# Performance of an Algorithm for Estimation of Flux, Background and Location on One-Dimensional Signals

## TL;DR

This paper develops and tests a maximum likelihood algorithm for accurately estimating flux, background, and location in one-dimensional signals, crucial for astrometric and photometric measurements in Gaia data analysis.

## Contribution

It introduces a maximum likelihood framework for joint estimation of flux, background, and position, with two algorithm versions tested for efficiency and accuracy.

## Key findings

- Estimates are unbiased across tested conditions.
- The combined parameter estimation algorithm is more efficient.
- Correlation between flux and background is well-characterized.

## Abstract

Optimal estimation of signal amplitude, background level, and photocentre location is crucial to the combined extraction of astrometric and photometric information from focal plane images, and in particular from the one-dimensional measurements performed by Gaia on intermediate to faint magnitude stars. Our goal is to define a convenient maximum likelihood framework, suited to efficient iterative implementation and to assessment of noise level, bias, and correlation among variables. The analytical model is investigated numerically and verified by simulation over a range of magnitude and background values. The estimates are unbiased, with a well-understood correlation between amplitude and background, and with a much lower correlation of either of them with location, further alleviated in case of signal symmetry. Two versions of the algorithm are implemented and tested against each other, respectively, for independent and combined parameter estimation. Both are effective and provide consistent results, but the latter is more efficient because it takes into account the flux-background estimate correlation.