Abstract: To cope with the significant nonlinearity and weak observability problems in the passive target motion analysis(TMA),a new nonlinear filter based on second-order extended Kalman technology and square-root Kalman algorithm is developed.By orthogonalizing the state vectors with the square root of covariance matrixes,the computational complexity in second-order extended Kalman algorithm is reduced,and then a second-order extended Kalman algorithm based on square-root Kalman technology,which improves the numerically stability of a filter,is deduced.The new algorithm is applied to a TMA problem and proves with both numerical simulation and actual experimentation that it performs well in the significant nonlinear systems.