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Joint synchronization and localization using time of arrival (TOA) measurements is a very important research topic for many wireless ad hoc sensor network applications. For such TOA based joint synchronization and localization, the least square (LS) criterion and its corresponding solution have been shown to exhibit optimum estimation performance but generally at a very high computational complexity. Due to its importance and difficulty, in this paper we consider the issue how to approach the estimation performance of such LS solution at low computational complexity: We propose a low-complexity algorithm, which is based on the linearized equations from TOA measurements and applies a weighted least square (WLS) criterion in a computationally efficient way to closely approach the LS solution in estimation performance; Via analyzing and simulating its estimation performance we evidently demonstrate the proposed algorithm of its superior trade-off between estimation performance and computational complexity. The proposed algorithm is also applicable to similar application areas involving TOA base joint timing and positioning.