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By employing Gauss decomposition, we establish a direct and explicitisomorphism between the twisted $q$-Yangians (in R-matrix presentation) andaffine $\imath$quantum groups (in current presentation) associated to symmetricpair of type AI introduced by Molev-Ragoucy-Sorba and Lu-Wang, respectively. Asa corollary, we obtain a PBW type basis for affine $\imath$quantum groups oftype AI.

Isomorphism between twisted $q$-Yangians and affine $\imath$quantum groups: type AI