  Channel estimation is one of the key challenges for the deployment of
extremely large-scale reconfigurable intelligent surface (XL-RIS) assisted
multiple-input multiple-output (MIMO) systems. In this paper, we study the
channel estimation problem for XL-RIS assisted multi-user XL-MIMO systems with
hybrid beamforming structures. For this system, we propose an {\em unified}
channel estimation method that yields a notable estimation accuracy in the
near-field BS-RIS and near-field RIS-User channels (in short, near-near field
channels), far-near field channels, and far-far field channels. Our key idea is
that the effective (or cascaded) channels to be estimated can be each
factorized as the product of low-rank matrices (i.e., the product of the common
(or user-independent) matrix and the user-specific coefficient matrix). The
common matrix whose columns are the basis of the column space of the BS-RIS
channel matrix is efficiently estimated via a {\em collaborative} low-rank
approximation (CLRA). Leveraging the hybrid beamforming structures, we develop
an efficient iterative algorithm that jointly optimizes the user-specific
coefficient matrices. Via experiments and complexity analysis, we verify the
effectiveness of the proposed channel estimation method (named CLRA-JO) in the
aforementioned three classes of wireless channels.
