CONSTRAINED EXTENDED KALMAN FILTER FOR NONLINEAR STATE ESTIMATION

Constraints on state variables are commonly encountered in dynamic state estimation in the form of algebraic equality and/or inequality constraints. For weakly nonlinear systems, the extended Kalman filter (EKF) has found numerous uses as a suboptimal state estimator. Unfortunately the structure of the filter does not include constraints on the states. The failure of unconstrained EKF is frequently cited as motivation for moving horizon estimation (MHE) methods for constrained state estimation. However, work on actually imposing the constraints in the existing EKF framework is scarce. This paper presents analytical solutions to the state constrained EKF (CEKF) for a class of linear constraints. It is possible to implement the CEKF efficiently with little additional computation cost and avoid expensive online optimization in MHE. The MHE is a general suboptimal strategy to impose constraints on states, noise processes and inputs, but for a class of state constraints, the proposed CEKF is sufficient. The performance of CEKF is illustrated with a simulation study of a nonlinear batch reactor.