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#### Calculating the precision of tilt-to-length coupling estimation and noise subtraction in LISA using Fisher information

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##### Citation

George, D., Sanjuan, J., Fulda, P., & Mueller, G. (2023). Calculating the precision
of tilt-to-length coupling estimation and noise subtraction in LISA using Fisher information.* Physical
Review D,* *107*(2): 022005. doi:10.1103/PhysRevD.107.022005.

Cite as: https://hdl.handle.net/21.11116/0000-000C-AE22-A

##### Abstract

Tilt-to-length (TTL) noise from angular jitter in LISA is projected to be the

dominant noise source in the milli-Hertz band unless corrected in

post-processing. The correction is only possible after removing the

overwhelming laser phase noise using time-delay interferometry (TDI). We

present here a frequency domain model that describes the effect of angular

motion of all three spacecraft on the interferometric signals after propagating

through TDI. We then apply a Fisher information matrix analysis to this model

to calculate the minimum uncertainty with which TTL coupling coefficients may

be estimated. Furthermore, we show the impact of these uncertainties on the

residual TTL noise in the gravitational wave readout channel, and compare it to

the impact of the angular witness sensors' readout noise. We show that the

residual TTL noise post-subtraction in the TDI variables for a case using the

LISA angular jitter requirement and integration time of one day is limited to

the 8\,pm/$\sqrt{\rm Hz}$ level by angular sensing noise. However, using a more

realistic model for the angular jitter we find that the TTL coupling

uncertainties are 70 times larger, and the noise subtraction is limited by

these uncertainties to the 14\,pm/$\sqrt{\rm Hz}$ level.

dominant noise source in the milli-Hertz band unless corrected in

post-processing. The correction is only possible after removing the

overwhelming laser phase noise using time-delay interferometry (TDI). We

present here a frequency domain model that describes the effect of angular

motion of all three spacecraft on the interferometric signals after propagating

through TDI. We then apply a Fisher information matrix analysis to this model

to calculate the minimum uncertainty with which TTL coupling coefficients may

be estimated. Furthermore, we show the impact of these uncertainties on the

residual TTL noise in the gravitational wave readout channel, and compare it to

the impact of the angular witness sensors' readout noise. We show that the

residual TTL noise post-subtraction in the TDI variables for a case using the

LISA angular jitter requirement and integration time of one day is limited to

the 8\,pm/$\sqrt{\rm Hz}$ level by angular sensing noise. However, using a more

realistic model for the angular jitter we find that the TTL coupling

uncertainties are 70 times larger, and the noise subtraction is limited by

these uncertainties to the 14\,pm/$\sqrt{\rm Hz}$ level.