Exploiting persymmetry for low-rank Space Time Adaptive Processing

Abstract

Reducing the number of secondary data used to estimate the Covariance Matrix (CM) for Space Time Adaptive Processing (STAP) techniques is still an active research topic. Within this framework, the Low-Rank (LR) structure of the clutter is well-known and the corresponding LR STAP filters have been shown to exhibit a smaller Signal Interference plus Noise Ratio (SINR) loss than classical STAP filters, only 2r secondary data (where r is the clutter rank) instead of 2m (where m is the data size) are required to reach the classical 3dB SNR loss. By using other features of the radar system, other properties of the CM can be exploited to further reduce the number of secondary data: this is the case for active systems using a symmetrically spaced linear array with constant pulse repetition interval, which results in a persymmetric structure of the noise CM. In this context, we propose to combine this property of the CM and the LR structure of the clutter to perform CM estimation. In this paper, the resulting STAP filter is shown, both theoretically and experimentally, to exhibit good performance with fewer secondary data: 3dB SINR loss is achieved with only r secondary data.

Robust SAR STAP via Kronecker decomposition

“…A Bayesian approach using a parametric cross channel covariance generalizing ATI/DPCA to p channels was developed in [31], and a unstructured method fusing STAP and a test statistic in [8]. Space-time Adaptive Processing (STAP) learns a spatio-temporal covariance from clutter training data, and uses these correlations to filter out the stationary clutter while preserving the moving target returns [12], [19], [29].…”

“…By introducing structure and/or sparsity into the covariance matrix, the number of parameters and the number of samples required to estimate them can be reduced. As the spatiotemporal clutter covariance Σ is low rank [6], [19], [33], [12], Low Rank STAP (LR-STAP) clutter cancelation estimates a low rank clutter subspace from S and uses it to estimate and remove the rank r clutter component in the data [2], [19], reducing the number of parameters from O(p 2 q 2 ) to O(rpq). Efficient algorithms, including some involving subspace tracking, have been proposed [3], [37].…”

“…Let X ∈ C p×q be an array of radar returns from an observed range bin across p channels and q pulses. We model x = vec(X) as a spherically invariant random vector (SIRV) with the following decomposition [42], [33], [19], [17]:…”

“…Let the vector d be a spatio-temporal "steering vector" [19], that is, a matched filter for a specific target location/motion profile. For a measured array output vector x define the STAP filter output y = w T x, where w is a vector of spatio-temporal filter coefficients.…”

“…where Σ is the clutter plus noise covariance in (5). It can be shown [12], [19] that, if the clutter covariance is known, under the SIRV model the optimal filter for targets at locations and velocities corresponding to the steering vector d is given by the filter…”