Batch and Moving Horizon Estimation for Systems Subjected to Non-Additive Stochastic Disturbances

Abstract

Nonlinear state estimation techniques for state dynamics involving additive discrete zero mean white noise have received considerable attention in the past. The probabilistic formulation of the conventional moving horizon estimation (MHE) is also developed under this simplifying assumption. In reality, the unmeasured disturbances affect the states and measurements in much more complex way and thus cannot be treated in additive manner. In current work, we formally introduce a probabilistic formulation of MHE which can handle such nonlinear uncertainties in the state dynamics. The efficacy of the proposed MHE has been demonstrated by conducting stochastic simulation studies on a benchmark continuous stirred tank reactor (CSTR) system. It is found that the estimation performance of the proposed MHE formulation is comparable to estimation performance of a sampling based Bayesian estimator (unscented Kalman filter or UKF), which deals with non-additive disturbances systematically, and significantly better than the extended Kalman filter (EKF) that deals with non-additive disturbances through successive linearization.