This study introduces a novel partially parallel acquisition (PPA) method, Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA), which accelerates image acquisition using an RF coil array for spatial encoding. GRAPPA is an extension of both the PILS and VD-AUTO-SMASH reconstruction techniques, requiring no detailed RF field map prior to reconstruction. The method generates unaliased images from each component coil, improving SNR and image quality by decoupling image reconstruction and combination steps. The GRAPPA reconstruction algorithm is implemented using a sliding block approach, which allows for multiple reconstructions of missing lines, enhancing the fit and reducing artifacts. Computer simulations and in vivo imaging studies demonstrate that GRAPPA achieves higher SNR and better image quality compared to previous PPA techniques, particularly in challenging scenarios such as cardiac and abdominal imaging. The autocalibrating nature of GRAPPA makes it suitable for applications where accurate coil sensitivity maps may be difficult to obtain, such as in cardiac and abdominal imaging, and single-shot EPI applications.This study introduces a novel partially parallel acquisition (PPA) method, Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA), which accelerates image acquisition using an RF coil array for spatial encoding. GRAPPA is an extension of both the PILS and VD-AUTO-SMASH reconstruction techniques, requiring no detailed RF field map prior to reconstruction. The method generates unaliased images from each component coil, improving SNR and image quality by decoupling image reconstruction and combination steps. The GRAPPA reconstruction algorithm is implemented using a sliding block approach, which allows for multiple reconstructions of missing lines, enhancing the fit and reducing artifacts. Computer simulations and in vivo imaging studies demonstrate that GRAPPA achieves higher SNR and better image quality compared to previous PPA techniques, particularly in challenging scenarios such as cardiac and abdominal imaging. The autocalibrating nature of GRAPPA makes it suitable for applications where accurate coil sensitivity maps may be difficult to obtain, such as in cardiac and abdominal imaging, and single-shot EPI applications.