Minimizing uncertainty in determinants and ratios of determinants for invariant relationships employed in SAR imagery pattern recognition

Invariant relationships involving ratios of determinants have been proposed for the classification of an object in SAR imagery. The target detection decision-making process depends on the uncertainty involved in the measurements. At fixed experimental resolution, some determinants are simply better than others because they are much less sensitive to uncertainty. A geometrical interpretation of determinants is applied to assess the minimum relative uncertainty expected for a determinant employed in invariant relationships. Because much larger relative uncertainties can occur in some determinants, a method based on the perturbation of eigenvalues is proposed to identify determinants that are less sensitive to element errors. Symmetric alpha-stable probability distribution functions are employed to characterize error distributions in ratios of determinants.