  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.
