An Extended Object Poisson Multi-Bernoulli Filter with Zero-Inflated Poisson Model Using Belief Propagation

This paper presents an efficient implementation of the extended object Poisson multi-Bernoulli (PMB) filter under the zero-inflated Poisson (ZIP) object measurement model using particle belief propagation (BP). The ZIP measurement model separates a Bernoulli object detection event from the conditional Poisson generation of object measurements, enabling principled handling of empty measurement sets. Building upon the PMB mixture posterior, we present a factorized joint posterior over set of objects with object detection variables and a dual representation of data association using both object-oriented and measurement-oriented association variables. Notably, this representation replaces the implicit high-order global hypothesis constraint by local consistency factors, yielding a factor graph amenable to BP. In addition, we present a particle-based implementation, in which the Poisson intensity for undetected objects is analytic, whereas the single object densities of Bernoulli components for the detected objects are represented using particles. Simulation results demonstrate that the proposed method has superior performance than existing sampling-based implementations of extended object PMB filter with ZIP model in terms of both estimation accuracy and runtime.