标题： 基于优化的数据丰富化方法使用随机动力系统模型 显示英文标题

标题： Optimization Based Data Enrichment Using Stochastic Dynamical System Models

摘要： 我们开发了一个通用框架，用于在具有噪声污染的连续时间动态系统和离散时间噪声测量中进行状态估计。 我们的方法基于最大似然估计，并利用变分法推导出连续时间函数的最优条件。 我们不对从测量到状态估计的映射形式或噪声项的分布做出先验假设，使该框架比卡尔曼滤波/平滑更通用，在卡尔曼滤波/平滑中假设该映射是线性的且噪声是高斯的。 由此产生的最优解被解释为一个连续时间样条，其结构和时间依赖性由系统动态和过程噪声及测量噪声的分布决定。 类似于卡尔曼平滑，最优样条在测量时刻提供了更高的数据准确性，除了在测量时刻之外提供连续时间估计。 我们通过示例展示我们方法的实用性和通用性，这些示例根据特定系统呈现线性和非线性数据滤波器。 显示英文摘要

摘要： We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of variations to derive optimality conditions for continuous time functions. We make no prior assumptions on the form of the mapping from measurements to state-estimate or on the distributions of the noise terms, making the framework more general than Kalman filtering/smoothing where this mapping is assumed to be linear and the noises Gaussian. The optimal solution that arises is interpreted as a continuous time spline, the structure and temporal dependency of which is determined by the system dynamics and the distributions of the process and measurement noise. Similar to Kalman smoothing, the optimal spline yields increased data accuracy at instants when measurements are taken, in addition to providing continuous time estimates outside the measurement instances. We demonstrate the utility and generality of our approach via illustrative examples that render both linear and nonlinear data filters depending on the particular system.