The Mixed Ornstein-Uhlenbeck Model in Target Tracking for Mean-Reverting Motion and Weaving Motion
A 2nd Order Continuous Auto-Regressive Model
K.L. Bavelaar (TU Delft - Electrical Engineering, Mathematics and Computer Science)
J.N. Driessen – Mentor (Microwave Sensing, Signals & Systems)
Roberto Arnaiz Burgueño – Mentor (Thales Nederland B.V.)
Hannah Garcia Doherty – Mentor (Thales Nederland B.V.)
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Abstract
Targets tracked by radar may exhibit mean-reverting motion, such as motion along a nominal trajectory or weaving behavior. Conventional target tracking models typically do not account for this characteristic, which limits estimation and prediction performance. This study investigates the mixed Ornstein–Uhlenbeck model, also known as the second-order continuous auto-regressive model, as a framework for representing mean-reverting motion to model targets that follow a nominal trajectory or to model targets that display oscillatory motion. The model contains two unknown transition parameters per dimension, which are estimated offline by maximum likelihood estimation and online by joint estimation and a particle filter. Results show that joint estimation provides the best performance in both state and parameter estimation. Joint estimation is applied to real-world weaving motion from jet skis, water scooters, and RHIBs. The proposed approach improves position estimates and, in particular, velocity estimates, while also providing accurate trajectory predictions. These findings demonstrate that the mixed Ornstein–Uhlenbeck model can significantly enhance target-state estimation and prediction for mean-reverting motion.