Abstract-Unscented Kalman Filter (UKF) has been widely used in the estimation of dynamical systems defined by ordinary differential equations. For partial differential equations, their discretized systems often have very high dimensions, which result in covariance matrices that are computationally intractable. In this paper, we introduce sparse-grids and an associated reduced state space, called a surplus space, in which the covariance matrices have relatively small dimensions and the number of sigma points is significantly reduced. The covariance in the reduced space can be used to compute the correction term for the updating process of the UKF. The resulting sparse-grid UKF is illustrated using an example of shallow water equations.