Adaptive processing with signal contaminated training samples

We consider the adaptive beamforming or adaptive detection problem in the case of signal contaminated training samples, i.e., when the latter may contain a signal-like component. Since this results in a significant degradation of the signal to interference and noise ratio at the output of the adaptive filter, we investigate a scheme to jointly detect the contaminated samples and subsequently take this information into account for estimation of the disturbance covariance matrix. Towards this end, a Bayesian model is proposed, parameterized by binary variables indicating the presence/absence of signal-like components in the training samples. These variables, together with the signal amplitudes and the disturbance covariance matrix are jointly estimated using a minimum mean-square error (MMSE) approach. Two strategies are proposed to implement the MMSE estimator. First, a stochastic Markov Chain Monte Carlo method is presented based on Gibbs sampling. Then a computationally more efficient scheme based on variational Bayesian analysis is proposed. Numerical simulations attest to the improvement achieved by this method compared to conventional methods such as diagonal loading. A successful application to real radar data is also presented

Robust Adaptive Detection of Buried Pipes using GPR

International audienceDetection of buried objects such as pipes using a Ground Penetrating Radar (GPR) is intricate for three main reasons. First, noise is important in the resulting image because of the presence of several rocks and/or layers in the ground, highly influencing the Probability of False Alarm (PFA) level. Also, wave speed and object responses are unknown in the ground and depend on the relative permit-tivity, which is not directly measurable. Finally, the depth of the pipes leads to strong attenuation of the echoed signal, leading to poor SNR scenarios. In this paper, we propose a detection method: (1) enhancing the signal of interest while reducing the noise and layer contributions, and (2) giving a local estimate of the relative permittivity. We derive an adaptive detector where the signal of interest is parametrised by the wave speed in the ground. For this detector, noise is assumed to follow a Spherically Invariant Random Vector (SIRV) distribution in order to obtain a robust detection. We use robust maximum likelihood-type covariance matrix estimators called M-estimators. To handle the significant amount of data, we consider regularised versions of said estimators. Simulation will allow to estimate the relation PFA-Threshold. Comparison is performed with standard GPR processing methods, showing the aptitude of the method in detecting pipes having low response levels with a reasonable PFA

Tyler's and Maronna's M-estimators: Non-Asymptotic Concentration Results

Tyler's and Maronna's M-estimators, as well as their regularized variants, are popular robust methods to estimate the scatter or covariance matrix of a multivariate distribution. In this work, we study the non-asymptotic behavior of these estimators, for data sampled from a distribution that satisfies one of the following properties: 1) independent sub-Gaussian entries, up to a linear transformation; 2) log-concave distributions; 3) distributions satisfying a convex concentration property. Our main contribution is the derivation of tight non-asymptotic concentration bounds of these M-estimators around a suitably scaled version of the data sample covariance matrix. Prior to our work, non-asymptotic bounds were derived only for Elliptical and Gaussian distributions. Our proof uses a variety of tools from non asymptotic random matrix theory and high dimensional geometry. Finally, we illustrate the utility of our results on two examples of practical interest: sparse covariance and sparse precision matrix estimation