An Augmented Multiple Imputation Particle Filter for River State Estimation With Missing Observation

In this article, a new form of data assimilation (DA) method namely multiple imputation particle filter with smooth variable structure filter (MIPF–SVSF) is proposed for river state estimation. This method is introduced to perform estimation during missing observation by presenting new sets of data. The contribution of this work is to overcome the missing observation, and at the same time improve the estimation performance. The convergence analysis of the MIPF–SVF is discussed and shows that the method depends on the number of particles and imputations. However, the number of particles and imputations is influenced by the error difference in the likelihood function. By bounding the error, the ability of the method can be improved and the number of particles and computational time are reduced. The comparison between the proposed method with EKF during complete data and multiple imputation particle filter shows the effectiveness of the MIPF–SVSF. The percentage improvement of the proposed method compared to MIPF in terms of root mean square error is between 12 and 13.5%, standard deviation is between 14 and 15%, mean absolute error is between 2 and 7%, and the computational error is reduced between 73 and 90% of the length of time required to perform the estimation process.