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Abstract-A simple procedure to include state inequality constraints in the Unscented Kalman Filter is proposed. With this procedure, the information of active state constraints influences the state covariance matrix, resulting in better estimates. In a numerical example, the approach outperforms the Extended Kalman Filter implemented with constraint handling via "clipping". I. INTRODUCTIONIn the process industries one of the main goals is to make the end product at the lowest possible cost while satisfying product quality constraints. State estimation often play an important role in accomplishing this goal in process control and performance monitoring applications. There are many uncertainties to deal with in process control; model uncertainties, measurement uncertainties and uncertainties in terms of different noise sources acting on the system. In this kind of environment, representing the model state by an (approximated) probability density function (pdf) has distinct advantages. State estimation is a means to propagate the pdf of the system states over time in some optimal way. It is most common to use the Gaussian pdf to represent the model state, process and measurement noises. The Gaussian pdf can be characterized by its mean and covariance. The Kalman Filter (KF) propagates the mean and covariance of the pdf of the model state in an optimal (minimum mean square error) way in case of linear dynamic systems [5].All practical systems possess some degree of nonlinearity. Depending on the type of process and the operating region of the process, some processes can be approximated with a linear model and the KF can be used for state estimation. In some cases the linear approximation may not be accurate enough, and state estimator designs using nonlinear process models are necessary. The most common way of applying the KF to a nonlinear system is in the form of the Extended Kalman Filter (EKF). In the EKF, the pdf is propagated through a linear approximation of the system around the operating point at each time instant. In doing so, the EKF needs the Jacobian matrices which may be difficult to obtain for higher order systems, especially in the case of timecritical applications. Further, the linear approximation of the system at a given time instant may introduce errors in the state which may lead the state to diverge over time. In other words, the linear approximation may not be appropriate for some systems. In order to overcome the drawbacks of the

With increasing incentives for reducing the CO2 emissions offshore, optimization of energy usage on offshore platforms has become a focus area. Most of offshore oil and gas platforms use gas turbines to support the electrical demand on the platform. It is common to operate a gas turbine mostly under part-load conditions most of the time in order to accommodate any short term peak loads. Gas turbines with flexibility with respect to fuel type, resulting in low turbine inlet and exhaust gas temperatures, are often employed. The typical gas turbine efficiency for an offshore application might vary in the range 20–30%. There are several technologies available for onshore gas turbines (and low/medium heat sources) to convert the waste heat into electricity. For offshore applications it is not economical and practical to have a steam bottoming cycle to increase the efficiency of electricity production, due to low gas turbine outlet temperature, space and weight restrictions and the need for make-up water. A more promising option for use offshore is organic Rankine cycles (ORC). Moreover, several oil and gas platforms are equipped with waste heat recovery units to recover a part of the thermal energy in the gas turbine off-gas using heat exchangers, and the recovered thermal energy acts as heat source for some of the heat loads on the platform. The amount of the recovered thermal energy depends on the heat loads and thus the full potential of waste heat recovery units may not be utilized. In present paper, a review of the technologies available for waste heat recovery offshore is made. Further, the challenges of implementing these technologies on offshore platforms are discussed from a practical point of view. Performance estimations are made for a number of combined cycles consisting of a gas turbine typically used offshore and organic Rankine cycles employing different working fluids; an optimal media is then suggested based on efficiency, weight and space considerations. The paper concludes with suggestions for further research within the field of waste heat recovery for offshore applications.