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.

中文翻译：

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基于模型的视网膜激光治疗的状态和参数估计

我们提出了一种通过新型设置在视网膜激光治疗中进行状态和参数估计的方法，该方法通过单个激光器进行测量和加热。在这种医疗应用中，激光在患者眼内感应的温度对于成功且安全的治疗至关重要。为此，我们追求一种基于模型的方法，即使用圆柱域上的热扩散方程式给出的模型，其中源项由吸收的激光功率给出。该模型是参数化的，因为它涉及吸收系数，吸收系数取决于治疗点，并且在系统的输入输出行为中起着核心作用。离散化之后，我们应用了特别合适的参数模型阶数缩减，以确保实时易处理性，同时保留参数依赖性。我们使用参数估计来扩充已知的状态估计技术，即扩展的卡尔曼滤波和移动视界估计，以估计吸收系数和系统的当前状态。最终，我们显示了来自猪眼的模拟和实验数据的第一个结果。我们发现，就收敛速度而言，在参数和状态估计方面，移动视界估计在性能数据上略胜于扩展卡尔曼滤波器，但是在模拟数据上，结果却非常相似。