Full space-time clutter covariance estimation

For an airborne radar array, beamforming and detection are problems in both space and time. To null clutter, it is necessary to exploit both dimensions, and to do so optimally requires knowledge of the full space-time covariance matrix and the array steering vectors. This paper derives an expectation-maximization (EM) algorithm for the estimation of full space-time covariance matrices while simultaneously estimating array steering vectors. The EM approach iterates between estimating the spatial steering vectors and power associated with clutter scattering from different angles and the formation of a full space-time covariance matrix. The final result is an estimate of the set of array steering vectors and an estimate of the space-time covariance matrix. In practice, one would never need to form this covariance since all calculations could be performed using the SVD of the appropriately weighted clutter space-time steering vector matrix. The technique is capable of providing a positive definite estimate of the space-time covariance and complete array calibration with only a single space-time data sample