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One of the major issues with the application of Radio Interferometric Positioning System (RIPS) is the ambiguous measurement caused by a wrapped signal phase. Multiple transmissions at different frequencies have been used to resolve the phase ambiguity of a RIPS measurement in the existing approaches. In practice, the ways to solve the ambiguity problem are heavily dominated by the power consumption which is vital for extending the lift time of sensor networks. This paper considers an approach which localizes a free mote by directly using the ambiguous RIPS measurements in an attempt to reduce the number of transmissions. The latter roughly indicates the energy cost which has to be paid for the localization of a sensor in a low cost sensor network. In this work, we derive a condition for the choice of wavelengths such that a free mote can be localized with the minimal number of transmissions - as little as three distinct frequencies. Our simulation results demonstrate the effectiveness of the proposed algorithm.