Parity equations-based unknown input reconstruction for MIMO stochastic systems with an application

In this paper an approach for reconstructing an unknown input for multiple-input multiple-output systems is presented. It is assumed that the system is affected by process noise, whereas the available system inputs are contaminated by measurement noise. The novel approach is based on a parity equations concept and forms an extension of the idea developed previously by the authors. A modification of the algorithm is also provided, which allows the approach to deal with systems whose zero is close to unity. The order of the parity space can be treated as a tuning parameter allowing for a trade-off between the smoothness of the reconstructed unknown input and a phase lag. An analytical solution of the overall problem is obtained by making use of a Lagrange multiplier method. The utility of the scheme is demonstrated when applied to a practical hydrological system.