Bayesian Estimation of Unconstrained Nonlinear Dynamic Systems

Accurate estimation of state variables and model parameters is essential for efficient process operation. The Bayesian formulation of the estimation problem suggests a general solution for nonlinear systems. However, a practically feasible implementation of the solution has not been available until recently. Most existing methods have had to rely on simplifying assumptions to obtain an approximate solution. For example, extended Kalman filtering estimates the system state by linearizing the nonlinear model and assuming Gaussian distributions for all random variables. Moving horizon estimation assumes Gaussian or other fixed-shape distributions to formulate a constrained leastsquares optimization problem. In this paper, Bayesian estimation is implemented by sequential Monte Carlo sampling. This approach can represent non-Gaussian distributions accurately and efficiently with minimum assumptions and computes moments by Monte Carlo integration. The features of the Monte Carlo approach are demonstrated by application to a state estimation case study of a CSTR process. The proposed method exhibits 78% improvement in estimation error and takes 95% less time than moving horizon estimation to solve the problem.