A Time-frequency approach to the LISA Global Fit

The LISA observatory will detect millions of long duration, overlapping signals, necessitating a joint, "Global Fit" of the resolvable signals, the confusion noise from unresolved signals, and instrument noise. The confusion noise will be non-stationary due to the time varying LISA antenna pattern, and the instrument noise is also likely to be non-stationary over the many years long span of the mission. Wavelet domain, time-frequency methods can efficiently handle non-stationary noise, and provide a natural heterodyning of the signals that results in very efficient likelihood calculations. I will describe the latest update to the Global LISA Analysis Software Suite (GLASS) which includes fast and fully general wavelet domain time-delay-interferometry (TDI) responses to gravitational wave signals; detailed models of the confusion noise modulation of all the TDI channels for arbitrary galaxy shapes; and component wise modeling of the instrument noise. We show that this new approach removes the biases seen in traditional frequency domain analyses that assume the data are stationary.