Direction-of-arrival determination using 3-axis crossed array and ESPRIT

Improved structured least squares for the application of unitary ESPRIT to cross arrays

“…Consider the problem of estimating azimuth and elevation with the aid of the three-axis cross array of [2]. The array consists of identical elements located along three perpendicular linear arrays of elements each, which are aligned with the , , and -axes, as illustrated in Fig.…”

“…The SLS method is a popular technique for obtaining an approximate solution to (1) imperfect approximation of the true signal subspace and that an improved estimate can be obtained as (2) where is an error matrix whose Frobenius norm is generally small compared to that of . The method therefore proceeds by jointly minimizing the Frobenius norms of the residual matrices (3) and the Frobenius norm of .…”

“…This causes rank deficiency in the estimated signal subspace and Cross arrays are a specifically important category of multidimensional array geometries because they provide a larger maximum aperture and, hence, better resolution for a given number of array elements than any other array geometry with the same antenna spacing and number of dimensions [3]. The problem of rank deficiency in the estimated signal subspace was first pointed out in [2]. Here, it was shown that the problem can be solved by solving a set of nonlinear equations; however, this requires the use of additional and more complex numerical techniques.…”

Direction-of-arrival estimation for noncircular sources via structured least squares–based esprit using three-axis crossed array

“…As a result, the LS, TLS, and SLS methods will provide incorrect results on the particular ξ -axis. However, there is only one set of solutions, since the resulting matrices ϒ ξ , ξ ∈{x, y, z} share the same set of eigenvectors [11,24]. A necessary and sufficient condition for two matrices A and B to share the same set of eigenvectors is that AB = BA [12].…”

“…Such structures allow not only the azimuth angle but also the elevation angle to be taken into account. The ESPRIT algorithm has been developed for a three-axis crossed array in [11,12] for joint estimation of the azimuth and elevation angles. As the crossed array can provide a larger aperture, it offers better resolution for a given number of elements than other multidimensional uniform array geometries [11,13].…”