The position estimation problem based on received power measurements is investigated for visible light systems in the presence of luminous flux degradation of light emitting diodes (LEDs). When the receiver is unaware of this degradation and performs position estimation accordingly, there exists a mismatch between the true model and the assumed model. For this scenario, the misspecified Cram\'er-Rao bound (MCRB) and the mismatched maximum likelihood (MML) estimator are derived to quantify the performance loss due to this model mismatch. Also, the Cram\'er-Rao lower bound (CRB) and the maximum likelihood (ML) estimator are derived when the receiver knows the degradation formula for the LEDs but does not know the decay rate parameter in that formula. In addition, in the presence of full knowledge about the degradation formula and the decay rate parameters, the CRB and the ML estimator are obtained to specify the best achievable performance. By evaluating the theoretical limits and the estimators in these three scenarios, we reveal the effects of the information about the LED degradation model and the decay rate parameters on position estimation performance. It is shown that the model mismatch can result in significant degradation in localization performance at high signal-to-noise ratios, which can be compensated by conducting joint position and decay rate parameter estimation.

翻译：针对发光二极管（LED）光通量衰减情况下的可见光系统，研究了基于接收功率测量的位置估计问题。当接收端未感知到这种衰减并据此进行位置估计时，真实模型与假设模型间存在失配。针对该场景，推导了误指定克拉美罗界（MCRB）和失配最大似然（MML）估计器，以量化模型失配导致的性能损失。同时，在接收端已知LED衰减公式但未知该公式中衰减率参数的情况下，推导了克拉美罗下界（CRB）和最大似然（ML）估计器。此外，在完全掌握衰减公式及衰减率参数的情况下，获得了表征最佳可达性能的CRB和ML估计器。通过评估上述三种场景的理论极限与估计器，揭示了LED衰减模型信息及衰减率参数对位置估计性能的影响。结果表明，在高信噪比条件下，模型失配可能导致定位性能显著下降，而通过联合估计位置与衰减率参数可有效补偿该损失。