This work investigates the state estimation in a batch process based on the particle filter method. Considering that the two dimensional dynamics and the key parameters are obtained online with low accuracy or offline with large time delay

a two dimensional state transition model and delayed measurement model are developed. In addition

a two dimensional state estimation algorithm is proposed by using Bayesian method and the forward-backward smoothing algorithm. The proposed algorithm improves the estimation accuracy by fusing information of previous batches and delayed measurements

and overcomes the influence of the uncertainty of offline sampling period and time delay. The applications in a numerical example and a beer fermentation show the effectiveness of the proposed method.