Assessment of forward and forward–backward Bayesian filters

This paper investigates a forward–backward filtering approach comprised of forward filters and backward smoothers assimilating estimations of a moving horizon estimation. Those evaluations were carried out for extended, unscented, and cubature combinations of the Kalman filters, besides a particle filter, an ensemble Kalman filter, and a moving horizon estimation. Three simulation scenarios were defined for two nonlinear case studies with different complexity to evaluate the estimation accuracy and computational time under different uncertainty conditions. The backward smoothing was found to degenerate for longer horizons; however, it improved the estimation accuracy with smaller horizons in most simulation scenarios in comparison to the respective filters alone. In addition, the method successfully reduced steady-state estimation bias under model mismatch with a small increase in computational time. The performance of the forward–backward filtering was found to be sensitive to active constraint; however, this drawback does not outweigh the meaningful performance improvements found in this study.