Constrained particle filtering methods for state estimation of nonlinear process

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Increasingly in practical applications, nonlinearity, non‐Gaussianity, and constraint must be considered to obtain good state estimation. A constrained particle filter (PF) approach for state estimation, which involves three alternative strategies to impose the constraints on the prior particles, posterior particles, and state estimation has been proposed. First, to impose constraints on prior particles, a constrained Gibbs sampling method with a constrained inverse transform sampling is proposed to restrict sampling within the constraint region under cases of both univariate and coupling constraints. Second, to ensure validity of posterior particles, resampling is confined to the valid prior particles and the violated ones are discarded, which results in a similar formulation as the existing acceptance/rejection constrained PF method in literature. Third, if the state estimation violates the constraint, different from the existing methods that either discard all violated particles or accept all of them by projecting them onto the constraint region, the proposed method makes a balance between the prior and the likelihood function by adjusting the weights of violated and valid particles, respectively. Compared with the existing methods, the proposed method provides better physical interpretation and involves no restrictive assumptions about the distributions. Simulation results demonstrate effectiveness of the proposed methods. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2072–2082, 2014