The technical note presents a new technique for the adaptive parameter estimation in nonlinear parameterized dynamical systems. The technique proposes an uncertainty set-update approach that guarantees forward invariance of the true value of the parameters. In addition, it is shown that in the presence of sufficiently exciting state trajectories, the parameter estimates converge to the true values and the uncertainty set vanishes around the true value of the parameters. The set-based approach is also shown to identify when the parameter estimates are biased. Two simulation examples are presented that demonstrate the effectiveness of the technique.