  Previous work demonstrated effective laser frequency noise (LFN) suppression
for Laser Interferometer Space Antenna (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 enables gravitational wave
inferences to be marginalized over uncertainty in the spacecraft separations.
Here we extend the algorithm's capability to perform data-driven TDI on LISA in
Keplerian orbits, which introduce a time-dependence in the arm-length
parameters and at least $\mathcal{O}$(M) times greater computational cost since
the filter must be applied for every sample in the time series of sample size
M. We find feasibility of arm-length estimation on $\sim$day-long time scales
by using a novel Taylor-expanded version of the fractional delay interpolation
filter that allows half of the filter computation to be calculated and stored
before MCMC iterations 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.
