Unilateral Constrained Extended Kalman Filter

This letter proposes an extension of the Extended Kalman Filter (EKF) for the state estimation of systems with unilateral constraints. The extension is a Unilateral Constrained Extended Kalman Filter (UCEKF) able to estimate the state of such systems conformed by continuous and discontinuous phases and a switching rule among them. In the continuous phase, the UCEKF is the EKF. In the discontinuous phase, when the constraint is active, the Differential Riccati Equation (DRE) solution of the UCEKF is deliberately modified to keep a quadratic Lyapunov function bounded. Such a function is quadratic in the estimation error and dependent on the DRE solution. The boundedness of such a function guarantees the boundedness of the estimation error at the discontinuous phase due to its nature. This function is also employed to prove the internal asymptotic convergence of the proposed UCEKF. The performance of both UCEKF and EKF is compared on a discontinuous Van der Pol oscillator state estimation task. Results confirm that the UCEKF outperforms the EKF in such state estimation.