# Adaptive tracking of a time-varying field with a quantum sensor

## TL;DR

This paper introduces an adaptive Bayesian protocol for tracking non-periodic, Wiener-process magnetic fields using quantum sensors, significantly improving estimation accuracy and efficiency over traditional methods.

## Contribution

It presents a novel adaptive tracking protocol that incorporates statistical properties of the signal, reducing measurement time and estimation error for time-varying fields.

## Key findings

- Reduces estimation error by up to 4 times
- Decreases measurement time by adapting sensing parameters
- Effective for non-periodic, Wiener-process signals

## Abstract

Sensors based on single spins can enable magnetic field detection with very high sensitivity and spatial resolution. Previous work has concentrated on sensing of a constant magnetic field or a periodic signal. Here, we instead investigate the problem of estimating a field with non-periodic variation described by a Wiener process. We propose and study, by numerical simulations, an adaptive tracking protocol based on Bayesian estimation. The tracking protocol updates the probability distribution for the magnetic field, based on measurement outcomes, and adapts the choice of sensing time and phase in real time. By taking the statistical properties of the signal into account, our protocol strongly reduces the required measurement time. This leads to a reduction of the error in the estimation of a time-varying signal by up to a factor 4 compared to protocols that do not take this information into account.