Adaptive detectors for mismatched subspace target in clutter with lognormal texture

Due to factors such as array misalignment and waveform distortion, the target echo may not be precisely located within the nominal subspace in practical applications, resulting in mismatch issues. In response to this challenge, this paper investigates adaptive detection methods for detecting mismatched subspace targets amidst lognormal clutter background. To enhance the suppression of mismatched signal, we introduce a fictitious signal into the null hypothesis, which is situated within a subspace orthogonal to the nominal subspace in the whitened observation space. Following convention, we allow for the existence of a training dataset that shares the same covariance matrix (CM) structure as the main dataset. Subsequently, we propose two adaptive subspace detectors based on a two-step Generalized Likelihood Ratio Test (GLRT) and a two-step maximum a posteriori (MAP) GLRT. Both novel detectors have been validated to have constant false alarm rate (CFAR) properties for speckle CM. Numerical experiments are carried out using simulation data and measured sea clutter data, which demonstrate that our proposed methods exhibit robustness against non-mismatched signal and effective suppression of mismatches.