A Hybrid Statistical Technique for Modeling Recurrent Tracks in a Compact Set

Abstract

In this technical note we present a hybrid statistical approach for modeling a vehicle's behavior as it traverses a compact set in Euclidean space. We use Symbolic Transfer Functions (STF), developed by the authors for modeling stochastic input/output systems whose inputs and outputs are both purely symbolic. We apply STF to our problem by assuming that the input symbols represent regions of space through which a track is passing while the output represents specific linear functions that more precisely model the behavior of the track. A target's behavior is modeled at two levels of precision: The symbolic model provides a probability distribution on the next region of space and behavior (linear function) that a vehicle will execute, while the continuous model predicts the position of the vehicle using classical statistical methods. The following results are presented: (i) An algorithm that parsimoniously partitions the space of the vehicle and models the behavior in the partitions with linear functions. (ii) A demonstration of our approach using real-world ship track data.