  By incorporating reconfigurable intelligent surface (RIS) into
communication-assisted localization systems, the issue of signal blockage
caused by obstacles can be addressed, and passive beamforming can be employed
to enhance localization accuracy. However, existing works mainly consider ideal
channels and do not account for the effects of realistic impairments like
carrier frequency offset (CFO) and phase noise (PN) on localization. This paper
proposes an iterative joint estimation algorithm for CFO, PN, and user position
based on maximum a posteriori (MAP) criterion and gradient descent (GD)
algorithm. Closed-form expressions for CFO and PN updates are provided. The
hybrid Cram\'{e}r-Rao lower bound (HCRLB) for the estimation parameters is
derived, and the ambiguity in CFO and PN estimation is analyzed. To minimize
the HCRLB, a non-convex RIS shift optimization problem is formulated and is
transformed into a convex semidefinite programming (SDP) problem using the
technique of semidefinite relaxation (SDR) and Schur complement. After
optimizing the RIS phase shift, the theoretical positioning accuracy within the
area of interest (AOI) can be improved by two orders of magnitude, with a
maximum positioning root mean square error (RMSE) lower than $\rm 10^{-2}m$.
