  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.
