Space/time/frequency methods in adaptive radar - New Jersey ...

64Since the colored noise true covariance matrix is usually not known a priori, amaximum likelihood estimate is obtained from a secondary data set from neighboringrange cells around the cell under test. This estimate is referred to as the samplecovariance matrix and is given as:This sample covariance matrix needs to be continually updated since the baseenvironment may be considered stationary for only short periods of time.The correlation matrix R can be decomposed into eigenvalues and eigenvectorsusing the spectral theorem,where A l and q 1 are the lth eigenvalue and eigenvector, respectively. Eigenvalues aresorted from largest to smallest: A i > A2 > • > AL-1 > AL. The inverse of thecorrelation matrix can be expresses in terms of the eigen-decomposition,The eigenvectors are orthonormal,and form a complete set that spans an L-dimensional space:The signal free covariance matrix is comprised of the interference and the noisecontributions. If the covariance matrix is characterized by r < L large eigenvaluesthen the r associated eigenvectors span the interference subspace. The matrix representationof the interference subspace is obtained by using the first r eigenvectorscorresponding to the largest . eigenvalues. The matrix representation of the noise