  The localization-delocalization transition can be leveraged as a resource for
achieving quantum-enhanced sensitivity in parameter estimation. We demonstrate
that by employing different classes of localization-delocalization transition
potentials one can significantly enhance the precision of parameter estimation.
Specifically, we focus on the precision measurement of the Stark strength
parameter encoded in the ground state of a one-dimensional fermionic lattice
under the influence of Aubry-Andr{\'e}-Harper (AAH) localization-delocalization
transition. We consider the single-particle system and the system at
half-filling. Our work reveals that the Quantum Fisher Information (QFI) offers
a superior scaling with respect to the system size in comparison to the pure
stark case, leading to a better parameter estimation. However, experimentally
measuring fidelity-based QFI in a many-body system poses significant
challenges. To address this, we suggest experimentally relevant operators that
can be utilized to achieve precision surpassing the Heisenberg Limit (HL) or
can even saturate the QFI scaling. These operators, relevant for practical
experimental setups, provides a feasible pathway to harness the advantages
offered by the localization-delocalization transition by exploiting two
distinct localizing potentials for quantum-enhanced parameter estimation.
