Visible Light Positioning under Luminous Flux Degradation of LEDs

We investigate a position estimation problem based on received power measurements in visible light systems considering luminous flux degradation of light emitting diodes (LEDs) under three distinct scenarios. In Scenario 1, the receiver is unaware of this degradation and performs position estimation accordingly; hence, there exists a mismatch between the true model and the assumed model. The misspecified Cramér-Rao bound (MCRB) and the mismatched maximum likelihood (MML) estimator are derived to quantify the performance loss due to this model mismatch. In Scenario 2, where the receiver knows the degradation formula for the LEDs but does not know the decay rate parameter in that formula, the Cramér-Rao lower bound (CRB) and the maximum likelihood (ML) estimator are derived to analyze its position estimation performance. In Scenario 3, with full knowledge of both the degradation formula and decay rate parameters, we obtain the CRB and the ML estimator to specify the best achievable performance. By comparing the theoretical limits and the estimators in these three scenarios, we reveal the effects of the knowledge of the LED degradation model and the decay rate parameters on position estimation performance. In the simulation results, it is shown that precise knowledge of the degradation model and the decay rate parameter leads to the best possible localization accuracy. Also, the model mismatch can result in significant degradation in localization performance at high signal-to-noise ratios, which can be mitigated by conducting joint position and decay rate parameter estimation.