  The task of dynamic flow estimation is to construct an approximation of an
evolving flow---and particularly, its response to disturbances---using
measurements from available sensors. Building from previous work by Darakananda
et al.~(Phys Rev Fluids 2018), we further develop an ensemble Kalman filter
(EnKF) framework for aerodynamic flows based on an ensemble of
randomly-perturbed inviscid vortex models of flow about an infinitely-thin
plate. In the forecast step, vortex elements in each ensemble member are
advected by the flow and new elements are released from each edge of the plate;
the elements are aggregated to maintain an efficient representation. The vortex
elements and leading edge constraint are corrected in the analysis step by
assimilating the surface pressure differences across the plate measured from
the truth system. We show that the overall framework can be physically
interpreted as a series of adjustments to the position and shape of an
elliptical region of uncertainty associated with each vortex element. In this
work, we compare the previously-used stochastic EnKF with the ensemble
transform Kalman filter (ETKF), which uses a deterministic analysis step. We
examine the response of the flat plate at $20^\circ$ in two perturbed flows,
with truth data obtained from high-fidelity simulation at Reynolds number 500.
In the first case, we apply a sequence of large-amplitude pulses near the
leading edge of the plate to mimic flow actuation. In the second, we place the
plate in a vortex street wake behind a cylinder. In both cases, we show that
the vortex-based framework accurately estimates the pressure distribution and
normal force, with no {\em a priori} knowledge of the perturbations. We show
that the ETKF is consistently more robust than the stochastic EnKF. Finally, we
examine the mapping from measurements to state update in the analysis step
through SVD of the Kalman gain.
