Closed-form multidimensional multi-invariance ESPRIT

A closed-form multidimensional multi-invariance generalization of the ESPRIT algorithm is introduced to exploit the entire invariance structure underlying a (possibly) multiparametric data model, thereby greatly improving estimation performance. The multiple-invariance data structure that this proposed method can handle includes the following 1) multiple occurrence of a unisize invariance along any parametric dimension, 2) multiple sizes of invariances along any parametric dimension, 3) invariances that cross over two or more parametric dimensions. In this proposed algorithm, the basic (unidimensional uni-invariance) ESPRIT algorithm is applied in parallel to each multiple pair of matrixpencils that characterize the multiple invariance relationships in the data model, producing multiple sets of cyclically ambiguous estimates over the multidimensional parameter space. Recognizing the multidimensional linear inter-relation among these sets of cyclically ambiguous estimates, a weighted least-squares hyperplane may be fitted to these sets of estimates to yield very accurate and unambiguous estimates of the signal parameters. Simulation results show that the estimation standard deviation can reduced by up to 60% in a particular two-source 2-D direction-finding scenario.