Prospects of Normalizing Flow-Based Differentiable Particle Filters in Target Modelling

Abstract

Accurate target modelling is essential for modern air surveillance, particularly in the face of increasingly dynamic and unpredictable target behaviour, such as that exhibited by hypersonic missiles and UAVs. Traditional tracking methods, including Kalman Filters, Interacting Multiple Model (IMM) filters, and Particle Filters (PF), rely heavily on known target dynamics and are often limited in adaptability. This thesis explores the potential of Differentiable Particle Filters (DPFs), and in particular Normalizing Flow-based DPFs (NF-DPFs), as a data-driven alternative for modelling and tracking targets with unknown or highly non-linear dynamics. To address these challenges, a NF-DPF was implemented for radar-based target tracking. The filter was designed as a fully differentiable architecture that learns both the proposal distribution and the system dynamics using conditional normalizing flows based on the RealNVP framework. It incorporates optimal transport-based differentiable resampling and was trained end-to-end using a combination of a blockwise Evidence Lower Bound (ELBO) loss and the RMSE in position, velocity, and acceleration. The training was conducted on target data generated from stochastic differential equations (SDEs) simulating a range of motion patterns, including turning and accelerating trajectories. The NF-DPF was benchmarked against a bootstrap PF and a IMM filter across three experiments with increasing data complexity and variations in filter state dimensionality. Results showed that the NF-DPF provided competitive performance in low-dimensional settings and under specific dynamic behaviours, particularly turning trajectories that were not well captured by the IMM’s filters. However, it struggled to outperform the IMM in more complex scenarios involving higher-dimensional state representations. This performance gap was largely attributed to the increased difficulty of learning high-dimensional transition and proposal distributions, combined with computational limitations such as a restricted number of particles. The results highlight both the potential and current limitations of NF-DPFs for target modelling and contribute to the growing body of research exploring the integration of flexible, learning-based models into particle filtering frameworks for defence and surveillance applications.