Persymmetric parametric adaptive matched filters for detecting targets using space-time adaptive processing of radar signals

An apparatus for detecting a moving target using radar signals, comprising:

• a radar system emitting the radar signals as training signals and test signals;
• wherein the radar system further comprises:
• a persymmetric parametric adaptive matched filter (per-PAMF) wherein the per-PAMF system is configured to determine an estimated spatial correlation matrix {circumflex over (Q)} and an estimated temporal correlation matrix  using space-time adaptive processing, wherein a spatial correlation matrix A and a temporal correlation matrix Q are known from the training signals, and the per-PAMF is configured to determine a generalized likelihood ratio test (GLRT)
• T
• =
• max
• α
• ⁢
• p
• 1
• ⁡
• (
• x
• 0
• ;
• α
• ,
• A
• ,
• Q
• )
• p
• 0
• ⁡
• (
• x
• 0
• ;
• A
• ,
• Q
• )
• ,
• where {Pi}1i=0 are likelihood functions under a first hypothesis H0 that the target is present and a second hypothesis H1 that the target is not present in the test radar signals, α is an unknown complex-values amplitude of the test radar signals, x0 represents the test signals, and max is a function that evaluates to a maximum, and the per-PAMF is configured to determine a maximum likelihood (ML) of the spatial correlation matrix Q as {circumflex over (Q)} and the temporal correlation matrix A as Â, wherein the correlation matrix Q is subject to a persymmetric constraint, and the per PAMF is configured to replace the spatial correlation matrices A and the temporal correlation matrix Q in the GLRT with {circumflex over (Q)} and Â.