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Due to the strong nonlinear characteristics of COMPASS signal under highly dynamic circumstances, the high accuracy parameter estimation is hard to be achieved. Based on the analysis of the high-order nonlinear carrier model, an adaptive square-root cubature Kalman filter algorithm ( SCKF) is proposed to estimate the phase and its three-order derivatives. In the SCKF algorithm, cubature rule based on numerical integration method is directly used to calculate the mean and covariance of the nonlinear random function. By shifting the window, the latest measurement information in the process of recursion and filtering is used to improve the cross-covariance of noises, so the higher accuracy of state estimation can be achieved. The simulation results indicate that the higher accuracy and faster convergence are obtained compared with EKF and SCKF. [ABSTRACT FROM AUTHOR]