# Distributed Kalman-filtering: Distributed optimization viewpoint

## TL;DR

This paper reformulates distributed Kalman filtering as a consensus optimization problem and introduces a new algorithm based on distributed dual ascent, enabling sensor networks to perform filtering without a central fusion center.

## Contribution

It presents a novel reformulation of distributed Kalman filtering as a consensus optimization problem and develops a new dual ascent based algorithm for it.

## Key findings

- The new algorithm performs effectively in numerical experiments.
- Distributed optimization techniques can be applied to Kalman filtering.
- The approach eliminates the need for a central fusion center.

## Abstract

We consider the Kalman-filtering problem with multiple sensors which are connected through a communication network. If all measurements are delivered to one place called fusion center and processed together, we call the process centralized Kalman-filtering (CKF). When there is no fusion center, each sensor can also solve the problem by using local measurements and exchanging information with its neighboring sensors, which is called distributed Kalman-filtering (DKF). Noting that CKF problem is a maximum likelihood estimation problem, which is a quadratic optimization problem, we reformulate DKF problem as a consensus optimization problem, resulting in that DKF problem can be solved by many existing distributed optimization algorithms. A new DKF algorithm employing the distributed dual ascent method is provided and its performance is evaluated through numerical experiments.