The forward-backward averaging technique applied to TLS-ESPRIT processing

Certain array geometries greatly simplify and enhance high resolution array processing. Two techniques are used-the ESPRIT algorithm, which employs two shifted but otherwise identical subarrays, and forward-backward averaging, which can be applied to axis-symmetrical arrays. The former has been shown to provide an efficient solution to bearing estimation while the latter incorporates the a priori knowledge about the symmetry, effectively increasing the number of data vectors available and decorrelating coherent or highly correlated signals. A combination of the two techniques implies a special array geometry that includes uniformly spaced linear arrays. The resulting algorithm yields parameter estimates that are constrained on the unit circle, satisfying the postulated data model provided merely that the arguments of these estimates are distinct. However, if the arguments of some parameter estimates coincide in a given scenario, the ESPRIT algorithm does not yield different results for distinct signals and these estimates can be rejected. Perhaps the most significant advantage of combining forward-backward averaging with ESPRIT parameter estimation is the substantial reduction in computational complexity that can be achieved. Based on the centro-Hermitian property of the data and noise covariance matrices, the computational complexity of the ESPRIT solution is reduced almost by a factor of four and the algorithm can be formulated entirely over the field of real numbers.