A principal component analysis for LISA -- the TDI connection

TL;DR

This paper demonstrates that time delay interferometry (TDI) variables in LISA data are eigenvectors of the noise covariance matrix, enabling noise-insensitive data combinations for improved source parameter estimation.

Contribution

It formally connects TDI variables to principal component analysis, showing they are eigenvectors that allow likelihood functions to be based on noise-insensitive data combinations.

Findings

TDI variables are eigenvectors of the noise covariance matrix.

Likelihood functions can be constructed from TDI combinations without losing information.

TDI variables effectively isolate laser frequency noise in LISA data.

Abstract

Data from the Laser Interferometer Space Antenna (LISA) is expected to be dominated by frequency noise from its lasers. However the noise from any one laser appears more than once in the data and there are combinations of the data that are insensitive to this noise. These combinations, called time delay interferometry (TDI) variables, have received careful study, and point the way to how LISA data analysis may be performed. Here we approach the problem from the direction of statistical inference, and show that these variables are a direct consequence of a principal component analysis of the problem. We present a formal analysis for a simple LISA model and show that there are eigenvectors of the noise covariance matrix that do not depend on laser frequency noise. Importantly, these orthogonal basis vectors correspond to linear combinations of TDI variables. As a result we show that the likelihood function for source parameters using LISA data can be based on TDI combinations of the data without loss of information.