  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.
