Abstract: In the estimation of direction of arrival(DOA) for distributed sources,maximum likelihood estimation(MLE) has attracted much attention because of its good performance.MLE is a four-dimensional non-linear optimization problem with large computational cost,and is termed 4D MLE.We propose a lower dimensional MLE algorithm,which is simplified to a three dimensional nonlinear optimization problem,therefore called 3D MLE.Both 4D and 3D algorithms use the search algorithm of the Newton type to find the globe optimum.In a single search process,compared to the 4D method,the 3D MLE can reduce inverse operations of the covariance matrix by 51 times,and reduce matrix multiplications by 87 times.The search efficiency is improved and memory is saved.The Cramér-Rao bound(CRB) for the new 3D MLE algorithm is presented,showing reduction in the computation cost.Computer simulation shows that both methods have similar estimation accuracy.The 3D algorithm can also avoid loss of performance,and is more practicable.