# A scalable multi-step least squares method for network identification with unknown disturbance topology

arXiv: https://arxiv.org/abs/2106.07548 · HTML: https://mlsanity.com/paper/2106.07548/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 54 references that are in the map.
- First posted on arXiv 14 Jun 2021.

## Builds on (most cited first, 9 of 9)

- [Prediction error identification of linear dynamic networks with rank-reduced noise](https://mlsanity.com/paper/1711.06369/) (2017)
- [Learning linear modules in a dynamic network using regularized kernel-based methods](https://mlsanity.com/paper/2005.06266/) (2020)
- [A local direct method for module identification in dynamic networks with correlated noise](https://mlsanity.com/paper/1908.00976/) (2019)
- [Topology Identification under Spatially Correlated Noise](https://mlsanity.com/paper/2012.04175/) (2020)
- [Signal selection for estimation and identification in networks of dynamic systems: a graphical model approach](https://mlsanity.com/paper/1905.12132/) (2019)
- [Identifiability of linear dynamic networks](https://mlsanity.com/paper/1609.00864/) (2016)
- [A practical method for the consistent identification of a module in a dynamical network](https://mlsanity.com/paper/1811.01943/) (2018)
- [Parametric Identification Using Weighted Null-Space Fitting](https://mlsanity.com/paper/1708.03946/) (2017)
- [Bayesian topology identification of linear dynamic networks](https://mlsanity.com/paper/1903.06205/) (2019)

## Built on by (most cited first, 1 of 1)

- [Learning linear modules in a dynamic network with missing node observations](https://mlsanity.com/paper/2208.10995/) (2022)

## Abstract (arXiv)

Identification methods for dynamic networks typically require prior knowledge of the network and disturbance topology, and often rely on solving poorly scalable non-convex optimization problems. While methods for estimating network topology are available in the literature, less attention has been paid to estimating the disturbance topology, i.e., the (spatial) noise correlation structure and the noise rank in a filtered white noise representation of the disturbance signal. In this work we present an identification method for dynamic networks, in which an estimation of the disturbance topology precedes the identification of the full dynamic network with known network topology. To this end we extend the multi-step Sequential Linear Regression and Weighted Null Space Fitting methods to deal with reduced rank noise, and use these methods to estimate the disturbance topology and the network dynamics in the full measurement situation. As a result, we provide a multi-step least squares algorithm with parallel computation capabilities and that rely only on explicit analytical solutions, thereby avoiding the usual non-convex optimizations involved. Consequently we consistently estimate dynamic networks of Box Jenkins model structure, while keeping the computational burden low. We provide a consistency proof that includes path-based data informativity conditions for allocation of excitation signals in the experimental design. Numerical simulations performed on a dynamic network with reduced rank noise clearly illustrate the potential of this method.