We consider a class of high-dimensional spatial filtering problems, where the spatial locations of the observations are unknown and driven by the unobserved signal. This problem is exceptionally challenging as not only is the problem of high-dimensions in the signal, but the model for the signal yields longer-range time dependencies on this object. Motivated by this model we revisit a lesser-known and $\textit{exact}$ computational methodology from Centanni $\&$ Minozzo (2006a) (see also Martin et al. (2013)) designed for filtering of point-processes. We adapt the methodology for this new class of problem. The algorithm is implemented on high-dimensional (of the order of $10^4$) rotating shallow water model with real and synthetic observational data from ocean drifters. In comparison to existing methodology, we demonstrate a significant improvement in speed and accuracy.

翻译：我们考虑一类高维空间滤波问题，其中观测点的空间位置未知且受未观测信号驱动。该问题极具挑战性，不仅因为信号具有高维特性，更在于信号模型会导致对象产生长程时间依赖性。受此模型启发，我们重新审视了Centanni & Minozzo (2006a)（另见Martin等人(2013)）提出的一种鲜为人知但具有$\textit{精确}$计算特性的点过程滤波方法，并将其适配到这类新型问题中。我们将该算法应用于高维（量级达$10^4$）旋转浅水模型，并采用来自海洋漂流浮标的实测与合成观测数据。相较于现有方法，我们展示了该方法在计算速度与精度上的显著提升。