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In this letter, we consider the received-signal-strength (RSS) based localization problem with unknown transmit power and unknown path loss exponent (PLE). For the case of unknown transmit power, we derive a weighed least squares (WLS) formulation to jointly estimate the sensor node location and the transmit power, based on the unscented transformation (UT). For the case of unknown PLE, we propose an alternating estimation procedure to alternatively estimate the sensor node location and the PLE. The estimation procedure can also be applied to the case when both the transmit power and the PLE are unknown. Simulation results confirm the effectiveness of the proposed method.