Bayesian Estimation of the Intensity for Independent Cluster Point Processes: An analytic solution

Abstract

This paper presents an approach for estimating clusters of points from a sequence of data with false alarms. The cluster process is characterised by a hierarchical point process, where each member of the cluster is conditioned on a parent centre process. An explicit formula for the Bayesian estimation of the intensity function of an independent cluster process is presented. An analytic form for this approach is proposed based upon the assumption that the observations of the cluster process have Gaussian noise, conditioned on the cluster centre. Simulated results are presented demonstrating the effectiveness of the formulation along with suggested methods such as gating for ensuring that the estimation process is computationally tractable.