Point-Process Theory and the Surveillance of Many Objects

Abstract

The development of the methodologies of surveillance (i.e., detection and tracking) must confront emerging situations in which large random numbers of moving objects may be present under conditions of high noise and low resolution. Conventional approaches based upon extended Kalman filter theory require executions of detection and tracking in separate time intervals and require relatively favorable noise and resolution conditions. In this paper we discuss a new approach based upon point-process theory that to a significant degree obviates the above requirements. Furthermore, it entails a computational burden that does not increase significantly with the number of objects present. A central feature of our new methodology is an exact infinite hierarchy of coupled equations giving the time evolution of all orders of mean densities of representative points in single-object state space. A simple closure approximation yields a truncated hierarchy composed of a single equation involving only the first-order density. The corresponding algorithm, called STRIDE (Superresolution in TRacking via Integro-Differential Equations), is also capable of superresolution in both static and dynamic situations.