# Consensus-Based Distributed Estimation in the Presence of Heterogeneous, Time-Invariant Delays

arXiv: https://arxiv.org/abs/2104.00394 · HTML: https://mlsanity.com/paper/2104.00394/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2021.

## Built on by (most cited first, 5 of 5)

- [Discretized Distributed Optimization over Dynamic Digraphs](https://mlsanity.com/paper/2311.07939/) (2023)
- [Log-Scale Quantization in Distributed First-Order Methods: Gradient-based Learning from Distributed Data](https://mlsanity.com/paper/2406.00621/) (2024)
- [Logarithmically Quantized Distributed Optimization over Dynamic Multi-Agent Networks](https://mlsanity.com/paper/2410.20345/) (2024)
- [D-SVM over Networked Systems with Non-Ideal Linking Conditions](https://mlsanity.com/paper/2304.06667/) (2023)
- [Machine Learning and CPU (Central Processing Unit) Scheduling Co-Optimization over a Network of Computing Centers](https://mlsanity.com/paper/2510.25176/) (2025)

## Abstract (arXiv)

Classical distributed estimation scenarios typically assume timely and reliable exchanges of information over the sensor network. This paper, in contrast, considers single time-scale distributed estimation via a sensor network subject to transmission time-delays. The proposed discrete-time networked estimator consists of two steps: (i) consensus on (delayed) a-priori estimates, and (ii) measurement update. The sensors only share their a-priori estimates with their out-neighbors over (possibly) time-delayed transmission links. The delays are assumed to be fixed over time, heterogeneous, and known. We assume distributed observability instead of local observability, which significantly reduces the communication/sensing loads on sensors. Using the notions of augmented matrices and Kronecker product, the convergence of the proposed estimator over strongly-connected networks is proved for a specific upper-bound on the time-delay.