Accuracy of estimation of parameters with space-borne gravitational wave observatory

Chao Zhang, Yungui Gong, Bin Wang, Chunyu Zhang

Employing the Fisher information matrix approximation, we estimate the errors
of parameters with TianQin and LISA for monochromatic gravitational waves. With
the long-wavelength approximation we give analytical formulas for the parameter
estimation errors. We analyze the amplitude modulation due to the changing
orientation of the detector plane and the Doppler effect due to the
translational motion of the center of the detector around the Sun. We disclose
that in the low frequency regimes there exist different patterns in angular
resolutions and estimation errors of the signal's parameters between LISA and
TianQin. The angular resolutions and the estimation errors of the signal's
parameters fall off as $S_n(f)/f^2$ for TianQin but $S_n(f)$ for LISA. However
in the medium frequency regimes we observe the same patterns where the angular
resolutions fall off as $S_n(f)/f^2$ and the estimation errors of the signal's
parameters fall off as $S_n(f)$ for both TianQin and LISA. In the high
frequency regimes, the long-wavelength approximation fails, we numerically
calculate the parameter estimation errors for LISA and TianQin and find that
the parameter estimation errors measured by TianQin are better than those by
LISA.