This note proposes a new form of nonlinear state estimator, for which we can establish robust global asymptotic stability (RGAS) in the case of bounded disturbances. In this estimator, a max term is added to the usual sum of stage costs, and one additional assumption is made relating the initial state stage cost to the system’s detectability condition. A simulation example is presented to illustrate the estimator’s performance. Two open issues are presented: (i) the proof of estimator convergence for convergent disturbances and (ii) changing from full information estimation to moving horizon estimation (MHE), which has a smaller and more tractable online computational complexity.