Real-time causal processing of anomaly detection

Abstract

Anomaly detection generally requires real time processing to find targets on a timely basis. However, for an algorithm to be a real time processing it can only use data samples up to the sample currently being visited and no future data samples can be used for data processing. Such a property is generally called “causality”, which has unfortunately received little interest in the past. Recently, a causal anomaly detector derived from a well-known anomaly detector, called RX detector, referred to as causal RXD (C-RXD) was developed for this purpose where the sample covariance matrix, K used in RXD was replaced by the sample correlation matrix, R ( n ) which can be updated up to the currently being visited data sample, r n . However, such proposed C-RXD is not a real processing algorithm since the inverse of the matrix R ( n ), R -1 (n) is recalculated by entire data samples up to r n . In order to implement C-RXD the matrix R ( n ) must be carried out in such a fashion that the matrix R -1 ( n ) can be updated only through previously calculated R -1 ( n -1) as well as the currently being processed data sample r n . This paper develops a real time processing of CRXD, called real time causal anomaly detector (RT-C-RXD) which is derived from the concept of Kalman filtering via a causal update equation using only innovations information provided by the pixel currently being processed without re-processing previous pixels.