The exterior orientation parameters (EOPs) provided by the self-developed position and orientation system (POS) of the first Chinese airborne three-line scanner mapping system, AMS-3000, are impacted by jitter, resulting in waveform distortions in rectified images. This study introduces a Gaussian Markov EOP refinement method enhanced by cubic spline interpolation to mitigate stochastic jitter errors. Our method first projects tri-view images onto a mean elevation plane using POS-provided EOPs to generate Level 1 images for dense matching. Matched points are then back-projected to the original Level 0 images for the bundle adjustment based on the Gaussian Markov model. Finally, cubic spline interpolation is employed to obtain EOPs for lines without observations. Experimental comparisons with the piecewise polynomial model (PPM) and Lagrange interpolation model (LIM) demonstrate that our method outperformed these models in terms of geo-referencing accuracy, EOP refinement metric, and visual performance. Specifically, the line fitting accuracies of four linear features on Level 1 images were evaluated to assess EOP refinement performance. The refinement performance of our method showed improvements of 50%, 45.1%, 29.9%, and 44.6% over the LIM, and 12.9%, 69.2%, 69.6%, and 49.3% over the PPM. Additionally, our method exhibited the best visual performance on these linear features.