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Bounds for estimating the parameters of low-rank compound-Gaussian clutter and white Gaussian noise

We consider the problem of estimating the parameters of a mixture of low-rank compound-Gaussian clutter and white Gaussian noise. Using a minimal and unconstrained parametrization of the clutter covariance matrix, we derive lower bounds for estimation of its parameters. First, assuming the textures are deterministic, the Cramér-Rao bound is derived, which enables one to assess the impact of the time-varying textures on the estimation performance. Then, considering the textures as random, hybrid bounds are considered. Furthermore, a lower bound for estimating the projector on the clutter subspace is presented. Numerical simulations enable one to evaluate the impact of random, time-varying textures compared to constant textures (Gaussian case).