  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
star's 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.
