We present a moving horizon estimation (MHE) application for multi-zone low-density (LDPE) polyethylene tubular reactors. The strategy incorporates a first-principles dynamic model comprised of large sets of nonlinear partial, differential and algebraic equations (PDAEs). It was found that limited temperature measurements distributed along the reactor are sufficient to infer all the model states in space and time and to track uncertain time-varying phenomena Such as fouling. A full discretization strategy and a state-of-the-art nonlinear programming (NLP) solver are used to enable the computational feasibility of the approach. It is demonstrated that the MHE estimator exhibits fast performance and is well suited for applications of industrial interest. Published by Elsevier Ltd.