Persymmetric Adaptive Subspace Detectors for Range-Spread Targets in Compound-Gaussian Clutter

‍ ‍In this paper， the persymmetric adaptive detection problem of multidimensional subspace range spread targets under the background of non-Gaussian clutter is studied. Considering that the high-resolution radar targets echo has a translational component along the radial direction of the radar， the rotational components such as yaw， roll， and pitch can also be observed， thus the target signal is modeled as a range spread subspace signal to make full use of the Doppler information. In order to weaken the difficulty of the prior distribution selection of texture components and reduce the detection performance loss caused by model mismatch， the clutter is modeled as a compound Gaussian clutter model with a texture component of unknown constant and the speckle component with a persymmetric covariance matrix. The generalized likelihood ratio test （GLRT）， Rao， and Wald detectors are designed according to the two-step method. Firstly， the detectors are derived under the premise that the clutter covariance matrix is assumed known， and then the estimation of the clutter covariance matrix is obtained by using the training data around the cell to be detected， and finally the estimates are brought into the previously obtained detector to obtain its adaptive version. In order to solve the problem of sharp decline in adaptive detector performance under limited training samples， the persymmetric structure feature of speckle covariance matrix is used in the detector design stage to reduce the number of samples required for clutter covariance matrix estimation. The independently repeated Monte Carlo experiments based on both simulation data and measured data show that compared with the existing traditional detectors， the range spread target subspace detectors based on persymmetric structure proposed in this paper has better detection performance， especially when the number of training samples is limited， for example， taking the P-Wald detector as an example， the signal-to-clutter ratio required is about 20 dB lower than that of the Wald detector when the detection probability reaches 0.5. In addition， with the increase of the number of training samples， the detection performance of the persymmetric detectors also improves to a certain extent. At the same time， theoretical analysis and numerical experiments show that the three proposed persymmetric adaptive detectors all have constant false alarm characteristics for the speckle covariance matrix.