Outlier Resistant Rapid Adaptive Matched Filter

Abstract

This paper presents an outlier-resistant implementation of the Doppler Domain Localized (DDL) Adaptive Matched Filter (AMF). Outliers, defined as training data vectors closely correlated with the test cell’s vector, can severely degrade adaptive detector performance. Existing outlier-resistant detectors have limitations: some assume prior knowledge of the number of outliers, while others estimate this using prior statistical distributions. Both approaches involve complex computations, requiring many matrix inversions per cell under test. Additionally, these designs focus on censoring efficiency rather than the detectors’ overall detection and false alarm performance. This research aims to design an outlier-censoring algorithm, as an inherent part of the outlier-resistant DDL-AMF detector, that is computationally efficient and ensures near-optimal and robust detector performance regarding false alarm and detection probability without using prior outlier information. The designed two-step censoring algorithm uses the generalized inner product (GIP) values to remove outlier-infected vectors, retaining those with the lowest GIP values. Tyler’s covariance matrix estimator is employed at both steps to compute GIP values. The optimal number of retained vectors maximizes detection probability across various outlier counts. The refined training set is used to calculate the sample covariance matrix for detection tests across multiple cells under tests. Statistical simulations demonstrate the proposed detector’s superior outlier resistance and computational efficiency. These properties enhance the DDL-AMF detector’s operational capability in real scenarios with complex interference environments and limited training data.

Keywords

• Adaptive detection
• adaptive matched filter (AMF)
• Doppler domain localized (DDL) adaptivity
• limited training data
• outlier censoring
• rapid AMF