Second order multi-object filtering with target interaction using determinantal point processes - Teoh, Timothy Zhisheng (2019)
The Probability Hypothesis Density (PHD) filter is an algorithm that propagates the first-order moment of random finite sets for use in multi-target tracking based on sensor measurements. This algorithm usually assumes that targets behave independently, an hypothesis which may not hold in practice due to potential target interactions. We begin by discussing some general properties, functionals and branching dependency associated with spatial point processes that constitute the foundations in the construction of the filtering equations. Next, we show some extended computations incorporating Janossy densities in the derivation of closed-form solutions to the first and second order posterior factorial moment densities of the PHD filter. Implementation of the PHD filter using Sequential Monte Carlo (SMC) method on independent and interactive multi-target environments were explored, and the results obtained motivated the advancement to the Determinantal Point Processes (DPPs) setting.