On the difference between bounded jacobian and lipschitz observers for nonlinear estimation applications

This paper examines the performance of bounded Jacobian and Lipschitz observer design techniques for nonlinear estimation applications. The bounded Jacobian observer technique utilizes the mean value theorem to express the nonlinear estimation error dynamics as a convex combination of known matrices with time varying coefficients. The Lipschitz based observers are the most popular observer design technique used for nonlinear systems. But they are derived from more conservative Lipschitz conditions on the nonlinearity. Both observers are evaluated for longitudinal velocity estimation, vehicle roll angle estimation, and estimation in a polynomial nonlinear system with a large Lipschitz constant. The results show that the bounded Jacobian observer is the more appropriate observer for these problems.