Improved Moving Target Detection in Homogeneous and Heterogeneous Clutter With Limited Secondary Data Using Unit Circle Roots Constraints

This article proves that the roots of the $z$-polynomial corresponding to the ideal adaptive matched filter (AMF) lie on the unit circle (UC). Motivated by this proof, we propose UC roots-constrained AMF (UCRC-AMF), which enforces this fundamental UC roots property while maximizing the SINR to determine the detector polynomials. The UCRC algorithm exploits polynomial conjugate symmetry and applies it to the problem of radar moving target detection (MTD) in homogeneous and heterogeneous clutter. The algorithm splits the multidimensional AMF optimization problem into multiple 1-D AMF problems. Simulation studies show that the UCRC-based AMF for Gaussian clutter, as well as UCRC versions of NAMF and $\alpha$-AMF for compound Gaussian clutter significantly outperform existing state-of-the-art detection algorithms in the presence of limited secondary data and the performance gain is persistent for larger secondary data as well. This work will show that the combined enforcement of UC roots property on detector polynomials and complex-persymmetry of covariance matrices is most effective for superior detection performance. It is also shown that the proposed UCRC-AMF outperforms the existing methods when there is a mismatch with respect to the true target velocity and ideal covariance matrix structure. In addition, it will be demonstrated via simulation that the proposed UCRC-based detectors have approximate constant false alarm rate (CFAR) with respect to the unknown covariance matrix.