标题： 基于路径积分蒙特卡罗评估的状态和参数估计 显示英文标题

标题： State and parameter estimation using Monte Carlo evaluation of path integrals

摘要： 将动力系统观测信息传递到估计系统模型的固定参数和未观测状态可以表述为在模型状态空间中对离散时间路径积分进行评估。 观测值作为引导势，与模型的动力学规则共同作用，引导状态空间中的系统轨道。 路径积分表示允许直接数值计算通过状态空间的条件均值路径以及该均值周围的条件矩。 使用一种蒙特卡洛方法来选择状态空间中的路径，我们展示了如何计算这些矩，并在一个有趣的模型系统中演示了观测信息传递作用的显式影响。 我们探讨了需要多少观测值才能估计未观测的状态变量，并检查了底层条件概率的高斯性假设。 显示英文摘要

摘要： Transferring information from observations of a dynamical system to estimate the fixed parameters and unobserved states of a system model can be formulated as the evaluation of a discrete time path integral in model state space. The observations serve as a guiding potential working with the dynamical rules of the model to direct system orbits in state space. The path integral representation permits direct numerical evaluation of the conditional mean path through the state space as well as conditional moments about this mean. Using a Monte Carlo method for selecting paths through state space we show how these moments can be evaluated and demonstrate in an interesting model system the explicit influence of the role of transfer of information from the observations. We address the question of how many observations are required to estimate the unobserved state variables, and we examine the assumptions of Gaussianity of the underlying conditional probability.