Syntactic Models for Trajectory Constrained Track-Before-Detect

In this paper, a track before detect approach utilizing trajectory shape constraints is proposed to track dimly lit targets. The shape of the target trajectory is modeled syntactically using stochastic context-free grammar models (SCFG) that arise in natural language processing. The directional vector of the target acceleration modes are used as geometric primitives called tracklets. The tracklets are syntactic sub-units of complex spatial trajectory shapes. Stochastic context-free grammars are a generalization of Markov chains (regular grammars) and can model such complex spatial patterns with long range dependencies. Knowledge about the evolution of the trajectory is used in enhancing the track before detect algorithm. A novel multiple model SCFG particle filter is proposed and numerical results are presented to show significant improvement over conventional jump Markov models in track before detect.