Arithmetic averaging for tracking: From density fusion to trajectory fusion

Recently, it has been validated that the arithmetic average (AA) fusion exhibits robust theoretical properties and demonstrates significant practical efficacy in multi-sensor multi-target tracking contexts. The fusion density in question may pertain to either the single-target probability density function (PDF) or the multi-target probability hypothesis density (PHD) function. In this study, we extend the applicability of AA fusion from the conventional PDF/PHD fusion to the domain of trajectory fusion. In this context, the spatiotemporal trajectory is modeled as stochastic processes (SPs) with mean function represented as a curve function of time (FoT). Specifically, we explore the Gaussian process and the Student's t process within this letter. This extension substantially broadens the scope of the existing AA fusion methodology. Nonetheless, it introduces novel challenges, particularly in preserving fusion closure and addressing practical implementation requirements. This letter analyzes these challenges and proposes preliminary solutions. Simulation studies are also provided.