From Target Tracking to Targeting Track -- Part III: Stochastic Process Modeling and Online Learning

--This is the third part of a series of studies that model the target trajectory, which describes the target state evolution over continuous time, as a sample path of a stochastic process (SP). By adopting a deterministic-stochastic decomposition framework, we decompose the learning of the trajectory SP into two sequential stages: the first fits the deterministic trend of the trajectory using a curve function of time, while the second estimates the residual stochastic component through parametric learning of either a Gaussian process (GP) or Student's-t process (StP). This leads to a Markov-free data-driven tracking approach that produces the continuous-time trajectory with minimal prior knowledge of the target dynamics. It does not only take advantage of the smooth trend of the target but also makes use of the long-term temporal correlation of both the data noise and the model fitting error . Simulations in four maneuvering target tracking scenarios have demonstrated its effectiveness and superiority in comparison with existing approaches. ARGET tracking that involves the online estimation of the trajectory of a target has been a long-standing research topic and plays a significant role in aerospace, traffic, defense, robotics, etc. [1] In essence, target tracking is more about estimating the continuous-time trajectory of the target rather than merely a finite number of point states. The continuous-time trajectory enables the acquisition of a point estimate of the state at any time in the trajectory period. However, the converse is not true. X, defined in spatio-temporal space, where X denotes the state space. Manuscript created Feb 2025; This work was supported in part by the National Natural Science Foundation of China under Grants 62422117 and 62201316 and in part by the Fundamental Research Funds for the Central Universities.