Low-performing GPS receivers, often used in challenging scenarios such as attitude maneuver and attitude rotation, are frequently encountered for micro–nano satellites. To address these challenges, this paper proposes a modified robust adaptive hierarchical filtering algorithm (named IARKF). This algorithm leverages robust adaptive filtering to dynamically adjust the distribution of innovation vectors and employs a fading memory weighted method to estimate measurement noise in real time, thereby enhancing the filter’s adaptability to dynamic environments. A segmented adaptive filtering strategy is introduced, allowing for flexible parameter adjustment in different dynamic scenarios. A micro–nano satellite equipped with a miniaturized dual-frequency GPS receiver is employed to demonstrate precise orbit determination capabilities. On-orbit GPS data from the satellite, collected in two specific scenarios—slow rotation and Earth-pointing stabilization—are analyzed to evaluate the proposed algorithm’s ability to cope with weak GPS signals and satellite attitude instability as well as to assess the achievable orbit determination accuracy. The results show that, compared to traditional Extended Kalman Filters (EKF) and other improved filtering algorithms, the IARKF performs better in reducing post-fit residuals and improving orbit prediction accuracy, demonstrating its superior robustness. The three-axes orbit determination internal consistency precision can reach the millimeter level. This work explores a feasible approach for achieving high-performance orbit determination in micro–nano satellites.