Abstract: Inter-satellite observations realize continuous tracing for mobile satellites, to enhance accuracy of satellite clock comparisons. This paper focuses on time comparison technology combining satellite-ground and Inter-satellite observations, and derives a time comparison model for satellite-ground and inter-satellite observations. It details a method to calculate satellite-ground clock error from inter-satellite clock error. Theoretically, the prediction accuracy of mobile satellite clocks can be greatly enhanced after adding inter-satellite clock error. However, the heterogeneous nature of observation devices results in a discontinuity in the sequence of clocks, which affects the prediction accuracy of satellite clocks. We research a detection and compensation technology for slight jump clock error, and propose a combined method with traditional gross error detection and subtraction adjacent epochs, which can eliminate the heterogeneous clock errors caused by inconsistent observation equipment to enhance prediction accuracy. An experiment with real and simulation data verified the validity and effectiveness for the proposed theories and methods.