Finite-time mean-square boundedness, H2, and H∞-properties of the discrete-time extended Kalman filter for systems with independent sensor failures

The discrete-time extended Kalman filter designed for systems with independent sensor failures is analyzed for its finite-time mean-square boundedness as a function of initial conditions and its ability to attenuate effects of finite-energy disturbances as a function of the disturbance magnitudes. In addition to this extended Kalman filter being designed as a locally optimal minimum variance estimator, this work proves that it also has local finite-time mean-square boundedness of the estimation error, stochastic H
₂
, and H
_∞
properties. Simulations are provided that analyze the effect of the initial estimation error and the disturbance magnitude.