A new robust extended Kalman filter is proposed for the discrete-time nonlinear systems with norm-bounded parameter uncertainties. After linearization of the nonlinear systems, the uncertainties described by the energy bounded constraint can be converted into an indefinite quadratic cost function to be minimized. The solution to the minimization problem is given by the extended Kalman filter derived in a Krein space, which leads to a robust version of the extended Kalman filter. Since the resulting robust filter has the same structure as a standard extended Kalman filter, the proposed filter can be readily designed by simply including the uncertainty terms in its formulas. The results of simulations are presented to demonstrate that the proposed filter achieves the robustness against parameter variation and performs better than the standard extended Kalman filter.

An instrumental variable (IV) based linear estimator is proposed for effective target localization in sensor network by using time-difference-of-arrival (TDOA) measurement. Although some linear estimation approaches have been proposed in much literature, the target localization based on TDOA measurement still has a room for improvement. Therefore, we analyze the estimation errors of existing localization estimators such as the well-known quadratic correction least squares (QCLS) and the robust least squares (RoLS), and demonstrate advantages of the proposition by comparing the estimation errors mathematically and showing localization results through simulation. In addition, a recursive form of the proposition is derived to consider a real time application.