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Precise estimation of state variables and model parameters is essential for efficient process operation. Bayesian formulation of the estimation problem suggests a general solution for all types of systems. Even though the theory of Bayesian estimation of nonlinear dynamic systems has been available for 4 decades, practical implementation has not been feasible because of computational and methodological challenges. Consequently, most existing methods rely on simplifying assumptions to obtain a tractable but approximate solution. For example, extended Kalman filtering linearizes the process model and assumes Gaussian prior and noise. Movinghorizon-based least-squares estimation also assumes Gaussian or other fixed-shape prior and noise to obtain a least-squares optimization problem. This approach can impose constraints but is nonrecursive and requires computationally expensive nonlinear or quadratic programming. This paper introduces sequential Monte Carlo sampling for Bayesian estimation of chemical process systems. This recent approach approximates computationally expensive integration by recursive Monte Carlo sampling and can obtain posterior distributions accurately and efficiently with minimum assumptions. This approach has not been compared with estimation methods popular for chemical processes including moving-horizon estimation. In addition to comparing various methods, this paper also develops a novel empirical Bayes approach to deal with practical challenges due to degeneracy and a poor initial guess. The ability of the proposed approach to be more computationally efficient and at least as accurate as moving-horizon-based least-squares estimation is demonstrated via several case studies.

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The conditional probability density function (pdf) is the most complete statistical representation of the state from which optimal inferences may be drawn. The transient pdf is usually infinite-dimensional and impossible to obtain except for linear Gaussian systems. In this paper, a novel density-based filter is proposed for nonlinear Bayesian estimation. The approach is fundamentally different from optimization- and linearization-based methods. Unlike typical density-based methods such as probability grid filters (PGF) and sequential Monte Carlo (SMC), the cell filter poses an off-line probabilistic modeling task and an on-line estimation task. The probabilistic behavior is described by the Foias or Frobenius−Perron operators. Monte Carlo simulations are used for computing these transition operators, which represent approximate aggregate Markov chains. The approach places no restrictions on system model or noise processes. The cell filter is shown to achieve the performance of PGF and SMC filters at a fraction of the computational cost for recursive state estimation.