Functional Principal Component Analysis of Radio–Optical Reference Frame Tie

The Gaia optical reference frame is intrinsically undefined with respect to global orientation and spin, so it needs be anchored in the radio-based International Celestial Reference Frame (ICRF) provide a referenced quasi-inertial celestial coordinate system. link between two fundamental frames realized through samples of distant extragalactic sources, mostly AGNs quasars, but only smaller sample radio-loud ICRF sources counterparts available determine mutual orientation. robustness this can mathematically formulated framework functional principal component analysis using set vector spherical harmonics represent differences positions common objects. weakest eigenvectors are computed, which describe greatest deficiency link. deficient or poorly determined terms specific fields on sphere carry largest errors absolute astrometry ICRF. This provides guidelines future development maximizing accuracy over entire sphere. A measure least-squares solution, applied any linear model fitting problem, introduced help discriminate tie models different degrees.