We develop a blind deconvolution scheme for input-output systems described by distributed parameter systems with boundary input and output. An abstract functional analytic theory based on results for the linear quadratic control of infinite dimensional systems with unbounded input and output operators is presented. The blind deconvolution problem is then reformulated as a series of constrained linear and nonlinear optimization problems involving infinite dimensional dynamical systems. A finite dimensional approximation and convergence theory is developed. The theory is applied to the problem of estimating blood or breath alcohol concentration (respectively, BAC or BrAC) from biosensor-measured transdermal alcohol concentration (TAC) in the field. A distributed parameter model with boundary input and output is proposed for the transdermal transport of ethanol from the blood through the skin to the sensor. The problem of estimating BAC or BrAC from the TAC data is formulated as a blind deconvolution problem. A scheme to identify distinct drinking episodes in TAC data based on a Hodrick Prescott filter is discussed. Numerical results involving actual patient data are presented.

中文翻译：

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具有无界输入和输出的分布式参数系统的盲解卷积并从透皮生物传感器数据确定血液酒精浓度

我们为由具有边界输入和输出的分布式参数系统描述的输入-输出系统开发了一种盲解卷积方案。一个抽象的泛函分析理论基于无限维系统的线性二次控制与无界输入和输出算子的结果。然后将盲解卷积问题重新表述为一系列涉及无限维动力系统的约束线性和非线性优化问题。开发了有限维近似和收敛理论。该理论应用于从现场生物传感器测量的透皮酒精浓度 (TAC) 估计血液或呼吸酒精浓度（分别为 BAC 或 BrAC）的问题。提出了一种具有边界输入和输出的分布式参数模型，用于乙醇从血液通过皮肤到传感器的透皮传输。从 TAC 数据估计 BAC 或 BrAC 的问题被表述为盲解卷积问题。讨论了基于 Hodrick Prescott 过滤器在 TAC 数据中识别不同饮酒事件的方案。显示了涉及实际患者数据的数值结果。