In this paper, we use the optimization formulation of nonlinear Kalman filtering and smoothing problems to develop second-order variants of iterated Kalman smoother (IKS) methods. We show that Newton's method corresponds to a recursion over affine smoothing problems on a modified state-space model augmented by a pseudo measurement. The first and second derivatives required in this approach can be efficiently computed with widely available automatic differentiation tools. Furthermore, we show how to incorporate line-search and trust-region strategies into the proposed second-order IKS algorithm in order to regularize updates between iterations. Finally, we provide numerical examples to demonstrate the method's efficiency in terms of runtime compared to its batch counterpart.

翻译：本文利用非线性卡尔曼滤波与平滑问题的优化形式，发展了迭代卡尔曼平滑器（IKS）方法的二阶变体。我们证明牛顿法对应于对由伪测量增强的修正状态空间模型上仿射平滑问题的递归，该方法所需的一阶和二阶导数可通过广泛可用的自动微分工具高效计算。此外，我们展示了如何将线性搜索与信赖域策略纳入所提出的二阶IKS算法，以规范迭代间的更新。最后，通过数值算例证明了该方法相较于其批处理版本在运行时间上的效率。