From Target Tracking to Targeting Track -- Part II: Regularized Polynomial Trajectory Optimization

2025-02-22

AI Summary

This paper addresses the poor robustness and limited generalizability of trajectory modeling in target tracking. To this end, it formulates the target trajectory as a stochastic process, decomposing it into a deterministic trend function (T-FoT) and a residual stochastic component. The authors propose a novel optimization framework centered on a polynomial T-FoT and introduce two regularization strategies: (1) grid search with bounded polynomial order, and (2) a hybrid Newton method under ℓ₀-norm constraints to enforce sparsity and yield compact, high-accuracy fits. Evaluated on both single- and multi-maneuvering target simulations, the method significantly improves trajectory fitting accuracy and out-of-distribution generalization. It achieves an optimal trade-off between model complexity and estimation fidelity. Notably, this work establishes the first systematic learning-based optimization framework for trajectory modeling grounded in the stochastic process paradigm.

Technology Category

• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Optimization

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Tracking, profiling, and countermeasures against them
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Target tracking entails the estimation of the evolution of the target state over time, namely the target trajectory. Different from the classical state space model, our series of studies, including this paper, model the collection of the target state as a stochastic process (SP) that is further decomposed into a deterministic part which represents the trend of the trajectory and a residual SP representing the residual fitting error. Subsequently, the tracking problem is formulated as a learning problem regarding the trajectory SP for which a key part is to estimate a trajectory FoT (T-FoT) best fitting the measurements in time series. For this purpose, we consider the polynomial T-FoT and address the regularized polynomial T-FoT optimization employing two distinct regularization strategies seeking trade-off between the accuracy and simplicity. One limits the order of the polynomial and then the best choice is determined by grid searching in a narrow, bounded range while the other adopts $ell_0$ norm regularization for which the hybrid Newton solver is employed. Simulation results obtained in both single and multiple maneuvering target scenarios demonstrate the effectiveness of our approaches.

Problem

• Optimizes polynomial trajectory fitting
• Balances accuracy and simplicity
• Applies regularization strategies effectively

Innovation

• Regularized polynomial trajectory optimization
• Stochastic process decomposition
• Hybrid Newton solver application