  A method is proposed to estimate the velocity field of an unsteady flow using
a limited number of flow measurements. The method is based on a non-linear
low-dimensional model of the flow and on expanding the velocity field in terms
of empirical basis functions. The main idea is to impose that the coefficients
of the modal expansion of the velocity field give the best approximation to the
available measurements and that at the same time they satisfy as close as
possible the non-linear low-order model. The practical use may range from
feedback flow control to monitoring of the flow in non-accessible regions. The
proposed technique is applied to the flow around a confined square cylinder,
both in two- and three-dimensional laminar flow regimes. Comparisons are
provided. with existing linear and non-linear estimation techniques.
