On the condition number of Gaussian sample-covariance matrices

We examine the reasons behind the fact that the Gaussian autocorrelation-fu nction model, widely used in remote sensing, yields a particularly ill-cond itioned sample-covariance matrix in the case of many Strongly correlated sa mples. We explore the question numerically and relate the magnitude of the matrix-condition number to the nonnegativity requirement satisfied by all c orrelation functions. We show that the condition number exhibits explosive growth near the boundary of the allowed-parameter space. Simple numerical r ecipes are suggested in order tb avoid this instability.