This paper explores the sensing capabilities of Stark probes in estimating nonlinear gradient fields, both in single-particle and many-body interacting systems. The study reveals that the precision of estimating nonlinear gradient fields can achieve super-Heisenberg scaling, which increases linearly with the degree of nonlinearity. A universal algebraic relation between the scaling of precision and the nonlinearity degree is found, valid in both single-particle and many-body systems. This behavior is reflected in the phase transition from an extended to a localized phase, determined through finite-size scaling analysis. The system's phase diagram is analyzed in terms of both linear and nonlinear gradient fields, showing how the nonlocalized phase transitions to a localized one as Stark fields increase. The sensing precision of both linear and nonlinear Stark fields follows the same universal algebraic relation found for single-parameter sensing. The study demonstrates that simple and experimentally available measurements can reach theoretical precision bounds. Quantum-enhanced sensitivity is achievable even when considering the probe preparation time in resource analysis. The paper begins with an introduction to quantum sensing and estimation theory, including single- and multi-parameter quantum sensing. It then presents results for single-parameter estimation using single-particle and many-body interacting probes. The results for estimating a parabolic gradient potential, and hence multi-parameter estimation, are reported. The study shows that the QFI (Quantum Fisher Information) scales with the system size and nonlinearity degree, with the QFI in the localized phase decaying algebraically. The analysis reveals that the QFI in the localized phase is universal and independent of the nonlinearity degree. The study also shows that the critical exponents for the Stark transition depend on the nonlinearity degree, with the exponent 1/ν decreasing as nonlinearity increases. The results indicate that the super-Heisenberg scaling precision of Stark probes improves with increasing nonlinearity, and that the nonlinearity of the gradient field plays a stronger role in many-body probes, leading to sharper growth of the scaling exponent β. The study also shows that the quantum-enhanced sensitivity is achievable in both single-particle and many-body probes, with the QFI scaling linearly with the system size in the half-filled probe. The results confirm that the super-Heisenberg scaling precision offered by Stark probes is indeed obtainable using experimentally available measurements. The study also includes resource analysis, showing that the preparation time of the probe can be considered as another resource, and that the ultimate scaling of the QFI matrix elements is obtained after considering the preparation time. The results confirm that quantum-enhanced sensitivity is achievable even when considering the probe preparation time in resource analysis.This paper explores the sensing capabilities of Stark probes in estimating nonlinear gradient fields, both in single-particle and many-body interacting systems. The study reveals that the precision of estimating nonlinear gradient fields can achieve super-Heisenberg scaling, which increases linearly with the degree of nonlinearity. A universal algebraic relation between the scaling of precision and the nonlinearity degree is found, valid in both single-particle and many-body systems. This behavior is reflected in the phase transition from an extended to a localized phase, determined through finite-size scaling analysis. The system's phase diagram is analyzed in terms of both linear and nonlinear gradient fields, showing how the nonlocalized phase transitions to a localized one as Stark fields increase. The sensing precision of both linear and nonlinear Stark fields follows the same universal algebraic relation found for single-parameter sensing. The study demonstrates that simple and experimentally available measurements can reach theoretical precision bounds. Quantum-enhanced sensitivity is achievable even when considering the probe preparation time in resource analysis. The paper begins with an introduction to quantum sensing and estimation theory, including single- and multi-parameter quantum sensing. It then presents results for single-parameter estimation using single-particle and many-body interacting probes. The results for estimating a parabolic gradient potential, and hence multi-parameter estimation, are reported. The study shows that the QFI (Quantum Fisher Information) scales with the system size and nonlinearity degree, with the QFI in the localized phase decaying algebraically. The analysis reveals that the QFI in the localized phase is universal and independent of the nonlinearity degree. The study also shows that the critical exponents for the Stark transition depend on the nonlinearity degree, with the exponent 1/ν decreasing as nonlinearity increases. The results indicate that the super-Heisenberg scaling precision of Stark probes improves with increasing nonlinearity, and that the nonlinearity of the gradient field plays a stronger role in many-body probes, leading to sharper growth of the scaling exponent β. The study also shows that the quantum-enhanced sensitivity is achievable in both single-particle and many-body probes, with the QFI scaling linearly with the system size in the half-filled probe. The results confirm that the super-Heisenberg scaling precision offered by Stark probes is indeed obtainable using experimentally available measurements. The study also includes resource analysis, showing that the preparation time of the probe can be considered as another resource, and that the ultimate scaling of the QFI matrix elements is obtained after considering the preparation time. The results confirm that quantum-enhanced sensitivity is achievable even when considering the probe preparation time in resource analysis.