Structured least squares to improve the performance of ESPRIT-type algorithms

ESPRIT-type (spatial) frequency estimation techniques obtain their frequency estimates from the solution of a highly structured, overdetermined system of equations (the so-called invariance equation). Here, the structure is defined in terms of two selection matrices applied to a matrix spanning the estimated signal subspace. Structured least squares (SLS) is a new algorithm that solves the invariance equation by preserving its structure. Formally, SLS is derived as a linearized iterative solution of a nonlinear optimization problem. If SLS is initialized with the least squares solution of the invariance equation, only one “iteration,” i.e., the solution of one linear system of equations, is performed to achieve a significant improvement of the estimation accuracy. Therefore, the proposed estimation scheme (that uses only one “iteration” of SLS) is not iterative in nature.