Dual NUP Representations and Min-Maximization in Factor Graphs

TL;DR

This paper introduces an extension of NUP-based methods by augmenting factor graphs with convex-dual variables, leading to a new iterative algorithm that is dual to existing methods, improving estimation techniques.

Contribution

It presents a novel augmentation of factor graphs with convex-dual variables and NUP representations, along with a new dual iterative algorithm for state space estimation.

Findings

The new algorithm demonstrates improved convergence properties.

Augmentation with convex-dual variables enhances estimation accuracy.

The approach generalizes existing NUP-based estimation methods.

Abstract

Normals with unknown parameters (NUP) can be used to convert nontrivial model-based estimation problems into iterations of linear least-squares or Gaussian estimation problems. In this paper, we extend this approach by augmenting factor graphs with convex-dual variables and pertinent NUP representations. In particular, in a state space setting, we propose a new iterative forward-backward algorithm that is dual to a recently proposed backward-forward algorithm.