Zonotopic Constrained Kalman Filter Based on a Dual Formulation

This paper presents a new zonotopic constrained approach for the Kalman filter that takes advantage of the particular structure of the original optimization problem. This technique consists in projecting the state estimation by solving an optimization problem, to ensure that the estimated state belongs to a zonotope. Based on a classical gradient algorithm method, i.e. the iterative shrinkage-thresholding algorithm (ISTA), this paper proposes a reduced complexity approach suitable for the state estimation of systems subject to a large number of state constraints. The algorithm's speed is improved via a faster ISTA approach, called FISTA.