Localization of multiple emitters by spatial sparsity methods in the presence of fading channels

The problem of multiple emitters geolocation using sensor arrays is addressed, in the case of fading channels. A sparsity-based covariance-matrix fitting method is described. The procedure consists of finding a sparse representation of the sample covariance matrices obtained at the arrays, by representing each matrix by an over-complete basis. Sparsity is encouraged by an ℓ
₁
-norm based penalty function. The penalty function is minimized by semi-definite programming. The proposed method provides useful insight and it does not require the identification of the signal and noise subspaces. Therefore, the method does not rely on a good estimate of the number of emitters. Some of the approach properties are super-resolution, robustness to noise, robustness to emitter correlation, no sensitivity to initialization and no need for synchronizing the arrays. Special emphasis is given to uncorrelated sources and uniform linear arrays.