H∞-property of the discrete-time extended Kalman filter with stochastic ℓ2 disturbances

This work analyzes the energy gain of the discrete-time extended Kalman filter used as a nonlinear observer in the presence of stochastic ℓ₂ type disturbances to highlight another theoretical property of the ubiquitous extended Kalman filter. The stochastic analysis provides a bound on the ratio of estimation error energy to disturbance energy, which shows that along with being the locally optimal minimum variance estimator, the extended Kalman filter inherently has the H_∞-property. A special case of this result is also shown to be the H₂-property of the extended Kalman filter.