A principal component analysis for LISA -- the TDI connection

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.

7 pages, 3 figures, 1 table

References in corpus (11)

• Time Delay Interferometry with Moving Spacecraft Arrays
• Time-Delay Interferometry
• Data Combinations Accounting for LISA Spacecraft Motion
• LISA Data Analysis using MCMC methods
• Algebraic approach to time-delay data analysis for LISA
• Geometric Time Delay Interferometry
• Bayesian estimation of pulsar parameters from gravitational wave data
• The Effects of Orbital Motion on LISA Time Delay Interferometry
• Operating LISA as a Sagnac interferometer
• Bayesian modeling of source confusion in LISA data
• LISA source confusion: identification and characterization of signals

Cited by in corpus (14)

• Stochastic Gravitational Wave Backgrounds
• LISA technology and instrumentation
• Sensitivity and parameter-estimation precision for alternate LISA configurations
• Second-Generation Time-Delay Interferometry
• TDI-infinity: time-delay interferometry without delays
• Refined clock-jitter reduction in the Sagnac-type time-delay interferometry combinations
• Frequency response of time-delay interferometry for space-based gravitational wave antennas
• A statistical inference approach to time-delay interferometry for gravitational-wave detection
• Matrix Representation of Time-Delay Interferometry
• A combinatorial algebraic approach for the modified second-generation time-delay interferometry
• The Varied Avatars of Time-delay Interferometry
• Fully data-driven time-delay interferometry with time-varying delays
• Model-independent time-delay interferometry based on principal component analysis
• Sky localization of space-based detectors with time-delay interferometry