Unscented Kalman Filter (UKF) is a popular method for state and parameter estimation of nonlinear dynamic systems. An attractive feature of UKF is that it utilizes deterministically chosen points (called sigma points), and the number of such points depends linearly on the dimension of the state space. However, an implicit assumption in UKF is that the underlying probability densities are Gaussian. To mitigate the Gaussianity assumption, Gaussian Sum-UKF has been proposed in literature that approximates all underlying densities using a sum of Gaussians. For accurate approximation, the number of sigma points required in this approach is significantly higher than UKF, thereby making the Gaussian Sum-UKF computationally intensive. In this work, we propose an alternate approach labeled unscented Gaussian Sum Filter (UGSF) that leverages the ability of Sum of Gaussians to approximate an arbitrary density, while using the same number of sigma points as in UKF. This is achieved by making suitable design choices of the various parameters in the Gaussian Sum representation. Thus, our approach requires similar computational effort as in UKF and hence does not suffer from the curse of dimensionality. We implement the proposed approach on a nonlinear state estimation case study and demonstrate its superior performance over UKF.