论文标题
部分观察到的随机对流扩散方程的联合在线参数估计和最佳传感器位置
Joint Online Parameter Estimation and Optimal Sensor Placement for the Partially Observed Stochastic Advection-Diffusion Equation
论文作者
论文摘要
在本文中，我们考虑了共同执行在线参数估计和最佳传感器位置的问题，以部分观察到的无限尺寸线性扩散过程。我们以连续时间的两次尺度随机梯度下降算法的形式提出了一种新的解决方案，该算法递归地寻求最大程度地相对于未知模型参数，以最大程度地利用对数模型的性格，并最大程度地减少隐藏状态估计的预期平方平方误差与传感器位置相对于传感器的估计。我们还提供了广泛的数值结果，说明了所提出的方法的性能，即隐藏信号受二维随机反流扩散方程的控制。
In this paper, we consider the problem of jointly performing online parameter estimation and optimal sensor placement for a partially observed infinite dimensional linear diffusion process. We present a novel solution to this problem in the form of a continuous-time, two-timescale stochastic gradient descent algorithm, which recursively seeks to maximise the log-likelihood with respect to the unknown model parameters, and to minimise the expected mean squared error of the hidden state estimate with respect to the sensor locations. We also provide extensive numerical results illustrating the performance of the proposed approach in the case that the hidden signal is governed by the two-dimensional stochastic advection-diffusion equation.
