrarily Changing Unknown Inputs

Abstract

In this paper we present a receding horizon estimation method for linear time invariant systems, subject to unknown inputs. The proposed approach is based on the idea of asymptotically decoupling the state estimation problem from the unknown input estimation problem. Consequently, the latter is formulated as a weighted least squares problem in a receding horizon manner. The proposed method does not assume a dynamic model for the unknown input, but it allows to incorporate prior knowledge about its abrupt nature by adding ℓ1-regularization terms to the cost function of the weighted least squares problem. The receding horizon input estimation method and the necessary conditions for it to hold are outlined. The proposed method is illustrated in simulation for the case of abruptly changing piece-wise constant unknown inputs.