New offshore oil and gas discoveries are located at deep waters with long tie-back distances. Development of such fields require compact gas-liquid separation technologies. Efficient operation of such separators require multiple sensors and advanced controllers. However, the number of available sensors at the seabed is often limited due to low reliability (failures and low sampling frequency), lack of suitable sensor technology and/or high cost. Therefore, this paper develops a nonlinear MHE and UKF for estimation of indirectly measured and unmeasured variables. The estimates are used as state feedback to a linear MPC to study their estimation performance in simulations.