Particle filters for state and parameter estimation in batch processes

In process engineering, on-line state and parameter estimation is a key component in the modelling of batch processes. However, when state and/or measurement functions are highly non-linear and the posterior probability of the state is non-Gaussian, conventional filters, such as the extended Kalman filter, do not provide satisfactory results. This paper proposes an alternative approach whereby particle filters based on the sequential Monte Carlo method are used for the estimation task. Particle filters are initially described prior to discussing some implementation issues, including degeneracy, the selection of the importance density and the number of particles. A kernel smoothing approach is introduced for the robust estimation of unknown and time-varying model parameters. The effectiveness of particle filters is demonstrated through application to a benchmark batch polymerization process and the results are compared with the extended Kalman filter.