Develope an approximate

recursive Gaussian filters for nonlinear dynamics with additive noise

square-root quadrature Kalman filter (SRQKF).This filter is the square-root implementation on the basis of the quadrature Kalman filter (QKF)

it linearizes the nonlinear functions using statistical linear regression method through a set of Gaussian-Hermite quadrature points that parameterize the Gaussian density.The squre-root implementation of the new filter not only enhances the numerical stability

guarantees positive semi-definiteness of the state covariance

but also increases the filtering accuracy.The simulation shows that the tracking accuracy of the SRQKF is 12% higher than that of QKF

and the tracking accuracy of QKF is higher than that of the unscented Kalman filter (UF) and extended Kalman filter (EKF)

but the computational cost of them are all higher than that of UF and EKF.The new filter is an effective nonlinear filtering algorithm in the place required high filtering accuracy.