  LISA is considered to be launched alongside the Athena to probe the energetic
astrophysical processes. LISA can determine the direction of sources for
Athena's follow-up observation. As another space gravitational wave mission,
TAIJI is expected to be launched in the 2030s. The LISA-TAIJI network would
provide abundant merits for sources understanding. In this work, we simulate
the joint LISA-TAIJI observations for gravitational waves from coalescing
supermassive black hole binaries and monochromatic sources. By using the
numerical mission orbits, we evaluate the performances of sky localization for
various time-delay interferometry channels. For 30 days observation until
coalescence, the LISA-TAIJI network in optimal operation can localize all
simulated binary sources, $(10^7,\ 3.3 \times 10^6)\ M_\odot$, $(10^6,\ 3.3
\times 10^5)\ M_\odot$ and $(10^5,\ 3.3 \times 10^4)\ M_\odot$ at redshift
$z=2$, in 0.4 deg$^2$ (field of view of Wide Field Imager on Athena). The
angular resolution can be improved by more than 10 times comparing to LISA or
TAIJI single detector at a given percentage of population. The improvements for
monochromatic sources at 3 mHz and 10 mHz are relatively moderate in one-year
observation. The precision of sky localization could be improved by around 1 to
3 times comparing to single LISA at a given percentage of sources. For a
simulated 90 days observation for monochromatic waves, the LISA-TAIJI network
still represents a considerable localization advantage which could be more than
10 times better.
