A comparative study of Extended Kalman Filter and an optimal nonlinear observer for state estimation

A recently developed nonlinear H
_∞
observer and Extended Kalman Filter (EKF) offer two filters for state estimation in nonlinear systems. The Riccati equation that arises while developing the nonlinear H
_∞
observer is compared with the Riccati equation arising from the Extended Kalman Filter (EKF). Variations between the two Riccati equations translate into the differences in the performance of these alternative estimation methods. The H
_∞
filter offers faster convergence of the estimation covariance at large estimation errors during the transience of the filter. The Extended Kalman Filter, on the other hand, maintains higher levels of optimality at steady state at the expense of higher computational load. An LMI formulation for the H
_∞
filter is also presented that allows leveraging the bound on the nonlinearity to seek a stable filter for nonlinear systems.