Fully data-driven time-delay interferometry with time-varying delays

We recently introduced the basic concepts of an approach to filtering strongly laser-noise dominated space-based gravitational-wave data, like LISA's phase comparison data streams, which does not rely on independent knowledge of a temporal delays pattern in the dominant noise that generates the data. Instead, our automated Principal Component Interferometry (aPCI) approach only assumes that one can produce some linear combinations of the temporally nearby regularly spaced phase measurements, which cancel the laser noise. Then we let the data reveal those combinations, thus providing us with a set of laser-noise-free data channels. Our basic approach relied on the simplifying additional assumption that laser-noise-cancelling data combinations or the filters which lead to the laser-noise-free data streams are time-independent. In LISA, however, these filters will vary as the constellation armlengths evolve. Here, we discuss a generalization of the basic aPCI concept compatible with data dominated by a still unmodeled but slowly varying dominant noise covariance. We find that despite its independence on any model, the aPCI processing successfully mitigates laser frequency noise below the other noise sources level, and that its sensitivity to gravitational waves is the same as the state-of-the-art second-generation time-delay interferometry, up to a 2% error