On the condition number of Gaussian sample-covariance matrices

The authors examine the reasons behind the fact that the Gaussian autocorrelation-function model, widely used in remote sensing, yields a particularly ill-conditioned sample-covariance matrix in the case of many strongly correlated samples. The authors explore the question numerically and relate the magnitude of the matrix-condition number to the nonnegativity requirement satisfied by all correlation functions. They show that the condition number exhibits explosive growth near the boundary of the allowed-parameter space, simple numerical recipes are suggested in order to avoid this instability.