We present an observer design for systems with controlled nonlinear dynamics and nonlinear observation. The design is a development of earlier work, which was motivated by nonlinear filtering asymptotics. The basic design requires that the initial conditions belong to a bounded region determined by the data and design parameters. However, for a certain class of systems, no such a priori knowledge is required. To illustrate the utility of our design, several examples are given. In particular, we obtain an observer for bilinear control systems.