# Particle filtering of dynamical networks: Highlighting observability issues

## TL;DR

This paper introduces a particle filtering framework to evaluate observability in high-dimensional dynamical networks, revealing how dynamics and topology influence sensor placement and network state reconstruction.

## Contribution

It proposes a novel particle filtering approach to assess network observability, incorporating the effects of dynamics, topology, and sensor variable choices.

## Key findings

- Heterogeneous nodal dynamics improve observability with dynamical affinity.
- Sensor variable selection impacts particle filtering performance.
- PF framework aligns with established observability metrics in benchmarks.

## Abstract

In a network of high-dimensionality, it is not feasible to measure every single node. Thus, an important goal in the literature is to define the optimal choice of sensor nodes that provides a reliable state reconstruction of the network system state-space. This is an observability problem. In this paper, we propose a particle filtering (PF) framework as a way to assess observability properties of a dynamical network, where each node is composed by an individual dynamical system. The PF framework is applied on two benchmarks, networks of Kuramoto and R\"ossler oscillators, to investigate how the interplay between dynamics and topology impacts the network observability. Based on the numerical results, we conjecture that, when the network nodal dynamics are heterogeneous, better observability is conveyed for sets of sensor nodes that share some dynamical affinity to its neighbourhood. Moreover, we also investigate how the choice of an internal measured variable of a multidimensional sensor node affects the PF performance. The PF framework effectiveness as an observability measure is compared to a well-consolidated nonlinear observability metric for a small network case and some chaotic systems benchmarks.