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The position estimation problem based on received power measurements isinvestigated for visible light systems in the presence of luminous fluxdegradation of light emitting diodes (LEDs). When the receiver is unaware ofthis degradation and performs position estimation accordingly, there exists amismatch between the true model and the assumed model. For this scenario, themisspecified Cram\'er-Rao bound (MCRB) and the mismatched maximum likelihood(MML) estimator are derived to quantify the performance loss due to this modelmismatch. Also, the Cram\'er-Rao lower bound (CRB) and the maximum likelihood(ML) estimator are derived when the receiver knows the degradation formula forthe LEDs but does not know the decay rate parameter in that formula. Inaddition, in the presence of full knowledge about the degradation formula andthe decay rate parameters, the CRB and the ML estimator are obtained to specifythe best achievable performance. By evaluating the theoretical limits and theestimators in these three scenarios, we reveal the effects of the informationabout the LED degradation model and the decay rate parameters on positionestimation performance. It is shown that the model mismatch can result insignificant degradation in localization performance at high signal-to-noiseratios, which can be compensated by conducting joint position and decay rateparameter estimation.

Visible Light Positioning under Luminous Flux Degradation of LEDs