Gravity matching is a key technology in gravity-aided inertial navigation. The traditional Sandia inertial matching algorithm introduces linearization errors using the linear error model, which can diminish navigation accuracy. To address this issue, we propose a novel gravity-matching algorithm based on modified adaptive transformed cubature quaternion estimation (MA-TCQUE), designed for a nonlinear error model to enhance accuracy in gravity-aided navigation. Additionally, the proposed algorithm can estimate the measurement noise matrix demonstrating improved filtering stability in complex and dynamic environments. Finally, simulation and experimental results validate the advantages of the proposed matching algorithm compared to existing state-of-the-art methods.