State and parameter estimation for retinal laser treatment

Abstract: Adequate therapeutic retinal laser irradiation needs to be adapted to the local absorption. This leads to time-consuming treatments as the laser power needs to be successively adjusted to avoid under- and overtreatment caused by too low or too high temperatures. Closed-loop control can overcome this burden by means of temperature measurements. To allow for model predictive control schemes, the current state and the spot-dependent absorption need to be estimated. In this paper, we thoroughly compare moving horizon estimator (MHE) and extended Kalman filter (EKF) designs for joint state and parameter estimation. We consider two different scenarios, the estimation of one or two unknown absorption coefficients. For one unknown parameter, both estimators perform very similar. For two unknown parameters, we found that the MHE benefits from active parameter constraints at the beginning of the estimation, whereas after a settling time both estimators perform again very similar as long as the parameters are inside the considered parameter bounds.