A theoretical analysis of the effects of dual frequency ionosphere propagation correction on GNSS code tracking noise is presented. The effect on tracking noise of using different combinations of the proposed Galileo signals for ionosphere propagation correction is investigated. It is concluded that, for the open or commercial service user, the Galileo signals E2-L1-E1 near to and around GPS L1 should be used to apply ionosphere propagation corrections to the E5 signals. This produces a tracking noise standard deviation about three times larger than that on an E5 signal alone. An ionosphere correction-smoothing algorithm is presented that reduces the tracking noise on the corrected pseudo-range measurements.