H_∞-Property of the Continuous-Time Extended Kalman Filter Available to Purchase

This work elucidates another theoretical property of the ubiquitous extended Kalman filter by analyzing the energy gain of the continuous-time extended Kalman filter used as a nonlinear observer in the presence of finite-energy disturbances. The analysis provides a bound on the ratio of estimation error energy to disturbance energy, which shows that the extended Kalman filter inherently has the H_∞-property along with being the locally optimal minimum variance estimator. A special case of this result is also shown to be the H₂-property of the extended Kalman filter.