Short-data-record Adaptive Detection

The classical problem of detecting a complex signal of unknown amplitude in colored Gaussian noise is revisited in the context of adaptive detection with limited training data via the auxiliary-vector (AV) filter estimation algorithm. Based on statistical conditional optimization criteria, the iterative AV algorithm starts from the target vector and adding non-orthogonal auxiliary vector components generates an infinite sequence of tests that converges to the ideal matched filter (MF) processor for any positive definite input autocorrelation matrix. Computationally, the algorithm is a simple recursive procedure that avoids explicit matrix inversion, decomposition, or diagonalization operations. When the input autocorrelation matrix is replaced by a conventional sample-average estimate, the algorithm effectively generates a sequence of MF estimators; their bias converges rapidly to zero and the covariance trace rises slowly and asymptotically to the covariance trace of the familiar adaptive matched filter (AMF). For finite data records, the generated sequence of estimators offers favorable bias/covariance balance and members of the sequence are seen to outperform in probability of detection (for any given false alarm rate) all known and tested adaptive detectors (for example AMF and the multistage Wiener After algorithm). White the issues treated refer to general adaptive detection procedures, the presentation herein is given in the context of joint space-time adaptive processing for array radar.