(301af) Development of Systematic Tuning Procedures for Extended Kalman Filtering

Methods for assisted tuning of extended Kalman filters are presented. A well-known drawback of Kalman filters is that knowledge about process and measurement noise statistics is required from the user. It may be possible to determine the measurement noise covariance from measurements but determining the process noise covariance is more difficult. Furthermore, it is often the case that the covariances change during filter operation, which means that methods for adapting the covariance matrices on-line are needed. Tuning the filter, i.e. choosing the values of the process and measurement noise covariances so that the filter performance is optimized with respect to some performance index, is a challenging task. Performing it manually is time-consuming with no guarantee for optimality. Moreover, a user applying an extended Kalman filter may not possess the necessary skills for the task and poor tuning may result in unsatisfactory performance of an otherwise powerful algorithm. It is therefore desirable to develop systematic procedures for extended Kalman filter tuning.

In this paper, the extended Kalman filter is used for state estimation of nonlinear stochastic continuous-discrete time systems. These systems consist of a stochastic differential equation describing the state evolution and a stochastic algebraic measurement equation. Methods for filter tuning are initially evaluated on numerical examples. The performance is demonstrated with soft sensors developed for estimation of biomass and product activity on an industrial fed-batch cultivation. The demonstration includes the initial adaptation of a few cultivation specific parameters.