ABSTRACT
Estimating bearings of multiple narrowband signals from measurements collected by an array of sensors has been a very active research problem for the last two decades. Typical applications of this problem are radar, communication, and underwater acoustics. Many algorithms have been proposed to solve the bearing estimation problem. One of the first techniques that appeared was beamforming which has a resolution limited by the array structure. Spectral estimation techniques were also applied to the problem. However, these techniques fail to resolve closely spaced arrival angles for low signalto-noise ratios (SNRs). Another approach is the maximum-likelihood (ML) solution. This approach has been well documented in the literature. In the stochastic ML method [29], the sbgv signals are assumed to be Gaussian whereas they are regarded as arbitrary and deterministic in the deterministic ML method [37]. The sensor noise is modeled as Gaussian in both methods, which is a reasonable assumption due to the central limit theorem. The stochastic ML estimates of the bearings achieve the Cramer-Rao bound (CRB). On the other hand, this does not hold for deterministic ML estimates [32]. The common problem with the ML methods in general is the necessity of solving a nonlinear multidimensional (MD) optimization problem which has a high computational cost and for which there is no guarantee of global convergence. ‘‘Subspace-based’’ (or, super-resolution) approaches have attracted much attention, after the work of Schmidt [29], due to their computational simplicity as compared to the ML approach, and their possibility of overcoming the Rayleigh bound on the resolution power of classical direction-finding methods. Subspace-based direction-finding methods are summarized in this section.
