As one of the most important means to achieve a High-Resolution and Wide-Swath (HRWS) imaging of the earth, multichannel in azimuth Synthetic Aperture Radar (SAR) have attracted considerable attention in recent years. However, prior to the unambiguous reconstruction of the multichannel SAR signal, each channel needs to be well calibrated, otherwise the performance of the reconstruction processor may degrade or even lose its effectiveness. Accurate baseband Doppler centroid estimation are critical for channel mismatch calibration and high-resolution imaging in the multichannel SAR systems. However, in the multichannel HRWS SAR system, the signal acquired by each channel is under-sampled that renders the traditional Doppler centroid estimation methods obsolete. In this paper, an eigen-structure method has been used to achieve a robust estimation of the baseband Doppler centroid and the phase mismatch in the multichannel SAR system. Processing with simulated and experimental C-band, four-channel airborne SAR data validates the effectiveness of this method.