Representing the Extended H _∞ Filter (EHF) as a Modified Extended Kalman Filter (EKF) for Predicting the Range of the Robustness Bound

In this paper, the extended H _∞ filter (EHF) has been logically reformulated as a modification of the extended Kalman filter (EKF). Thereafter, a robustness metric and a sensitivity metric have been defined, analogous to that in Saha et al. (IEEE Trans Instrum Meas 63(4):964–971, 2014 [1]), for the EHF which is used to determine a suitable combination of the filter tuning parameters. The major objective of this paper is to predict the usable range of the robustness bound γ for obtaining reliable filter performances. For this purpose, the same problem as in Saha et al. (IEEE Trans Instrum Meas 63(4):964–971, 2014 [1]) of tracking a 2D ballistic target has been studied and the desired states of the EHF have been chosen to be the same as the measurements. The plots of the metrics have been obtained for various choices of γ. The corresponding RMSE performances have then been plotted for each of these choices of γ, while the filter process noise covariance has been varied over the range obtained from the metric plot. It is observed that the metrics are useful in determining the usable range of γ for which the designer is able to obtain the desired trade-off between robustness and sensitivity.