1. A Geometric Approach to Covariance Matrix Estimation and its Applications to Radar Problems
- Author
-
Luca Pallotta, Antonio De Maio, Augusto Aubry, Aubry, A., De Maio, A., Pallotta, L., Aubry, Augusto, De Maio, Antonio, and Pallotta, Luca
- Subjects
FOS: Computer and information sciences ,Mathematical optimization ,Computer science ,Maximum likelihood ,projection ,02 engineering and technology ,Statistics - Applications ,law.invention ,Matrix (mathematics) ,0203 mechanical engineering ,law ,0202 electrical engineering, electronic engineering, information engineering ,Applications (stat.AP) ,Electrical and Electronic Engineering ,Invariant (mathematics) ,Radar ,Condition number ,Adaptive radar signal processing ,Eigenvalues and eigenvectors ,020301 aerospace & aeronautics ,Covariance matrix ,unitary invariant matrix norm ,Estimator ,020206 networking & telecommunications ,Covariance ,Sample mean and sample covariance ,Norm (mathematics) ,Signal Processing ,Convex optimization ,Clutter ,Algorithm ,structured covariance matrix estimation ,condition number - Abstract
A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample covariance matrix projection into a specific set of structured covariance matrices. Regardless of the considered norm, an efficient solution technique to handle the resulting constrained optimization problem is developed. Specifically, it is shown that the new family of distribution-free estimators shares a shrinkagetype form; besides, the eigenvalues estimate just requires the solution of a one-dimensional convex problem whose objective function depends on the considered unitary norm. For the two most common norm instances, i.e., Frobenius and spectral, very efficient algorithms are developed to solve the aforementioned one-dimensional optimization leading to almost closed form covariance estimates. At the analysis stage, the performance of the new estimators is assessed in terms of achievable Signal to Interference plus Noise Ratio (SINR) both for a spatial and a Doppler processing assuming different data statistical characterizations. The results show that interesting SINR improvements with respect to some counterparts available in the open literature can be achieved especially in training starved regimes., Comment: submitted for journal publication
- Published
- 2017
- Full Text
- View/download PDF