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The Space-based GNSS navigation receiver has the advantages of high precision, low cost and global coverage. It mainly provides information such as time reference, position and speed for spacecraft. With the release of GPS IGS products, it is based on the after-the-fact measurement of satellites. The development of precision post-processing technology is becoming more and more perfect. The Beidou system independently constructed in China has initially completed the verification of post-processing technology in the Asia-Pacific region. With the completion of the Beidou global navigation system in 2020, global coverage will be realized, and the application of precision post-processing technology will be implemented afterwards. The satellite orbit determination accuracy and load pointing accuracy are greatly improved, and a new implementation path for spaceborne gravity measurement is also provided. However, more and more satellites have proposed to be compatible with the Beidou system on the basis of the original GPS system, so as to realize the after-the-fact precision processing of the Beidou. In order to ensure the accuracy of the original observation measurement, the amount of data that needs to be generated and transmitted is often large. Star data storage, transmission and downlink channel capacity have caused a relatively large burden. Therefore, it is of great significance to provide a theory of raw measurement data compression for on-board GNSS receivers. The method of sparse representation and compressed sensing can effectively A set of primitive observations is represented by three parameters and a set of observation matrix methods, effectively reducing the satellite storage space and reducing the pressure of the downstream channel.