#### Abstract

An algorithm is developed for estimating characteristic parameters associated with a "scene" of radiating sources given the data derived from a pair of translationally invariant arrays, the X and Y arrays, which are displaced relative to one another. The algorithm is referred to as PR O—E SPRIT and is predicated on invoking two recent mathematical developments: (1) the SVD based solution to the Procrustes problem of optimally approximating an invariant subspace rotation and (2) the Total Least Squares method for perturbing each of the two estimates of a common subspace in a "minimal" fashion until the two perturbed spaces are the same. For uniform linear array scenarios, the use of forward-backward averaging (FBAVG) in conjunction with PR O—E S PR IT is shown to effect a substantial reduction in the computational burden, a significant improvement in performance, a simple scheme for estimating the number of sources and source decorrelation. These gains may be attributed to FBAVG’s judicious exploitation of the diagonal invariance operator relating the Direction of Arrival matrix of the Y array to that associated with the X array. Similar gains may be achieved in the case where the X and Y arrays are either not linear or not uniformly spaced through the use of pseudo-forward-backward averaging (PFBAVG). However, the use of PFBAVG does not effect source decorrelation and reduces the maximum number of resolvable sources by a factor of two. Simulation studies and the results of applying PR O—E S PR IT to real data demonstrate the excellent performance of the method.

#### Date of this Version

5-1-1990

## Comments

Prepared for the National Science Foundation under contract number ECS-8707681