In this paper, we discuss a number of high-resolution direction finding methods for determining the two-dimensional directions of arrival of a number of plane waves, impinging on a sensor array. The array consists of triplets of sensors that are identical, as an extension of the 1D ESPRIT scenario to two dimensions. New algorithms are devised that yield the correct parameter pairs while avoiding an extensive search over the two separate one-dimensional parameter sets. EDICS: 5.2.2., 5.2.4.
PRELIMINARIES
The data modelConsider m sensor triplets, each composed of three identical sensors with unknown gain and phase patterns, which may vary from triplet to triplet. For every triplet, the displacement vectors d xy and d xz between its components are required to be the same (and, for convenience, are assumed to be orthogonal). This way, assigning the three sensor of each triplet to each of the sensor-arrays X, Y, Z, respectively, three identical although displaced arrays are obtained. This is a direct extension of the 1D ESPRIT scenario to two dimensions (see also [9]). Impinging on every array are d narrowband non-coherent signals s k t,
The subspace approachMatrix polynomials of the form E − αF;α ∈ | C ; are called matrix pencils. Forming the pencilsit is seen that, in the noise free case, numbers λ = λ i and µ = µ j , i; j = 1; 2; : : : ; d , that reduce the rank of the pencil by one are equal to φ −1 i and θ −1 j respectively. With square data matrices, these rank reducing numbers are the generalized eigenvalues of the matrix pairs X ; Y and X ; Z.With noise present, however, a large number of samples are taken to improve accuracy. As a result, X, Y and Z will not be square. Noise will also increase the rank of the pencils, and this will introduce new rank reducing numbers. By computing a Total Least Squares projection of the data matrices (see e.g., [10] on