Nonlinear filtering based on lattice trajectory piecewise linear approximation with application to a wastewater treatment plant

State estimation is a vital part of state-feedback controller design. The extended Kalman filter (EKF) approximates the original nonlinear system through successive linearization. The linearization points are selected at each sample instant, which is computational complex and may not reflect the overall trend of the nonlinear system. In this paper, we propose a nonlinear filtering method based on lattice trajectory piecewise linear (LTPWL) approximation, named LTPWL-KF, in which the nonlinear system is approximated by the LTPWL model offline, and the online state estimation is then based on the constructed piecewise linear (PWL) system. The boundedness of the variances of the estimation error is proved. A simulation study on a wastewater treatment plant (WWTP) is performed. The results show that the estimation performance of LTPWL-KF is comparable with that of EKF, and the online computational burden of LTPWL-KF is less.