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The VLBI correlator is a key data processor of VLBI system. According to the correlator model parameters, complex cross correlations are performed and interferometric fringes are obtained. By analysis of radio signal flow through S/X dual bands and multi-channel receiving system, an advanced correlator model has been developed for differential VLBI observations of satellites. The accuracy of correlator model for satellites and radio sources has been verified respectively with other independent software. The whole VLBI correlation system incorporated with the correlator model has been working smoothly and successfully in the real time tracking of Chang'e 1 lunar satellite.