This paper presents a novel approach to design estimators for nonlinear systems. The approach is based on a combination of linear Moving Horizon Estimation (MHE) and Direct Virtual Sensor (DVS) techniques, and allows the design of estimators with guaranteed stability, which can account for convex constraints on the variables to be estimated. It is also shown that the designed estimators are optimal, in the sense that they give minimal worst-case estimation error, on the basis of the available finite number of noise-corrupted data, with respect to an ideal MHE filter (obtained by assuming exact knowledge of the system dynamics and of the global solution of the related nonlinear program). The approach is tested on a nonlinear mass-spring-damper system. (C) 2012 Elsevier Ltd. All rights reserved.