Diffusion Models for Generative Modelling of a Posteriori Probability Measures in Target Tracking

Sammanfattning

Recent advancements in the field of generative machine learning, Diffusion Models (DMs) in particular, have made it possible to learn and sample according to complex conditional probability distributions. In surveillance applications, the state estimation task is challenged with increasingly unpredictable targets, and it is therefore of interest to explore new methods to perform statistical inference. This thesis investigates modern approaches to condition score-based DMs to allow for sampling of target trajectories, expressed as Stochastic Differential Equations (SDEs), adjusted for partial and noisy observations. DM network architectures developed for time series data are used and conditioned with techniques that work during inference. We find that a wide variety of motion models can be accurately generated according to the underlying distribution with high fidelity, showing successful conditioning using at least one of the tested methods. However, the models used require substantial computational resources, which is why dimensionality reduction techniques are needed for real-world applications. We thus discuss and explore latent diffusion ideas, which show promising results for unconditional modelling—and it is plausible that future work can allow for extension to accurate conditioning as well.