Detection 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 permittivity, 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.

The Ground Penetrating Radar (GPR) consists in an electromagnetic signal which is transmitted at different positions through the ground in order to obtain an image of the subsoil. In particular, the GPR is used to detect buried objects like pipes. Their detection and localisation are intricate for three main reasons. First, the noise is important in the resulting image due to the presence of several rocks and/or layers. Second, the wave speed and the response of the pipe depend on the characteristics of the different layers. Finally, the signal attenuation could be important because of the depth of pipes. In this paper, we propose to derive an adaptive detector where the steering vector is parametrised by the wave speed in the ground and the noise follows a Spherically Invariant Random Vector (SIRV) distribution in order to obtain a robust detector. To estimate the covariance matrix, we propose to use robust maximum likelihoodtype estimators called M-estimators. To handle the large size of data, we consider regularised versions of such M-estimators. Simulations will allow to estimate the relation Probability of False Alarm (PFA)-Threshold. Application on real datasets will show the relevancy of the proposed analysis for detecting buried objects like pipes.

Regularized Tyler Estimator's (RTE) have raised attention over the past years due to their attractive performance over a wide range of noise distributions and their natural robustness to outliers. Developing adaptive methods for the selection of the regularisation parameter α is currently an active topic of research. Indeed, the bias-performance compromise of RTEs highly depends on the considered application. Thus, finding a generic rule that is optimal for every criterion and/or data configurations is not straightforward. This issue is addressed in this paper for undersampled configurations (number of samples lower than the dimension of the data). The paper proposes a new regularisation parameter selection based on a subspace reduction approach. The performance of this method is investigated in terms of estimation accuracy and for adaptive detection purposes, both on simulation and real data.