Estimating the states of a dynamic system employing moving horizon estimation (MHE)

This paper deals with estimating the states of a wastewater treatment plant (WWTP) regarding equality constraints acting on the states. First a reduced nonlinear model is presented, which is based on the rate of biomass growth in a continuous bioreactor. Then, a simulation study is performed to observe the state fluctuation of the presented model EKF is deficient in dealing with constraint problems and there is no way to involve the constraints which often act on the system. Therefore, it leads us to introduce moving horizon estimation (MHE) as a solution to this problem. MHE is actually an optimization problem which can be solved with various methods. We will introduce Shor´s r-algorithm which is selected to realize this goal. Finally, the results obtained of both unconstrained extended Kalman filter and moving horizon estimation techniques are compared with each other. The result of this comparison demonstrates that in spite of possessing more processing time, MHE has less error during the period of simulation.