  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 Princeton's 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.
