A new class of disturbance covariance matrix estimators for radar signalprocessing applications is introduced following a geometric paradigm. Eachestimator is associated with a given unitary invariant norm and performs thesample covariance matrix projection into a specific set of structuredcovariance matrices. Regardless of the considered norm, an efficient solutiontechnique to handle the resulting constrained optimization problem isdeveloped. Specifically, it is shown that the new family of distribution-freeestimators shares a shrinkagetype form; besides, the eigenvalues estimate justrequires the solution of a one-dimensional convex problem whose objectivefunction depends on the considered unitary norm. For the two most common norminstances, i.e., Frobenius and spectral, very efficient algorithms aredeveloped to solve the aforementioned one-dimensional optimization leading toalmost closed form covariance estimates. At the analysis stage, the performanceof the new estimators is assessed in terms of achievable Signal to Interferenceplus Noise Ratio (SINR) both for a spatial and a Doppler processing assumingdifferent data statistical characterizations. The results show that interestingSINR improvements with respect to some counterparts available in the openliterature can be achieved especially in training starved regimes.
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