Recent progress in the estimation of laminar and turbulent wall-bounded flows

We present recent progress on a range of techniques to estimate the flow state based on a history of noisy measurements from an array of flush-mounted skin-friction and pressure sensors on a wall:\\ (A) {\bf Model predictive estimation} (a.k.a. 4D-var) in a ``{\bf multiscale retrograde}'' framework {\small (Bewley \& Protas, {\it Physica D} 2004)};\\ (B) {\bf Kalman filtering} based on an artificial (but sufficiently smooth) stochastic model for the covariance matrix characterizing the statistics of the state disturbance forcing {\small (Hoepffner {\it et al.}, {\it JFM} 2005)};\\ (C) {\bf Extended Kalman filtering} based on a covariance matrix derived from a DNS of a turbulent flow {\small (Chevalier {\it et al.}, {\it JFM} submitted)}; and\\ (D) {\bf Weiner filtering} derived from DNS-based impulse response functions.