LISA Non-Linear Dynamics and Tilt-To-Length Coupling

Abstract: For the LISA mission, Tilt-To-Length (TTL) coupling is expected to be one of the dominant instrumental noise contributions after laser frequency noise is suppressed based, on assumptions on the size of the coupling and angular jitter levels. This work uses for the first time a closed-loop, non-linear, and time-varying dynamics implementation to simulate detailed angular jitters for the spacecraft and optical benches. In turn, this gives an improved expectation of the TTL contribution to the interferometric output. It is shown that the TTL coupling impact is limited given current estimates on the size of coupling coefficients. A time-domain Least Squares estimator is used to infer the TTL parameters from the simulated measurements. The bias and correlations limit the estimator in the case of regular datasets with amplified TTL coefficients to a relative error of $10\%$, but the subtraction of the TTL signal still works well. For lower readout noises, the estimation error diverges, which can be mitigated using a regularization term. Alternatively, using sinusoidal maneuvers improves the inference to a high accuracy of $0.1\%$ for TTL coefficients around the expected level, removing all correlations in the inferred parameters. This validates the maneuver design by Wegener et al. (2025) in this closed-loop setting.