Research ArticleA new class of nonlinear Rauch-Tung-Striebel cubature Kalman smoothers

- A new class of nonlinear Gaussian approximation smoothers is proposed to enhance the estimation performance.
- The arbitrary degrees of estimation accuracy can be achieved by using high degree cubature integration rules in the smoothing algorithm.
- The new smoothing approach outperforms many popular nonlinear estimation techniques such as extended Kalman smoother, unscented Kalman smoother, and the conventional third-degree cubature Kalman smoother.
- The smoothing algorithm is computationally efficient to implement.

In this paper, a new Rauch-Tung-Striebel type of nonlinear smoothing method is proposed based on a class of high-degree cubature integration rules. This new class of cubature Kalman smoothers generalizes the conventional third-degree cubature Kalman smoother using the combination of Genz׳s or Mysovskikh׳s high-degree spherical rule with the moment matching based arbitrary-degree radial rule, which considerably improves the estimation accuracy. A target tracking problem is utilized to demonstrate the performance of this new smoother and to compare it with other Gaussian approximation smoothers. It will be shown that this new cubature Kalman smoother enhances the filtering accuracy and outperforms the extended Kalman smoother, the unscented Kalman smoother, and the conventional third-degree cubature Kalman smoother. It also maintains close performance to the Gauss-Hermite quadrature smoother with much less computational cost.