Conditional variance LMMSE estimator for a GARCH process clutter model

A radar detection scheme based on a GARCH clutter model has been proposed recently. This adaptive detector depends on the conditional variance of the GARCH process. We present a linear minimum mean square error (LMMSE) estimator for the conditional variance of a GARCH process that allows us to update the conditional variance at each decision instant. We derive the estimation algorithm with an approach analogous to the Kalman filter, though system matrices turn out to be random ones. We illustrate the LMMSE algorithm behavior by means of simulations with a particular GARCH process.