Identification of Noise Covariances for State Estimation of a Continuous Fermenter Using Extended EM Algorithm

Despite developments in sensor technology, monitoring a biological process using regular sensor measurements is often difficult. Development of Bayesian state observers, such as extended Kalman filter(EKF), is an attractive alternative for soft-sensing of such complex systems. The performance of EKF is dependent on the accurate characterisation of the uncertainties in the state dynamics and in the measurements. In this work, an extended expectation maximisation (EM) algorithm is developed for estimation of the state and measurement noise covariances for the EKF using irregularly sampled multi-rate measurements. The efficacy of the proposed approach is demonstrated on a benchmark continuous fermenter system. The simulation results reveal that the proposed approach generates fairly accurate estimates of the noise covariances.