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Parallel magnetic resonance imaging ink-space such as generalized auto-calibrating partially parallel acquisition exploits spatial correlation among neighboring signals over multiple coils in calibration to estimate missing signals in reconstruction. It is often challenging to achieve accurate calibration information due to data corruption with noises and spatially varying correlation. The purpose of this work is to address these problems simultaneously by developing a new, adaptive iterative generalized auto-calibrating partially parallel acquisition with dynamic self-calibration. With increasing iterations, under a framework of the Kalman filter spatial correlation is estimated dynamically updating calibration signals in a measurement model and using fixed-point state transition in a process model while missing signals outside the step-varying calibration region are reconstructed, leading to adaptive self-calibration and reconstruction. Noise statistic is incorporated in the Kalman filter models, yielding coil-weighted de-noising in reconstruction. Numerical and in vivo studies are performed, demonstrating that the proposed method yields highly accurate calibration and thus reduces artifacts and noises even at high acceleration.