We propose an adaptive observer for a class of nonlinear time-varying systems, for which the regressor depends not only on the known inputoutput signals but also on all the unmeasured states. There are state disturbances, and measurements are corrupted by noise. The Lyapunov function method is used to prove that the coupled system-observer dynamics admits a state-independent input-to-output stability property in estimation errors from unknown inputs. Numerical simulations illustrate the presented approach on a three-dimensional crop irrigation model.