Chromatographic separation is a powerful technique based on the differential adsorption of the components of a mixture. In simulated moving bed (SMB) chromatographic processes, a counter-current movement of the liquid and the solid phases is achieved by periodically switching the inlet and the outlet ports in a closed loop of chromatographic columns. This paper addresses the problem of state observation of simulated moving bed (SMB) chromatographic processes. The proposed approach is based on a reduced model obtained via the proper orthogonal decomposition (POD) method. The state estimation is performed using a nonlinear observer designed for Lipschitz LPV (linear parameter varying) systems. Numerical simulations are provided to validate the proposed approach.