Flexible assembly has emerged as the dominant technique for the compliant assembly of low-stiffness aircraft wall panels. Critical to this process is the online measurement of key geometric parameters—such as panel positioning targets and real-time surface profiles—to ensure high precision and minimal residual stress. However, the restricted accessibility within the confined, near-enclosed tooling environment, coupled with the inherently poor shape stability of low-stiffness panels, renders direct measurement methods inefficient and prone to errors, creating significant obstacles for real-time monitoring. To address these challenges, this paper introduces a computational measurement approach for estimating key geometric parameters during flexible panel assembly. By combining sparse measurable data with physics-based analytical models, the method enables real-time estimation of parameters that are otherwise difficult to access directly. Specifically, a modal superposition-based technique is developed to compute the global displacement of positioning tooling from limited displacement measurements, facilitating continuous tracking of panel positioning targets. Additionally, a surface profile reconstruction method is proposed, which integrates geometric constraints and the displacement-strain relationship to fuse discrete strain data for real-time shape estimation. Validation was conducted on a downscaled platform simulating the flexible assembly of aircraft horizontal tail panels. The results demonstrate that the proposed method achieves positioning target measurement errors below 75.1 μm and surface profile errors under 18.11%, with computation times shorter than 0.005 s and 0.01 s, respectively. This method provides reliable real-time data support for compliant aircraft panel assembly and advances the development of flexible assembly technologies in aerospace manufacturing.