A Recursive Newton Method for Smoothing in Nonlinear State Space Models
Abstract
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.
Cite
@article{arxiv.2306.09148,
title = {A Recursive Newton Method for Smoothing in Nonlinear State Space Models},
author = {Fatemeh Yaghoobi and Hany Abdulsamad and Simo Särkkä},
journal= {arXiv preprint arXiv:2306.09148},
year = {2023}
}