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An improved quadrature nonlinear filter named delayed Genz-Keister sequences-based sparse-grid quadrature filter (DGKSGQF) is developed for the target tracking problems. The filter changes the non-nested Gaussian quadrature points of the quadrature filters to the nested Genz-Keister points for selecting the unvariate points, which are the basis point sets extended to form a multidimensional grid using the sparse-grid theory. As a result, the points used for lower accuracy levels DGKSGQF can be reused for any higher accuracy level. Thus, it can further reduce the number of total points used for the conventional Gauss-Hermite SGQF without sacrificing performance. The proposed filter is applied to the reentry ballistic target tracking problem. The simulation results show that the DGKSGQF achieves higher accuracy than the EKF and the UKF. In addition, it can more flexibly control the performance in terms of the number of points and accuracy level.