Data driven approach for performance assessment of linear and nonlinear Kalman filters

A new technique is developed for assessing the performance of linear and nonlinear Kalman filter based state estimators. The proposed metric will indicate the performance of these state estimators which will be primarily influenced by: (i) difference between the model dynamics and process dynamics and, (ii) various approximations of the nonlinear plant dynamics used in nonlinear Kalman filters. Currently, there exists no such quantification method to analyze the performance of linear and nonlinear Kalman filters, a key requirement for improvement and a practical benchmark for comparison of these state estimation algorithms. The proposed technique uses the generalized Hurst exponent of the prediction errors (difference in measured output and a posteriori estimates) obtained from the state estimators to quantify the performance. This technique could be implemented on-line as it requires only plant operating data and the predicted outputs (from the linear and nonlinear Kalman filters) to assess the performance. Several simulation studies demonstrate the applicability of the proposed performance metric to both linear and non-linear Kalman filters.