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

TL;DR

This paper introduces a novel regularized polynomial trajectory optimization method for target tracking, modeling the target's state as a stochastic process with a deterministic trend and residuals, and employs regularization strategies to improve accuracy and simplicity.

Contribution

It proposes a new regularized polynomial trajectory fitting framework for target tracking, using order limitation and $ ext{l}_0$ regularization with a hybrid Newton solver.

Findings

Effective in single and multiple maneuvering target scenarios.

Regularization improves trajectory estimation accuracy.

Trade-off between model complexity and fit quality demonstrated.

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.