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The problem of node localization in a wireless sensor network (WSN) with the use of the incomplete and noisy distance measurements between nodes as well as anchor position information is currently an an important yet challenging research topic. Most WSN localization studies at present have assumed that the anchor positions are perfectly known which is not valid in the underwater and underground scenarios. In this paper, semi-definite programming (SDP) algorithms are devised for finding the localizations of unknown-position nodes in the presence of anchor position uncertainty. Computer simulations are included to contrast the performance of the proposed algorithms with the conventional SDP method and Cramer-Rao lower bound.