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arXiv · 2306.09148

A Recursive Newton Method for Smoothing in Nonlinear State Space Models

Fatemeh Yaghoobi·Hany Abdulsamad·Simo Särkkä
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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.

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Fatemeh Yaghoobi, Hany Abdulsamad, Simo Särkkä. 2023-06-15. A Recursive Newton Method for Smoothing in Nonlinear State Space Models. https://arxiv.org/abs/2306.09148

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