In this paper, we present a new scheme called the maximum log‐likelihood sum (MLSUM) algorithm to simultaneously determine the number of closely‐spaced sources and their locations by uniform linear sensor arrays. Based on the principle of the maximum likelihood (ML) estimator and a newly proposed orthogonal‐projection decomposition technique, the multivariate log‐likelihood maximization problem is transformed into a multistage one‐dimensional log‐likelihood‐sum maximization problem. The global‐optimum solution of the approximated ML localization is obtained by simply maximizing the single one‐dimensional log‐likelihood function. This algorithm is applicable to coherent sources as well as incoherent sources. The computer simulations show that the MLSUM algorithm is much superior to the MUSIC when the element SNR is low and/or the number of snapshots is small.