In this paper, we propose a hierarchical discretized-parameter polynomial adaptive estimator (HDPAE) to estimate parameters that occur non-linearly in dynamic systems that are non-linear and Lipschitz continuous. A non-linear persistent excitation ( NLPE) condition is introduced under which it is shown that the HDPAE is able to estimate the unknown parameters. This NLPE condition is shown to be entirely equivalent to and is no more restrictive than the linear persistent excitation (LPE) condition for linearly parameterized systems.