# Prediction error identification of linear dynamic networks with rank-reduced noise

arXiv: https://arxiv.org/abs/1711.06369 · HTML: https://mlsanity.com/paper/1711.06369/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2017.

## Built on by (most cited first, 5 of 5)

- [A scalable multi-step least squares method for network identification with unknown disturbance topology](https://mlsanity.com/paper/2106.07548/) (2021)
- [Dealing with collinearity in large-scale linear system identification using Bayesian regularization](https://mlsanity.com/paper/2203.13633/) (2022)
- [Learning linear modules in a dynamic network with missing node observations](https://mlsanity.com/paper/2208.10995/) (2022)
- [Dealing with Collinearity in Large-Scale Linear System Identification Using Gaussian Regression](https://mlsanity.com/paper/2302.10959/) (2023)
- [Probabilistic Reduced-Dimensional Vector Autoregressive Modeling with Oblique Projections](https://mlsanity.com/paper/2401.07206/) (2024)

## Abstract (arXiv)

Dynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of redidentifying a dynamic network with known topology, on the basis of measured signals, for the situation of additive process noise on the node signals that is spatially correlated and that is allowed to have a spectral density that is singular. A prediction error approach is followed in which all node signals in the network are jointly predicted. The resulting joint-direct identification method, generalizes the classical direct method for closed-loop identification to handle situations of mutually correlated noise on inputs and outputs. When applied to general dynamic networks with rank-reduced noise, it appears that the natural identification criterion becomes a weighted LS criterion that is subject to a constraint. This constrained criterion is shown to lead to maximum likelihood estimates of the dynamic network and therefore to minimum variance properties, reaching the Cramer-Rao lower bound in the case of Gaussian noise.