Local module identification in dynamic networks with correlated noise: the full input case

TL;DR

This paper develops an identification method for local modules in dynamic networks with correlated noise, extending previous uncorrelated noise assumptions to handle noise correlations via MIMO setups and predictor input selection.

Contribution

It introduces an algorithm that selects predictor inputs and outputs for MISO or MIMO identification in networks with correlated disturbances, improving estimation consistency.

Findings

Algorithm effectively handles correlated noise in network modules.

Extension from uncorrelated to correlated noise scenarios.

Provides a systematic predictor input selection method.

Abstract

The identification of local modules in dynamic networks with known topology has recently been addressed by formulating conditions for arriving at consistent estimates of the module dynamics, typically under the assumption of having disturbances that are uncorrelated over the different nodes. The conditions typically reflect the selection of a set of node signals that are taken as predictor inputs in a MISO identification setup. In this paper an extension is made to arrive at an identification setup for the situation that process noises on the different node signals can be correlated with each other. In this situation the local module may need to be embedded in a MIMO identification setup for arriving at a consistent estimate with maximum likelihood properties. This requires the proper treatment of confounding variables. The result is an algorithm that, based on the given network topology and disturbance correlation structure, selects an appropriate set of node signals as predictor inputs and outputs in a MISO or MIMO identification setup. As a first step in the analysis, we restrict attention to the (slightly conservative) situation where the selected output node signals are predicted based on all of their in-neighbor node signals in the network.