Visibility-domain matched filter ($\hat{a}=\frac{\mathrm{Re}(T^{†}{C}^{-1}d)}{T^{†}{C}^{-1}T}$)

For data $d=aT+n$, known complex source template $T$, real amplitude $a$, and known noise covariance $C$, generalized least squares gives the displayed amplitude. This convention takes $C$ in the quadratic objective $(d-aT{)}^{†}{C}^{-1}(d-aT)$; factors of two in the amplitude variance depend on whether complex-component or real-component covariance is used. Source position, shape and contaminants must be fitted or marginalized when uncertain. An extended-source complex visibility template accounts for resolved-out flux rather than assuming the source is unresolved.