  This paper studies an optimization-based state estimation approach for
discrete-time nonlinear systems under bounded process and measurement
disturbances. We first introduce a full information estimator (FIE), which is
given as a solution to minimize a cost function by using all the available
measurements. Then, we prove that the FIE of an incrementally
input/output-to-state stable system is robustly globally asymptotically stable
under a certain class of cost functions. Moreover, the implications and
relationships with related results in the literature are discussed. Finally, a
simple example is included to illustrate the theoretical results.
