Recursive state estimation of 2-D GM models with unknown but bounded errors

A method is proposed for estimating states of 2-D GM models by using noisy observations in the case when the input to the dynamic system and the observation errors are unknown except for bounds on their magnitude or energy. The designed state estimator is composed of a set in state space rather than a single vector. It is shown that the optimal estimator is the smallest set, which contains the unknown system state. A recursive algorithm is developed which calculates a time-varying ellipsoid in the state space.