Determination of an unknown input distribution matrix for non-linear discrete-time stochastic systems

The paper deals with the problem of estimating an unknown input distribution matrix for non-linear discrete-time stochastic systems. In particular, it is shown how to use the unscented Kalman filter as an unknown input filter. Subsequently, an analysis of the impact of unknown input decoupling on the fault detection is performed and a suitable fault detection condition is developed. Based on the achieved results, a numerical optimisation-based approach is proposed that can be used to estimate the unknown input distribution matrix. The final part of the paper presents an illustrative example with an induction motor, which confirms the performance of the proposed approach.