For nonlinear estimation with additive noise

we utilized the sparse-grid theory to propose a novel nonlinear filter

Sparse-grid Square-Root Quadrature Filter (SSRQF).The quadrature points for the conventional QF increases exponentially with the dimension.However

the new filter SSRQF uses the sparse-grid theory to reduce the number of quadrature points to a polynomial with the dimension

which alleviates the computation burden greatly.Through the theoretical analysis

we proposed that Unscented Kalman Filter (UKF) is only a special case for Sparse-grid Quadrature Filter (SQF)

thus SSRQF is more flexible in terms of choosing points and controlling accuracy.The simulation results show that the SSRQF achieves higher accuracy than the UKF and the Extended Kalman Filter (EKF).Thus

it is a high accuracy nonlinear filter algorithm with computationally efficient.