A strong tracking extended Kalman observer for nonlinear discrete-time systems

The authors show how the extended Kalman filter, used as an observer for nonlinear discrete-time systems or extended Kalman observer (EKO), becomes a useful state estimator when the arbitrary matrices, namely R_k and Q_k, are adequately chosen. As a first step, we use the linearization technique given by Boutayed et al. (1997), which consists of introducing unknown diagonal matrices to take the approximation errors into account. It is shown that the decreasing Lyapunov function condition leads to a linear matrix inequality (LMI) problem, which points out the connection between a good convergence behavior of the EKO and the instrumental matrices R_k and Q _k. In order to satisfy the obtained LMI, a particular design of Q_k is given. High performances of the proposed technique are shown through numerical examples under the worst conditions