Fast time delay interferometry: TDI on the fly

Space-based gravitational wave (GW) observatories, such as the future Laser Interferometer Space Antenna, employ synthetic time delay interferometry (TDI) to cancel the otherwise overwhelming laser frequency noise. The phase readouts at each spacecraft are combined with a carefully designed collection of time delays that cancel the laser frequency noise. The same collection of time delays must be applied to the GW signal models used for analysis, along with geometrical factors that encode the projection of the wave polarization tensor onto the arms of the interferometer. In principle, fully generic TDI calculations require the GW signal model to be evaluated at dozens of delay times for each data sample, a process that would require tens of millions of evaluations for a year-long signal. Here, a new method is presented that cuts the computational cost by a factor of 10,000 compared to a direct implementation at the data sample cadence, while incurring no loss in accuracy. The approach works for completely general spacecraft orbits and any flavor of TDI.