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.

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