Closed-form multi-dimensional multi-invariance ESPRIT

A closed-form multi-dimensional 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: (1) multiple occurrence of one size of invariance along one or multiple parametric dimensions, (2) multiple sizes of invariances along one or multiple parametric dimensions, and (3) invariances that cross over two or more parametric dimensions. The basic (uni-dimensional uni-invariance) ESPRIT algorithm is applied in parallel to each multiple pair of matrix-pencils characterizing the multiple invariance relationships in the data model, producing multiple sets of cyclically ambiguous estimates over the multi-dimensional parameter space. A weighted least-squares hyper-plane is then fitted to these set of estimates to yield very accurate and unambiguous estimates of the signal parameters.