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Performance of the Low-Rank Adaptive Normalized Matched Filter Test Under a Large Dimension Regime

Abstract : When a possible target is embedded in a Low Rank (LR) Gaussian clutter (which is contained in a low dimensional subspace) plus a white Gaussian noise, the detection process can be performed by applying the Low-Rank Adaptive Normalized Matched Filter (LR-ANMF) which is a function of the estimated projector. In a recent work, we derived an approximate distribution of the LR-ANMF under the H0 hypothesis by using a restrictive hypothesis (the target has to be orthogonal to the clutter subspace). In this paper, we propose to determine new approximations of the Pfa and the Pd of the LR-ANMF by relaxing this restrictive hypothesis. This new derivation is based on results concerning the convergence in a large dimension regime of quadratic forms. Simulations validate our result, in particular when the tested signal is close to the clutter subspace
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Alice Combernoux, Frédéric Pascal, Guillaume Ginolhac. Performance of the Low-Rank Adaptive Normalized Matched Filter Test Under a Large Dimension Regime. IEEE Transactions on Aerospace and Electronic Systems, Institute of Electrical and Electronics Engineers, 2019, 55 (1), pp.459-468. ⟨10.1109/TAES.2018.2847911⟩. ⟨hal-01825231⟩

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