A Recursive Newton Method for Smoothing in Nonlinear State Space Models

2023/06/15 by Yaghoobi, Fatemeh, Abdulsamad, Hany, Särkkä, Simo
#Computation (stat.CO) #FOS: Computer and information sciences #FOS: Electrical engineering #Signal Processing (eess.SP) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2306.09148

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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