Learning Neural SDEs for Bayesian Filtering and Smoothing

Abstract

This thesis investigates neural stochastic differential equations (neural SDEs) trained within a Wasserstein Generative Adversarial Network (WGAN) framework to approximate conditional probability distributions of trajectories, with applications in radar-based tracking. The study focuses on how different loss functions impact model performance for smoothing (estimating past states) and filtering (estimating current state) from noisy observations. Experiments in one- and two-dimensions show that neural SDEs effectively capture complex nonlinear dynamics and uncertainty relevant to radar tracking. Future research directions include extending the state space with additional physical quantities, incorporating Lévy jump processes, and refining loss functions for better accuracy around observations. In general, the study demonstrates the feasibility and versatility of WGAN-trained neural SDEs for Bayesian filtering and smoothing.