  Accurate localization can be performed in visible light systems in
non-line-of-sight (NLOS) scenarios by utilizing intelligent reflecting surfaces
(IRSs), which are commonly in the form of mirror arrays with adjustable
orientations. When signals transmitted from light emitting diodes (LEDs) are
reflected from IRSs and collected by a receiver, the position of the receiver
can be estimated based on power measurements by utilizing the known parameters
of the LEDs and IRSs. Since the orientation vectors of IRS elements (mirrors)
cannot be adjusted perfectly in practice, it is important to evaluate the
effects of mismatches between desired and true orientations of IRS elements. In
this study, we derive the misspecified Cramer-Rao lower bound (MCRB) and the
mismatched maximum likelihood (MML) estimator for specifying the estimation
performance and the lower bound in the presence of mismatches in IRS
orientations. We also provide comparisons with the conventional maximum
likelihood (ML) estimator and the CRB in absence of orientation mismatches for
quantifying the effects of mismatches. It is shown that orientation mismatches
can result in significant degradation in localization accuracy at high
signal-to-noise ratios.
