Markov random fields (MRFs) are invaluable tools across diverse fields, and spatiotemporal MRFs (STMRFs) amplify their effectiveness by integrating spatial and temporal dimensions. However, modeling spatiotemporal data introduces additional hurdles, including dynamic spatial dimensions and partial observations, prevalent in scenarios like disease spread analysis and environmental monitoring. Tracking high-dimensional targets with complex spatiotemporal interactions over extended periods poses significant challenges in accuracy, efficiency, and computational feasibility. To tackle these obstacles, we introduce the variable target MRF scalable particle filter (VT-MRF-SPF), a fully online learning algorithm designed for high-dimensional target tracking over STMRFs with varying dimensions under partial observation. We rigorously guarantee algorithm performance, explicitly indicating overcoming the curse of dimensionality. Additionally, we provide practical guidelines for tuning graphical parameters, leading to superior performance in extensive examinations.

翻译：马尔可夫随机场（MRFs）是各领域不可或缺的工具，而时空马尔可夫随机场（STMRFs）通过整合空间与时间维度进一步增强了其有效性。然而，对时空数据建模引入了额外挑战，包括动态空间维度和部分观测，这在疾病传播分析和环境监测等场景中普遍存在。在长时间跨度内跟踪具有复杂时空交互的高维目标对准确性、效率和计算可行性提出了重大挑战。为应对这些难题，我们提出了可变目标马尔可夫随机场可扩展粒子滤波器（VT-MRF-SPF），这是一种全在线学习算法，专用于在部分观测条件下对维度动态变化的STMRFs进行高维目标跟踪。我们严格保证了算法性能，明确表明克服了维度灾难。此外，我们提供了调优图参数的实际指导，在广泛实验中实现了卓越性能。