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In this study, a new non-linear filter based on second-order extended Kalman technology and square-root Kalman algorithm is proposed and applied to the problem of target motion analysis (TMA). By orthogonalising the state vectors with the square root of covariance matrix, the authors reduce the computational complexity in the second-order extended Kalman algorithm, and then we deduce a second-order extended Kalman algorithm based on square-root Kalman technology, which is more numerically stable and can guarantee positive and semi-definiteness of the state covariance. The authors apply the new algorithm to a TMA problem, and prove with both numerical simulation and actual experimentation that their algorithm performs well in the significant non-linear systems. [ABSTRACT FROM AUTHOR]