State Estimation for Continuous-Discrete-Time Nonlinear Stochastic Systems

State estimation incorporates the feedback in optimization based advanced process control systems and is very important for the performance of model predictive control. We describe the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and a particle filter for continuous-discrete time nonlinear systems involving stochastic differential equations. Continuous-discrete time nonlinear systems is a natural way to model physical systems controlled by digital controllers. We implement the state estimation methods in Matlab, illustrate and evaluate their performance using simulations of the modified four-tank system. This system is non-stiff and the state estimation methods are implemented numerically using an explicit numerical integration scheme. We evaluate the accuracy of the state estimation methods in terms of the mean absolute percentage error over the simulation horizon. Each method successfully estimates the states and unmeasured disturbances of the simulated modified four-tank system. The key contribution is an overview and comparison of state estimation methods for continuous-discrete time nonlinear stochastic systems. This can guide efficient implementations.