Direct exoplanet imaging via coronagraphy requires maintenance of high contrast in a dark hole for lengthy integration periods. Wavefront errors that change slowly over that time accumulate and cause systematic errors in the stars Point Spread Function (PSF) which limit the achievable signal-to-noise ratio of the planet. In this paper we show that estimating the speckle drift can be achieved via intensity measurements in the dark hole together with dithering of the deformable mirrors to increase phase diversity. A scheme based on an Extended Kalman Filter and Electric Field Conjugation is proposed for maintaining the dark hole during the integration phase. For the post-processing phase, an a posteriori approach is proposed to estimate the realization of the PSF drift process and the intensity of the planet light incoherent with the speckles.
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