  We present an approach for state and parameter estimation in retinal laser
treatment by a novel setup where both measurement and heating is performed by a
single laser. In this medical application, the temperature that is induced by
the laser in the patient's eye is critical for a successful and safe treatment.
To this end, we pursue a model-based approach using a model given by a heat
diffusion equation on a cylindrical domain, where the source term is given by
the absorbed laser power. The model is parametric in the sense that it involves
an absorption coefficient, which depends on the treatment spot and plays a
central role in the input-output behavior of the system. After discretization,
we apply a particularly suited parametric model order reduction to ensure
real-time tractability while retaining parameter dependence. We augment known
state estimation techniques, i.e., extended Kalman filtering and moving horizon
estimation, with parameter estimation to estimate the absorption coefficient
and the current state of the system. Eventually, we show first results for
simulated and experimental data from porcine eyes. We find that, regarding
convergence speed, the moving horizon estimation slightly outperforms the
extended Kalman filter on measurement data in terms of parameter and state
estimation, however, on simulated data the results are very similar.
