This paper proposes a new autonomous current sharing control strategy for islanded microgrids that is simple and robust under unbalanced load conditions. The strategy estimates the distributed generator output voltage and current positive sequence components from the internal variables of a resonant current and resonant voltage regulator, and then uses them to create an integrated virtual impedance sharing mechanism. This avoids control complexity and the need for output current measurements, while maintaining a balanced voltage and accurate current sharing. The approach has been verified using a detailed switched simulation.