Adaptive polarimetric persymmetric detection for distributed subspace targets in lognormal texture clutter

In this paper, the adaptive polarimetric persymmetric detection for distributed subspace targets under the background of compound Gaussian clutter is investigated, where the compound Gaussian clutter exhibits texture that follows a lognormal distribution. Based on the two-step Generalized Likelihood Ratio Test (2S GLRT), two-step maximum a posteriori Generalized Likelihood Ratio Test (2S MAP GLRT), two-step Rao (2S Rao) test and two-step Wald (2S Wald) test, we have proposed four polarimetric persymmetric detectors. Initially, we model the target echo as a distributed subspace signal, assuming known clutter texture and polarization speckle covariance matrix (PSCM), and derive the corresponding test statistics. Then, the estimation of the lognormal texture is obtained through maximum a posteriori (MAP). Conventionally, a set of secondary data, which share the same PSCM as the cells under test (CUTs), is assumed to participate in the estimation of the PSCM, leveraging its inherent persymmetric property during the estimation process. Finally, the estimated values are substituted into the proposed test statistics to obtain fully adaptive polarimetric persymmetric detectors. Numerical experimental results using simulated data and measured sea clutter data demonstrate that the proposed four adaptive polarimetric persymmetric detectors exhibit a constant false alarm rate (CFAR) characteristic relative to the PSCM and satisfactory detection performance for distributed subspace targets.