Calibrating spectral estimation for the LISA Technology Package with multichannel synthetic noise generation

TL;DR

This paper presents a method for generating synthetic multichannel noise with specific cross-correlation properties to calibrate data analysis tools for the LISA Pathfinder mission's LTP experiment.

Contribution

It introduces a flexible, frequency-by-frequency eigendecomposition approach to synthesize cross-correlated stationary noise for multichannel data calibration.

Findings

Successfully generated synthetic noise matching desired cross-spectral properties.

Validated the noise generator with a two-dimensional LTP dynamics case study.

Addressed initial transient issues with proper filter initialization.

Abstract

The scientific objectives of the Lisa Technology Package (LTP) experiment, on board of the LISA Pathfinder mission, demand for an accurate calibration and validation of the data analysis tools in advance of the mission launch. The levels of confidence required on the mission outcomes can be reached only with an intense activity on synthetically generated data. A flexible procedure allowing the generation of cross-correlated stationary noise time series was set-up. Multi-channel time series with the desired cross correlation behavior can be generated once a model for a multichannel cross-spectral matrix is provided. The core of the procedure is the synthesis of a noise coloring multichannel filter through a frequency-by-frequency eigendecomposition of the model cross-spectral matrix and a Z-domain fit. The common problem of initial transients in noise time series is solved with a proper initialization of the filter recursive equations. The noise generator performances were tested in a two dimensional case study of the LTP dynamics along the two principal channels of the sensing interferometer.