Design of Unknown Input Reconstruction Filter Based on Parity Equations for Errors-in-Variables Case

This paper presents a novel approach to the problem of unknown input estimation in the presence of measurement noise. The observer developed here is based on the parity equations concept, hence, in contrast to the Kalman filter-based approaches, it is orthogonal (independent) to the system state vector. Therefore, due to the reduction of the number of estimated signals, an increased accuracy of the input estimation is achieved. This makes the scheme advantageous in cases when the accuracy of the unknown input estimate is crucial and knowledge about the system states is not required. By increasing the order of the parity space, which is a tuning parameter of the proposed algorithm, the influence of measurement noise can be reduced. An errors-in-variables case is considered, i.e. both measured input and output signals are affected by noise. A Lagrange multiplier method is used to obtain an analytical solution for the filter parameters. The proposed technique is suitable for both minimum-phase and nonminimum-phase systems.