<title>Detection, estimation, and prediction of an unknown signal in unknown noise: the correlation filter</title>

Abstract

There is no question to most that Gauss developed the concept of least-square estimation which was stimulated by his astronomical studies. This concept was discribed in Gausss book, Theoria Mows. This contribution and insight provided by Gauss has inspired many researchers in estimation theory over the past 200 years. These developments include the Weiner Filter, Kalman Filter, Stochastic Estimation, Bayesian Estimation, Maximu m Likehood Estimation, Auto-Regression and the Robust Filtering, just to name a few. However, during the recent decades, the need for detection and estimation of unknown signal in unknown noise background necessitated the development of correlation techniques for detection ( many correlation techniques were developed for identification). The problems in detection of unknown signals in unknown noise are common in anti-submarine warfare (ASW), automatic target recognition (ATR) and in Infrared search ands Tracking (IRST) of IR images and ocean environment. Author's research in target detection in JR images and ocean environments let to his development of the "Correlation Filter". Correlation Filter became a part of his doctoral dissertation on a Generalized Filter where he has shown that all filters, Weiner, Kalman and Correlation Filters, are related through a "Constrained Gain Matrix" and that the Correlation Filter is a special case of the Weiner Filter, reference 2. This paper presents the derivation of the Correlation Filter for detection and estimation of unknown signals in unknown noise backgrounds and some applications. Reference 1 included two algorithms of his classified DoD applications.