The AECM Algorithm for Deterministic Maximum Likelihood Direction Finding in the Presence of Gaussian Mixture Noise

Gaussian mixture noise can model non-Gaussian noise and also be used when outliers are present. For deterministic maximum likelihood direction finding in Gaussian mixture noise, the Space-Alternating Generalized Expectation-maximization (SAGE) algorithm, an extension of the expectation-maximization algorithm, was applied and designed by Kozick and Sadler twenty odd years ago, which simultaneously updates direction of arrival (DOA) estimates at each iteration and cannot properly converge under unequal signal powers. In this article, the Alternating Expectation-Conditional Maximization (AECM) algorithm, an extension of the SAGE algorithm, is applied and designed, which utilizes multiple less informative versions of the complete data and the golden section search method to update DOA estimates at each iteration sequentially (one by one). Theoretical analysis shows that the AECM algorithm has almost the same computational complexity of each iteration as the SAGE algorithm. However, numerical results show that the AECM algorithm yields faster stable convergence and is computationally more efficient.

Angle Estimation of a Single Source with Massive Uniform Circular Arrays

Estimating the directions of arrival (DOAs) of incoming plane waves is an essential topic in array signal processing. Widely adopted uniform linear arrays can only provide estimates of source azimuth. Thus, uniform circular arrays (UCAs) are attractive in that they can provide $360^{\circ}$ azimuthal coverage and additional elevation angle information. Considering that with a massive UCA, its polar angles of array sensors can approximately represent azimuth angles over $360^{\circ}$ using angle quantization, a simple two-dimensional DOA estimation method for a single source is proposed. In this method, the quantized azimuth angle estimate is obtained by only calculating and comparing a number of covariances, based on which the elevation angle estimate is then obtained by an explicit formula. Thus, the proposed method is computationally simple and suitable for real-time signal processing. Numerical results verify that the proposed method can obtain azimuth as well as elevation angle estimates and the estimates can be used as starting points of multidimensional searches for methods with higher accuracy. Additionally, the proposed method can still work in the presence of nonuniform noise.