Bayesian Time Delay Interferometry for Orbiting LISA

Previous work demonstrated effective laser frequency noise (LFN) suppression for LISA data from raw phasemeter measurements using a Markov Chain Monte Carlo (MCMC) algorithm with fractional delay interpolation (FDI) techniques to estimate the spacecraft separation parameters required for time-delay interferometry (TDI) under the assumption of a rigidly rotating LISA configuration. Including TDI parameters in the LISA data model as part of a global fit analysis pipeline produces gravitational wave inferences that are marginalized over uncertainty in the spacecraft separations. Here we extend the algorithm's capability to perform data-driven TDI on LISA in orbit which introduces a time-dependence in the arm-length parameters and at least O(L) times greater computational cost since the filter must be applied for every sample in the time series of size L. We find feasibility of arm-length estimation on ~ day-long time scales by using a restructured time-varying FDI LaGrange filter that allows half of the filter computation to be constant for all proposed parameters in the MCMC and requires shorter filter lengths than previously reported. We demonstrate LFN suppression for orbiting LISA using accurate arm-length estimates parameterized by Keplerian orbital parameters under the assumption of unperturbed analytical Keplerian orbits, and explore the potential extension of these methods to arbitrary numerical orbits.