Constrained State Estimation - A Review

Increasingly for many real-world applications in signal processing, nonlinearity, non-Gaussianity, and additional constraints are considered while handling dynamic state estimation problems. This paper provides a critical review of the state of the art in constrained Bayesian state estimation for linear and nonlinear state-space systems. Specifically, we provide a review of unconstrained estimation using Kalman filters for the linear system, and their extensions for the nonlinear state-space system including extended Kalman filters, unscented Kalman filters, and ensemble Kalman filters. In addition, we present the particle filters for nonlinear state space systems and discuss recent advances. Next, we review constrained state estimation using all these filters where we highlighted the advantages and disadvantages of the different recent approaches.

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