Summary: The Gaussian mixture filter can solve the non-Gaussian problem of target tracking in complex environment by the multimode approximation method, but the weights of the Gaussian component of the conventional Gaussian mixture filter are only updated with the arrival of the measurement value in the measurement update stage. When the nonlinear degree of the system is high or the measurement value is missing, the weight of the Gauss component remains unchanged, and the probability density function of the system state cannot be accurately approximated. To solve this problem, this paper proposes an algorithm to update adaptive weights for the Gaussian components of a Gaussian mixture cubature Kalman filter (CKF) in the time update stage. The proposed method approximates the non-Gaussian noise by splitting the system state, process noise, and observation noise into several Gaussian components and updates the weight of the Gaussian components in the time update stage. The method contributes to obtaining a better approximation of the posterior probability density function, which is constrained by the substantial uncertainty associated with the measurements or ambiguity in the model. The estimation accuracy of the proposed algorithm was analyzed using a Taylor expansion. A series of extensive trials was performed to assess the estimation precision corresponding to various algorithms. The results based on the data pertaining to the lake trial of an unmanned underwater vehicle (UUV) demonstrated the superiority of the proposed algorithm in terms of its better accuracy and stability compared to those of conventional tracking algorithms, along with the associated reasonable computational time that could satisfy real-time tracking requirements.