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One of the major difficulties limiting ground-based direct imaging ofexoplanets with adaptive optics is quasi-static speckles in the science camera(SC) that obscure the planetary image. These speckles are caused byaberrations, called non-common path aberrations (NCPA), that are not correctedin the adaptive optics loop, and all attempts to subtract them inpost-processing have been problematic. The method of Frazin (2013) (F13) usessimultaneous millisecond telemetry from wavefront sensor (WFS) and the SC toestimate the both the NCPA and the exoplanet image in a self-consistent manner.Rodack et al. (2018) proposed correcting for the NCPA in real-time while on-skyusing the F13 estimation method, and called this procedure the "Real-TimeFrazin Algorithm." The original regression model underlying the F13 method didnot account for uncertainty in the WFS measurements, and this cannot be donewith standard statistical methodology since these uncertainties manifestthemselves in the independent variables (i.e., they cannot be treated asanother source of noise in the SC data). Further, simulations show that simplyusing the noisy wavefront measurements without accounting for theiruncertainties leads to estimates of the NCPA with unacceptably large bias.Here, the source of this bias is explained in terms of an "errors in variables"statistical model. Then, the method of F13 is generalized to account for WFSmeasurement error using a new sequential estimation technique that treats thenonlinear coupling between NCPA, WFS measurements and the error covariance ofthe WFS measurements. This new technique keeps a running estimate of the NCPA,the exoplanet image and their joint covariance matrix. The sequentialimplementation of the method should make it computationally efficient enough tobe suitable for on-sky correction of the NCPA as well as off-line analysis.

Treating Wavefront Measurement Error in Estimation of Non-Common Path Aberration for Direct Imaging of Exoplanets