Abstract
Most of the methodologies for the solution of state-space models are based on the Kalman Filter algorithm (Kalman, 1960), developed for the solution of linear, dynamic state-space models. The most straightforward extension to nonlinear systems is the Extended Kalman Filter (EKF). The Limiting EKF (LimEKF) is a new algorithm that obviates the need to compute the Kalman gain matrix on-line, as it can be calculated off-line from pre-computed gain matrices. In this research, several different strategies for the construction of the gain matrices are presented: e.g. average of previously computed matrices per interval per demand level and average of previously computed matrices per interval independent of demand level.
Two case studies are presented to investigate the performance of the LimEKF under the different assumptions. In the first case study, a detailed experimental design was developed and a large number of simulation runs was performed in a synthetic network. The results suggest that indeed the LimEKF algorithm is robust and - while not requiring the explicit computation of the Kalman gain matrix, and thus having vastly superior computational properties - its accuracy is close to that of the “exact” EKF. In the second case study, a smaller number of scenarios is evaluated using a real-world, large-scale network in Stockholm, Sweden, with similarly encouraging results. Taking the average of various pre-computed Kalman Gain matrices possibly reduces the noise that creeps into the computation of the individual Kalman gain matrices, and this may be one of the key reasons for the good performance of the LimEKF (i.e. increased robustness).