In this work, three algorithms are proposed to reduce the computational complexity of the Approximated Maximum Likelihood (AML) for wideband Direction of Arrival (DOA) estimation. The first two methods, conjugate gradient and Gauss-Newton, are iterative methods that are based on gradient information of the log-likelihood function. The third method, Alienor method, is based on function approximation theory which transform a multi-variable function into a one-variable function. Therefore, a multi-dimension search is reduced to a one-dimension search. Complexity as well as computational time of these methods are compared by simulations. Effectiveness of the AML algorithm is also demonstrated by experimental data.
In this paper, we derive the Cramér-Rao Bound (CRB) for wideband
source localization and DOA estimation. The resulting CRB formula
can be decomposed into two terms: one that depends on the signal
characteristic and one that depends on the array geometry. For a
uniformly spaced circular array (UCA), a concise analytical form of
the CRB can be given by using some algebraic approximation. We
further define a DOA beamwidth based on the resulting CRB formula.
The DOA beamwidth can be used to design the sampling angular spacing for the Maximum-likelihood (ML) algorithm. For a randomly distributed array, we use an elliptical model to determine the largest and smallest effective beamwidth. The effective beamwidth and the CRB analysis of source localization allow us to design an efficient algorithm for the ML estimator. Finally, our simulation results of the Approximated Maximum Likelihood (AML) algorithm are
demonstrated to match well to the CRB analysis at high SNR.