标题： 用于由时间-空间布朗片驱动的线性系统的卡尔曼滤波器 显示英文标题

标题： A Kalman filter for linear systems driven by time-space Brownian sheet

摘要： 我们研究一个线性滤波问题，其中信号和观测过程被描述为由时间-空间布朗片驱动的线性随机微分方程的解。 我们推导了在观测给定情况下信号的条件值的随机积分方程，这可以看作是经典卡尔曼滤波的时间-空间模拟。 结果通过涉及噪声观测的滤波问题示例进行了说明。 显示英文摘要

摘要： We study a linear filtering problem where the signal and observation processes are described as solutions of linear stochastic differential equations driven by time-space Brownian sheets. We derive a stochastic integral equation for the conditional value of the signal given the observation, which can be considered a time-space analogue of the classical Kalman filter. The result is illustrated with examples of the filtering problem involving noisy observations.