In this dissertation, the discrete-time extended Kalman filter is analyzed for its ability to attenuate finite-energy disturbances, known as the H infinity property. Though the extended Kalman filter is designed to be a locally optimal minimum variance estimator, this dissertation proves that it has additional properties, such as Hinfinity. This analysis is performed with the extended Kalman filter in direct form. Since this form reduces assumptions placed on the system in previous works on convergence and H2-properties of the extended Kalman filter, the extended Kalman filter used as a nonlinear observer for noise-free models is revisited using the direct form to demonstrate these properties.;Additionally, two representations for the discrete-time uncertain measurement model with finite-energy disturbances are considered: 1) each sensor in the measurement can fail independently with different failure rates and 2) all of the sensors in the measurement fail at the same time. The discrete-time extended Kalman filters designed for such models are analyzed for general convergence, the H2-property, and the Hinfinity-property.;As an extension of this work, the continuous-time extended Kalman filter is applied to systems with finite-energy disturbances. This continuous-time extended Kalman filter is shown to inherently have the Hinfinity-property. Simulation studies have been performed on all of the extended Kalman filters in this dissertation. These simulation studies demonstrate that when the extended Kalman filters converge, they will also exhibit the H2 and H infinity properties. The bounds developed on these properties are affected by the same constraints that affect convergence, i.e. magnitudes of the initial estimation error and the disturbance as well as the severity of the nonlinearities in the model.
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