Approximate Maximum Likelihood Algorithm for Moving Source Localization Using TDOA and FDOA Measurements

A closed-form approximate maximum likelihood（AML） algorithm for estimating the position and velocity of a moving source is proposed by utilizing the time difference of arrival（TDOA） and frequency difference of arrival（FDOA） measurements of a signal received at a number of receivers.The maximum likelihood（ML） technique is a powerful tool to solve this problem.But a direct approach that uses the ML estimator to solve the localization problem is exhaustive search in the solution space,and it is very computationally expensive,and prohibits real-time processing.On the basis of ML function,a closed-form approximate solution to the ML equations can be obtained,which can allow real-time implementation as well as global convergence.Simulation results show that the proposed estimator achieves better performance than the two-step weighted least squares（WLS） approach,which makes it possible to attain the Cramér-Rao lower bound（CRLB） at a sufficiently high noise level before the threshold effect occurs.

Exploiting AML algorithm for multiple acoustic source 2D and 3D DOA estimations

The approximate maximum likelihood (AML) algorithm shows promises for joint estimations of acoustic source spectrum and direction-of-arrival (DOA). For the multisource case, the AML algorithm remains feasible as one considers an alternating projection procedure based on sequential iterative search on single source parameters. In order to perform multisource beamforming operations, earlier, we used a two-dimensional (2D) sensor array with 2D AML to obtain the DOA estimations for sources in the far field of the array. Now, the 3D AML algorithm enables a 3D sensor array to collect acoustic data for estimation of DOA represented in azimuth and elevation angles. In this paper, we consider two acoustic sources being simultaneously active and derive Crame′r-Rao bound (CRB) on DOA estimation given by a 3D array. Also, we compare the two-source DOA estimation results of 2D AML and 3D AML, respectively. To construct reasonable constraints on sensor topology, we adopt the concept of isotropic array and decouple the interplay between azimuth and elevation angle variations. The 3D AML algorithm exhibits superior spatial separation over its 2D counterpart for multiple sources located at different azimuth and elevation angles. Although the 3D AML algorithm requires more demanding computational complexity, we have developed a number of efficiency enhancements to reduce the loading for the grid search.