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.

翻译：目标跟踪涉及对目标状态随时间演化的估计，即目标轨迹。与经典状态空间模型不同，本系列研究（包括本文）将目标状态的集合建模为一个随机过程，该过程可进一步分解为表示轨迹趋势的确定性部分和表示残差拟合误差的残差随机过程。随后，跟踪问题被表述为关于轨迹随机过程的学习问题，其关键部分在于估计一个在时间序列上最佳拟合观测值的轨迹函数型（T-FoT）。为此，我们考虑多项式T-FoT，并采用两种不同的正则化策略解决正则化多项式T-FoT优化问题，以权衡精度与简洁性。一种策略限制多项式阶数，通过在狭窄有界范围内进行网格搜索确定最优选择；另一种策略采用$\ell_0$范数正则化，并运用混合牛顿求解器。在单目标和多机动目标场景下的仿真结果验证了所提方法的有效性。