For imaging faint exoplanets and disks, a coronagraph-equipped observatory needs focal plane wavefront correction to recover high contrast. The most efficient correction methods iteratively estimate the stellar electric field and suppress it with active optics. The estimation requires several images from the science camera per iteration. To maximize the science yield, it is desirable both to have fast wavefront correction and to utilize all the correction images for science target detection. Exoplanets and disks are incoherent with their stars, so a nonlinear estimator is required to estimate both the incoherent intensity and the stellar electric field. Such techniques assume a high level of stability found only on space-based observatories and possibly ground-based telescopes with extreme adaptive optics. In this paper, we implement a nonlinear estimator, the iterated extended Kalman filter (IEKF), to enable fast wavefront correction and a recursive, nearly-optimal estimate of the incoherent light. In Princetons High Contrast Imaging Laboratory we demonstrate that the IEKF allows wavefront correction at least as fast as with a Kalman filter and provides the most accurate detection of a faint companion. The nonlinear IEKF formalism allows us to pursue other strategies such as parameter estimation to improve wavefront correction.
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