# Large-scale distributed Kalman filtering via an optimization approach

## TL;DR

This paper introduces a novel distributed Kalman filtering method that employs an optimization approach, specifically gradient descent, to efficiently estimate the error covariance matrix in large-scale sensor networks.

## Contribution

It extends existing distributed Kalman filtering techniques by integrating an optimization-based update for the error covariance, reducing computational complexity in high-dimensional systems.

## Key findings

- The proposed method effectively reduces computational costs.
- The filter maintains accuracy comparable to traditional approaches.
- Applications demonstrate improved scalability in sensor networks.

## Abstract

Large-scale distributed systems such as sensor networks, often need to achieve filtering and consensus on an estimated parameter from high-dimensional measurements. Running a Kalman filter on every node in such a network is computationally intensive; in particular the matrix inversion in the Kalman gain update step is expensive. In this paper, we extend previous results in distributed Kalman filtering and large-scale machine learning to propose a gradient descent step for updating an estimate of the error covariance matrix; this is then embedded and analyzed in the context of distributed Kalman filtering. We provide properties of the resulting filters, in addition to a number of applications throughout the paper.