The paper deals with state estimation of a spatially distributed system given noisy measurements from pointwise-in-time-and-space threshold sensors spread over the spatial domain of interest. A Maximum A posteriori Probability (MAP) approach is undertaken and a Moving Horizon (MH) approximation of the MAP cost-function is adopted. It is proved that, under system linearity and log-concavity of the noise probability density functions, the proposed MH-MAP state estimator amounts to the solution, at each sampling interval, of a convex optimization problem. Moreover, a suitable centralized solution for large-scale systems is proposed with a substantial decrease of the computational complexity. The latter algorithm is shown to be feasible for the state estimation of spatially-dependent dynamic fields described by Partial Differential Equations (PDE) via the use of the Finite Element (FE) spatial discretization method. A simulation case-study concerning estimation of a diffusion field is presented in order to demonstrate the effectiveness of the proposed approach. Quite remarkably, the numerical tests exhibit a noise-assisted behavior of the proposed approach in that the estimation accuracy results optimal in the presence of measurement noise with non-null variance.

中文翻译：

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应用于现场监测的阈值测量的 MAP 移动水平估计

该论文涉及空间分布式系统的状态估计，其中给出了来自分布在感兴趣空间域上的逐点时间和空间阈值传感器的噪声测量。采用最大后验概率 (MAP) 方法并采用 MAP 成本函数的移动地平线 (MH) 近似。证明了在噪声概率密度函数的系统线性和对数凹度下，所提出的 MH-MAP 状态估计器相当于在每个采样间隔，凸优化问题的解。此外，还提出了一种适用于大规模系统的集中式解决方案，大大降低了计算复杂度。通过使用有限元 (FE) 空间离散化方法，后一种算法对于偏微分方程 (PDE) 描述的空间相关动态场的状态估计是可行的。介绍了一个关于扩散场估计的模拟案例研究，以证明所提出方法的有效性。非常值得注意的是，数值测试表现出所提出方法的噪声辅助行为，因为在存在具有非零方差的测量噪声的情况下，估计精度结果最佳。