Random nyström approach to clutter subspace estimation for polarimetric space-time adaptive processing

A random Nyström (R-Nyström) scheme for clutter subspace estimation is proposed in the context of polarimetric space-time adaptive processing (pSTAP). Unlike the standard Nyström scheme making use of only partial columns of the clutter plus noise covariance matrix (CNCM), R-Nyström exploits full CNCM information with a properly designed selection procedure under the newly developed random ridge cross leverage score (RRCLS) criterion. With R-Nyström, sup-ported by the complete CNCM columns, upgraded clutter subspace estimation can be achieved at the expense of an insignificant increase in computational complexity, in contrast to the standard Nyström. The R-Nyström-based pSTAP, termed pR-Nyström, is shown to be superior over the current eigendecomposition-free subspace pSTAP in the signal to clutter plus noise loss and computational complexity. The efficacy of R-Nyström/pR-Nyström is validated by the simulation results.