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

To solve the target tracking problem with little a-priori information about the target dynamics, our series of studies, including this paper as the third part, propose a continuous-time trajectory estimation approach (dubbed targeting track) based on the stochastic process (SP) theory and a deterministic-stochastic decomposition framework. Specifically, 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 learning either a Gaussian process (GP) or Student’s-t process (StP). The former has been addressed in the companion paper and the latter is the focus of this paper. This leads to a data-driven tracking approach that produces the continuous-time trajectory with minimal prior knowledge of the target dynamics. Notably, our approach models the temporal correlations of the state sequence and of measurement noise using separate GP or StP. 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 and the model fitting error. Although the GP admits an exact closed-form expression for the linear system, approximations have to be adopted for StP modeling. Simulations in four maneuvering target tracking scenarios have demonstrated its effectiveness and superiority in comparison with existing approaches.