Regularization and particle filtering estimation of phase inter-system biases (ISB) and the lookup table for Galileo E1-GPS L1 phase ISB calibration

The between-receiver phase inter-system bias (ISB) in multi-GNSS integration needs to be calibrated when fixing the inter-system double difference (DD) ambiguities. As a result, the DD ambiguity fixing performance is affected by the accuracy of the ISB calibration; however, those effects have not been investigated until now. Also, the knowledge about the ISB characteristics is not enough which can lead to failure of ambiguity fixing with ISB calibration value such as obtained by the lookup table method. Our study first integrates the regularization method to the existing particle filtering fractional ISB (F-ISB) estimation to derive more precise F-ISB estimates. Afterward, the effects of the F-ISB accuracy on DD ambiguity fixing in single-epoch GPS L1-Galileo E1 integration are investigated. We show that the errors of F-ISB can degrade the success rate of single-epoch ambiguity fixing, and thus, more precise F-ISB values lead to higher empirical success rates. Finally, the characteristics of the F-ISB are investigated based on baselines shorter than 20 km from the GNSS network of International GNSS Services. According to the 132 F-ISB estimates obtained using data collected from day of year 001 2016 to DOY 001, 2019, the F-ISB values for 4 receiver brands including Leica, Septentrio, Trimble and Javad are analyzed. The receiver-type and software-version combinations from the same manufacturer and with similar F-ISB values are regarded as one group and all the receivers can be classified into 6 groups. With F-ISB of Leica receiver group set to zero value, the other groups have F-ISB values of 0.000 m, + 0.055 m and + 0.095 m and the L1-E1 F-ISBs between different groups are provided in a lookup table for practical use.