Massive multiple-input multiple-output low-Earth-orbit communication channels are highly time-varying due to severe Doppler shifts and propagation delays. While satellite-mobility-induced Doppler shifts can be compensated using known ephemeris data, those caused by user mobility require accurate user positioning information; the absence of such information contributes to amplified channel aging in conventional channel estimators. To address this challenge, we propose a data-aided channel estimator based on the expectation-maximization (EM) algorithm, combined with a discrete Legendre polynomial basis expansion model (DLP-BEM), to estimate the channel under imperfect Doppler compensation. The EM algorithm iteratively exploits hidden data symbols for improved channel estimation, while DLP-BEM regularizes the process by projecting the channel estimate onto a lower-dimensional subspace that mitigates estimation errors. Simulation results demonstrate the superiority of the proposed framework over existing methods in terms of normalized mean square error and symbol error rate.