  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.
