Closed-form 2D angle estimation with arbitrary sampling lattices over a circular aperture

Simultaneous estimation of the azimuth and elevation arrival angle of each of a number of co-channel signals incident upon an array of antennas is addressed. A new closed-form algorithm that works for filled circular arrays (FCAs) with any sampling lattice is developed. Although based on TLS-ESPRIT, the algorithm does not require arrays exhibiting translational symmetry. The only constraint imposed on the array for the algorithm to perform properly is that the spacing between adjacent sensors across the aperture be roughly a half-wavelength or less on average. A set of ESPRIT-like equations with unknowns are of the form sin(θ_i)e^jφi, where θ_i and φ_i are the elevation and azimuth of the i-th source, respectively, is constructed by means of linear combinations of the received signals exploiting a recurrence property satisfied by Bessel functions. Simulations verifying the efficacy of the algorithm in conjunction with rectangular, hexagonal, polar raster, and random sampling lattices have been performed. An illustrative simulation is presented and compared with performance predicted by theoretical analysis