Recursive state estimation: Unknown but bounded errors and system inputs

A method is discussed for estimating the state of a linear dynamic system using noisy observations, when the input to the dynamic system and the observation errors are completely unknown except for bounds on their magnitude or energy. The state estimate is actually a set in state space rather than a single vector. The optimum estimate is the smallest calculable set which contains the unknown system state, but it is usually impractical to calculate this set. A recursive algorithm is developed which calculates a time-varying ellipsoid in state space that always contains the system's true state. Unfortunately the algorithm is still unproven in the sense that its performance has not yet been evaluated. The algorithm is closely related in structure but not in performance to the algorithm obtained when the system inputs and observation errors are white Gaussian processes. The algorithm development is motivated by the problem of tracking an evasive target, but the results have wider applications.