Bayesian Time Delay Interferometry*

Laser frequency noise (LFN) is the dominant source of noise expected in the Laser Interferometer Space Antenna (LISA) mission, at 10⁷ orders of magnitude greater than the typical signal expected from gravitational waves (GWs). Time-delay interferometry (TDI) suppresses LFN to an acceptable level by linearly combining measurements delayed by durations that correspond to their relative separations. Knowledge of the delay durations is crucial for TDI effectiveness. This work extends upon previous studies using data-driven methods for inferring the delays during the post-processing of raw data, also known as TDI ranging (TDIR). Our TDIR analysis uses Bayesian methods designed to ultimately be included in the LISA data model as part of a ``Global Fit'' analysis pipeline. This allows for GW inferences which are marginalized over uncertainty in the spacecraft separations and independent estimation of the spacecraft orbits. We demonstrate Markov Chain Monte Carlo (MCMC) inferences of the six time-independent delays required in the rigidly rotating approximation of the spacecraft configuration (TDI 1.5) using simulated data. The MCMC uses fractional delay interpolation (FDI) to digitally delay the raw phase meter data, and we study the sensitivity of the analysis to the filter length. Varying levels of complexity in the noise covariance matrix are also examined. Delay estimations are found to result in LFN suppression well below the level of secondary noises and constraints on the armlengths to Ο(30) cm over the 2.5 Gm baseline. An outlook towards current work in implementing time-dependent delays (TDI 2.0) to account for the orbital motion of the spacecraft is provided.