Robustness and Sensitivity Metrics for Tuning the Extended Kalman Filter

In this paper, a robustness metric and a sensitivity metric have been defined, which can be used to determine a suitable combination of the filter tuning parameters of the extended Kalman filter. These metrics are related to the innovation covariance and their derivation necessitates a change of paradigm from the estimated states to the estimated measurements. The characteristics of these metrics have been inferred in detail and these have been used to predict the root-mean-squared error (RMSE) performances in a 2-D falling body problem. To do so, a general method has been proposed in this paper to obtain an initial choice of the filter tuning parameters based on the available literature. The RMSE performances are then obtained for a range of variation of the most critical tuning parameter, namely the filter process noise covariance. In general, the characteristics predicted from the metrics correlate significantly with the RMSE performances, and hence these can be used to obtain the desired tradeoff between robustness and sensitivity in various filter applications.