# Multi-agent estimation and filtering for minimizing team mean-squared error

## TL;DR

This paper introduces the concept of team mean-squared error (MTMSE) for multi-agent estimation, deriving closed-form solutions and demonstrating improved performance over traditional methods in vehicle platoon scenarios.

## Contribution

The paper develops the MTMSE framework for multi-agent estimation, providing closed-form solutions and recursive filtering algorithms that outperform existing methods.

## Key findings

- MTMSE estimates outperform MMSE and consensus Kalman filtering.
- Closed-form expressions for MTMSE are derived for linear systems.
- Simulation shows significant improvement in vehicle distance estimation.

## Abstract

Motivated by estimation problems arising in autonomous vehicles and decentralized control of unmanned aerial vehicles, we consider multi-agent estimation and filtering problems in which multiple agents generate state estimates based on decentralized information and the objective is to minimize a coupled mean-squared error which we call \emph{team mean-square error}. We call the resulting estimates as minimum team mean-squared error (MTMSE) estimates. We show that MTMSE estimates are different from minimum mean-squared error (MMSE) estimates. We derive closed-form expressions for MTMSE estimates, which are linear function of the observations where the corresponding gain depends on the weight matrix that couples the estimation error. We then consider a filtering problem where a linear stochastic process is monitored by multiple agents which can share their observations (with delay) over a communication graph. We derive expressions to recursively compute the MTMSE estimates. To illustrate the effectiveness of the proposed scheme we consider an example of estimating the distances between vehicles in a platoon and show that MTMSE estimates significantly outperform MMSE estimates and consensus Kalman filtering estimates.