Virtual Target Trajectory Prediction for Stochastic Targets

TL;DR

The paper tackles the problem of predicting stochastic target trajectories in guidance contexts by adopting Conditional Normalizing Flows to model the conditional distribution of future target positions. It enables fast sampling and exact density evaluation of $p(\mathbf{x}\mid t, \mathbf{x}_0, \mathbf{\psi})$, and then employs time-series k-means clustering to convert samples into a small set of representative 'virtual target' trajectories for deterministic planning. The approach is demonstrated on simple 2D maneuvering targets, complex 3D ballistic targets, and multi-target scenarios, showing favorable speedups over Monte Carlo methods and meaningful alignment with observed distributions. The work provides a practical, target-agnostic framework that can be integrated as a drop-in replacement for deterministic predictors in guidance and planning pipelines. Overall, it advances robust, probabilistic trajectory prediction with efficient downstream applicability in autonomous guidance systems.

Abstract

Trajectory prediction of aerial vehicles is a key requirement in applications ranging from missile guidance to UAV collision avoidance. While most prediction methods assume deterministic target motion, real-world targets often exhibit stochastic behaviors such as evasive maneuvers or random gliding patterns. This paper introduces a probabilistic framework based on Conditional Normalizing Flows (CNFs) to model and predict such stochastic dynamics directly from trajectory data. The learned model generates probability distributions of future target positions conditioned on initial states and dynamic parameters, enabling efficient sampling and exact density evaluation. To provide deterministic surrogates compatible with existing guidance and planning algorithms, sampled trajectories are clustered using a time series k-means approach, yielding a set of representative "virtual target" trajectories. The method is target-agnostic, computationally efficient, and requires only trajectory data for training, making it suitable as a drop-in replacement for deterministic predictors. Simulated scenarios with maneuvering and ballistic targets demonstrate that the proposed approach bridges the gap between deterministic assumptions and stochastic reality, advancing guidance and control algorithms for autonomous vehicles.

Figures (15)

• Figure 1: Illustration of the structure of the prediction framework.
• Figure 2: Illustration of the transformation of samples from a normal distribution to a complex distribution (and vice versa) using Normalizing Flows. Figure adapted from Schneider, M., Loureiro, R., Cunis, T., and Fichter, W., “Trajectory Prediction for Missile Targets: A Probabilistic Approach Using Machine Learning,” in CEAS EuroGNC Conference, 2024. Licensed under a Creative Commons Attribution 4.0 International License (CC-BY 4.0).
• Figure 3: Illustration of the Normalizing Flows concept with neural networks $\alpha_i$ and transformations $f_{\Theta_i}$ with parameters $\Theta_i$. Figure adapted from Schneider, M., Loureiro, R., Cunis, T., and Fichter, W., “Trajectory Prediction for Missile Targets: A Probabilistic Approach Using Machine Learning,” in CEAS EuroGNC Conference, 2024. Licensed under a Creative Commons Attribution 4.0 International License (CC-BY 4.0).
• Figure 4: Illustration of the Conditional Normalizing Flows concept with neural networks $\beta_i$ and transformations $f_{\Theta_i}$ with parameters $\Theta_i$, conditioned on the time $t$ and dynamics parameters $\psi$.
• Figure 5: Illustration of the translation (by $\bar{\mathbf{p}}$) and the rotation (by $\chi$) of the predicted target positions.