Dual NUP Representations and Min-Maximization in Factor Graphs

--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. V ariational representations of cost functions [1], [2] and 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 [3]-[7]. This applies, in particular, to linear state space models with non-Gaussian inputs and/or non-Gaussian observation noise or constraints.