# A Distributed Implementation of Steady-State Kalman Filter

arXiv: https://arxiv.org/abs/2101.10689 · HTML: https://mlsanity.com/paper/2101.10689/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2021.

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

- [Restless Bandit Problem with Rewards Generated by a Linear Gaussian Dynamical System](https://mlsanity.com/paper/2405.09584/) (2024)

## Abstract (arXiv)

This paper studies the distributed state estimation in sensor network, where m sensors are deployed to infer the n-dimensional state of a linear time-invariant (LTI) Gaussian system. By a lossless decomposition of optimal steady-state Kalman filter, we show that the problem of distributed estimation can be reformulated as synchronization of homogeneous linear systems. Based on such decomposition, a distributed estimator is proposed, where each sensor node runs a local filter using only its own measurement and fuses the local estimate of each node with a consensus algorithm. We show that the average of the estimate from all sensors coincides with the optimal Kalman estimate. Numerical examples are provided in the end to illustrate the performance of the proposed scheme.