Parameter estimation is a growing area of interest in statistical signal processing. Some parameters in real-life applications vary in space as opposed to those that are static. Most common methods in estimating parameters involve solving an optimization problem where the cost function is assembled variously; for example, maximum likelihood and maximum a posteriori methods. However, these methods do not have exact solutions to most real-life problems. It is for this reason that Monte Carlo methods are preferred. In this paper, we treat the estimation of parameters which vary with space. We use Metropolis-Hastings algorithm as a selection criteria for the maximum filter likelihood. Comparisons are made with the use of joint estimation of both the spatially varying parameters and the state. We illustrate the procedures employed in this paper by means of two hyperbolic SPDEs: the advection and the wave equation. The Metropolis-Hastings procedure registers better estimates.

翻译：参数估算是一个对统计信号处理越来越感兴趣的领域。空间实际应用中的一些参数与静态参数不同。估算参数的最常用方法涉及在成本函数组合各异的情况下解决优化问题;例如,最大可能性和最高后遗症方法。但是,这些方法没有确切解决大多数实际生活问题的办法。正因为如此,我们更喜欢蒙特卡洛方法。在本文中,我们处理与空间不同的参数的估计。我们使用大都会-哈斯廷算法作为最大过滤可能性的选择标准。比较是通过使用空间差异参数和状态的联合估计进行。我们用两种双曲SPDE(倾斜和波方程式)来说明本文使用的程序。Metropolis-Hasting程序记录更好的估计。