# Bias estimation in sensor networks

## TL;DR

This paper studies how to accurately estimate constant biases in sensor networks by analyzing network topology and proposing algorithms, ensuring bias correction even with many biased sensors.

## Contribution

It provides conditions under which biases can be uniquely estimated in different network topologies and introduces algorithms for bias estimation.

## Key findings

- Biases are always identifiable in non-bipartite graphs.
- More than half sensors must be unbiased in bipartite graphs for correct estimation.
- Only two unbiased sensors are needed if biases are heterogeneous.

## Abstract

This paper investigates the problem of estimating biases affecting relative state measurements in a sensor network. Each sensor measures the relative states of its neighbors and this measurement is corrupted by a constant bias. We analyse under what conditions on the network topology and the maximum number of biased sensors the biases can be correctly estimated. We show that for non-bipartite graphs the biases can always be determined even when all the sensors are corrupted, while for bipartite graphs more than half of the sensors should be unbiased to ensure the correctness of the bias estimation. If the biases are heterogeneous, then the number of unbiased sensors can be reduced to two. Based on these conditions, we propose some algorithms to estimate the biases.