# On observability and optimal gain design for distributed linear filtering and prediction

arXiv: https://arxiv.org/abs/2203.03521 · HTML: https://mlsanity.com/paper/2203.03521/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 39 references that are in the map.
- First posted on arXiv 7 Mar 2022.

## Builds on (most cited first, 4 of 4)

- [A Regret Minimization Approach to Multi-Agent Control](https://mlsanity.com/paper/2201.13288/) (2022)
- [Consensus+Innovations Distributed Kalman Filter with Optimized Gains](https://mlsanity.com/paper/1605.06096/) (2016)
- [All-in-one: Certifiable Optimal Distributed Kalman Filter under Unknown Correlations](https://mlsanity.com/paper/2105.15061/) (2021)
- [Distributed Design of Robust Kalman Filters over Corrupted Channels](https://mlsanity.com/paper/1907.00190/) (2019)

## Built on by (most cited first, 1 of 1)

- [An alternative approach for distributed parameter estimation under Gaussian settings](https://mlsanity.com/paper/2204.08317/) (2022)

## Abstract (arXiv)

This paper presents a new approach to distributed linear filtering and prediction. The problem under consideration consists of a random dynamical system observed by a multi-agent network of sensors where the network is sparse. Inspired by the consensus+innovations type of distributed estimation approaches, this paper proposes a novel algorithm that fuses the concepts of consensus and innovations. The paper introduces a definition of distributed observability, required by the proposed algorithm, which is a weaker assumption than that of global observability and connected network assumptions combined together. Following first principles, the optimal gain matrices are designed such that the mean-squared error of estimation is minimized at each agent and the distributed version of the algebraic Riccati equation is derived for computing the gains.