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In wireless location-aware networks, mobile nodes (agents) typically obtain their positions using the range measurements to the nodes with known positions. Transmit power allocation not only affects network lifetime and throughput, but also determines localization accuracy. In this paper, we present an optimization framework for robust power allocation in network localization with imperfect knowledge of network parameters. In particular, we formulate power allocation problems to minimize localization errors for a given power budget and show that such formulations can be solved via conic programming. Moreover, we design a distributed power allocation algorithm that allows parallel computation among agents. The simulation results show that the proposed schemes significantly outperform uniform power allocation, and the robust schemes outperform their non-robust counterparts when the network parameters are subject to uncertainty .