A Dynamical Model for the Statistical Variation of Clutter

Consider a scattering scenario illustrated in Figure 1. In one scenario, a swath sweeps across the scatterers as time passes. This sweeping of the swath results in different scatterers contributing to the return at different times. Similarly, in a different scenario, rather than scanning, the radar could dwell at a certain location but the environment, for example the surface of the sea, could cause the contributing scatterers to change with time. In either scenario, we might represent the area encompassed by the swath and contributing to the return by a variable “
$A$
”. If we denote the number of scatterers within the swath at time
$t$
as
$N_{A}(t)$
, then the quantity
$N_{A}(t)$
fluctuates randomly as a function of
$t$
, i.e.
$N_{A}(t)$
is a random process that fluctuates as the swath scans the surface or as the environment changes with time (or both).