Visible Light Positioning under Luminous Flux Degradation of LEDs

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.