Summary
We develop a fast data assimilation method for estimating the state of a dynamical system from its partial time series observations. Our method relies on discrete empirical interpolation method (DEIM) and therefore we refer to it as extended DEIM. Extended DEIM uses an auxiliary differential equation to approximate the optimal kernel vector which appears in DEIM. The dimension of the auxiliary equation is much smaller than the dimension of the original dynamical system. Therefore, our method is particularly attractive for data assimilation of high-dimensional systems. Furthermore, extended DEIM is intentionally designed to estimate the state of the system even when few sensor measurements are available.
