Prospects of neural SDEs for Bayesian smoothing

Abstract

Due to the importance of airspace defence for national security, the pursuit of efficient and accurate methods for tracking airborne targets is of great interest. An essential part of target tracking is to estimate the state of a target given (noisy) observations from a radar. This involves calculating conditional probability distributions given measurements (e.g. smoothing), which is associated with large computational costs for high-dimensional and/or nonlinear target models. This thesis investigates the possibility of alleviating such bottlenecks by employing neural stochastic differential equations (neural SDEs) as generative models for the smoothing problem - possibly allowing the use of more complex models in real-time applications. As part of this work, it is first shown that SDE models can be used as generative models for conditional distributions of target states given noisy measurements obtained at discrete points of time. Secondly, this thesis presents a detailed description of how the neural SDE is utilized as the generator of a so called Wasserstein Generative Adversarial Network (WGAN) in signature space, meaning it can be trained to approximate conditional probability distributions for the smoothing problem. Thirdly, the SDE-model is evaluated with respect to a series of test-problems. Findings indicate that the neural SDE can reproduce qualitative features for conditional distributions for nonlinear problems, while further developments of the method and paradigms for training are needed to achieve trained SDE-models which are perceived to (in distribution) closely resemble their theoretically exact counterparts.