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.

翻译：在非视距场景下，可通过采用智能反射面实现可见光系统中的精确定位。智能反射面通常采用方向可调的镜面阵列形式。当发光二极管发射的信号经智能反射面反射并被接收器收集时，可利用发光二极管和智能反射面的已知参数，基于功率测量值估计接收器的位置。由于智能反射面单元（镜面）的方向矢量在实践中无法完美调节，评估智能反射面单元期望方向与实际方向之间失配的影响至关重要。本研究推导了误指定克拉美-罗下界和失配最大似然估计器，用于在智能反射面方向存在失配时界定估计性能及其下界。同时，通过与无方向失配情况下的传统最大似然估计器及克拉美-罗下界进行比较，量化了方向失配的影响。研究表明，在高信噪比条件下，方向失配会导致定位精度显著下降。