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In this work, we present methods for state estimation in continuous-discretenonlinear systems involving stochastic differential equations. We present theextended Kalman filter, the unscented Kalman filter, the ensemble Kalmanfilter, and a particle filter. We implement the state estimation methods inMatlab. We evaluate the performance of the methods on a simulation of themodified four-tank system. We implement the state estimation methods fornon-stiff systems, i.e., using an explicit numerical integration scheme. Theimplementation of the extended Kalman filter utilises the Joseph stabilisingform for numerical stability. We evaluate the accuracy of the state estimationmethods in terms of the mean absolute percentage error over the simulationhorizon. We show that each method successfully estimates the states andunmeasured disturbances of the simulated modified four-tank system. Finally, wepresent conclusions.

State Estimation Methods for Continuous-Discrete Nonlinear Systems involving Stochastic Differential Equations