This paper presents windowing and random weighting (WRW) based adaptive cubature Rauch Tung Striebel (CRTS) smoother (WRWACRTS). The Unscented KF (WRWUKF) has already existed as an alternative to nonlinear smoothing solutions. In the proposed method, both windowing and random weighted estimation methods are combined together and used to estimate the noise statistics. Subsequently, the weights of each window are adjusting randomly, and update the process and measurement noise covariances matrices at each epoch. The developed WRWACRTS algorithm overcomes the limitation of the conventional CKS. The Lyapunov function-based approach is used to investigate the convergence proof of the WRWACRTS algorithm. A numerical example is shown to demonstrate the performance of the proposed algorithm.