# Distributed Kalman Filtering under Model Uncertainty

## TL;DR

This paper develops a distributed Kalman filter that is robust to model uncertainties within a specified Kullback-Leibler ball, enhancing sensor network performance under mismatch conditions.

## Contribution

It introduces a novel distributed Kalman filtering algorithm with diffusion steps that accounts for model uncertainty and derives its worst-case performance.

## Key findings

- The proposed filter is robust against model mismatch.
- Numerical examples demonstrate improved performance under uncertainty.
- The method effectively handles uncertainty within a Kullback-Leibler ball.

## Abstract

We study the problem of distributed Kalman filtering for sensor networks in the presence of model uncertainty. More precisely, we assume that the actual state-space model belongs to a ball, in the Kullback-Leibler topology, about the nominal state-space model and whose radius reflects the mismatch modeling budget allowed for each time step. We propose a distributed Kalman filter with diffusion step which is robust with respect to the aforementioned model uncertainty. Moreover, we derive the corresponding least favorable performance. Finally, we check the effectiveness of the proposed algorithm in the presence of uncertainty through a numerical example.