Linearly Constrained EKF for Non Linear Estimation Applied to Three-Wheeled Vehicles

The extended Kalman filter (EKF) is one of the most popular estimation techniques that has been largely investigated for state estimation of nonlinear systems. However, performance of the EKF depends on the accurate knowledge of the state space parametric model and is particularly sensitive to different types of mismatches between the assumed state space model and the actual state space model. In this communication we show how linear equality constraints can be incorporated to the EKF in order to mitigate misspecification of the state model, which yields a linearly constrained EKF (LCEKF). As a toy model, we consider the problem of the position estimation of a three-wheeled vehicle. We exemplify through simulations, the capability of the LCEKF to mitigate some state modeling errors.