Approximate distribution of the low-rank adaptive normalized matched filter test statistic under the null hypothesis

In this paper, we propose to derive an approximate theoretical distribution under the null hypothesis of the low-rank adaptive normalized matched filter (LR-ANMF). This detector is used to detect a target when the disturbance is composed of a low-rank Gaussian contribution (called clutter) and an additive white Gaussian noise. In the LR-ANMF, the estimated covariance matrix is replaced by the estimated orthogonal projector onto the subspace clutter. The method to derive this distribution is based on perturbation analysis and assumes a steering vector far from the clutter and a large clutter-to-noise ratio. Simulations on a space-time adaptive processing example validate our theoretical result. The impact of both hypotheses is also studied.