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Interspacecraft ranging is crucial for the suppression of laser frequencynoise via time-delay interferometry (TDI). So far, the effects of on-boarddelays and ambiguities on the LISA ranging observables were neglected in LISAmodelling and data processing investigations. In reality, on-board delays causeoffsets and timestamping delays in the LISA measurements, and pseudo-randomnoise (PRN) ranging is ambiguous, as it only determines the range up to aninteger multiple of the PRN code length. In this article, we identify the fourLISA ranging observables: PRN ranging, the sideband beatnotes at theinterspacecraft interferometer, TDI ranging, and ground-based observations. Wederive their observation equations in the presence of on-board delays, noise,and ambiguities. We then propose a three-stage ranging sensor fusion to combinethese observables in order to gain accurate and precise ranging estimates. Wepropose to calibrate the on-board delays on ground and to compensate theassociated offsets and timestamping delays in an initial data treatment (stage1). We identify the ranging-related routines, which need to run continuouslyduring operation (stage 2), and implement them numerically. Essentially, thisinvolves the reduction of ranging noise, for which we develop a Kalman filtercombining the PRN ranging and the sideband beatnotes. We further implementcrosschecks for the PRN ranging ambiguities and offsets (stage 3). We show thatboth ground-based observations and TDI ranging can be used to resolve the PRNranging ambiguities. Moreover, we apply TDI ranging to estimate the PRN rangingoffsets.

Ranging Sensor Fusion in LISA Data Processing: Treatment of Ambiguities, Noise, and On-Board Delays in LISA Ranging Observables