Development of grey-box unscented kalman filter for systems subjected to correlated unmeasured disturbances

The performance of Bayesian state estimators is dependent on accurate characterisation of the uncertainties in the unmeasured disturbances and in the measurements. The structure of the unmeasured disturbance dynamics is seldom known. Moreover, the disturbances could be correlated in time. In this work a constrained optimisation problem based on the MLE framework is presented to identify the dynamics of the process noise and the covariances of both, the measurement noise and the process noise. The unmeasured process disturbances are modelled as entering the process through known inputs. The efficacy of this approach is tested on a continuous fermenter, which is a benchmark simulation case study. The results on the simulation case study reveal that the proposed approach generates reasonably accurate estimates of the noise dynamics and the covariances.