The frequency division multiple access (FDMA) strategy used in GLONASS causes inter-frequency phase bias (IFPB) and inter-frequency code bias (IFCB) between receivers from different manufacturers. The existence of IFPB and IFCB significantly increases the difficulties of fixing GLONASS ambiguity and limits the accuracy and reliability of GLONASS positioning. Moreover, the initial value of IFPB and IFCB may be unavailable or unreliable with the increasing number of receivers from different manufacturers in recent years. In this study, a real-time and reliable calibration algorithm of IFPB and IFCB based on multi-GNSS assistance is proposed by providing a fixed solution. Real-time IFPB rate and IFCB can be obtained using this algorithm without the initial IFPB and IFCB. The IFPB rate for all GLONASS satellites and IFCB for each GLONASS satellite are estimated due to different characteristics of IFPB and IFCB. IFPB calibration can be divided into constant and real-time IFPB calibrations to meet the different positioning requirements. Results show that constant IFPB rate has only 2 mm difference from the mean value of real-time IFPB rate. The IFPB rate and IFCB estimated by this algorithm have excellent stability, and the change in reference satellite cannot affect the results of IFPB rate and the stability of IFCB. The centimetre-level positioning results can be obtained using two calibration methods, and the positioning results with real-time calibration method are 10%–20% better than those with the constant calibration method. Under satellite-deprived environments, the improvements of multi-GNSS positioning accuracy with constant inter-frequency bias calibration gradually increase as the satellite cut-off elevation angle increases compared with GPS/BDS, which can reach up to 0·9 cm in the vertical direction.

中文翻译：

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GLONASS 异频相位和码偏的实时估计和校准

GLONASS 中使用的频分多址 (FDMA) 策略会导致来自不同制造商的接收器之间出现频间相位偏差 (IFPB) 和频间码偏差 (IFCB)。IFPB和IFCB的存在显着增加了GLONASS模糊度修复的难度，限制了GLONASS定位的准确性和可靠性。此外，随着近年来不同制造商的接收机数量的增加，IFPB 和 IFCB 的初始值可能无法获得或不可靠。本研究提出了一种基于多GNSS辅助的IFPB和IFCB实时可靠标定算法，并提供了一个固定的解决方案。使用该算法无需初始 IFPB 和 IFCB 即可获得实时 IFPB 速率和 IFCB。由于 IFPB 和 IFCB 的特性不同，估计了所有 GLONASS 卫星的 IFPB 速率和每颗 GLONASS 卫星的 IFCB。IFPB标定可分为恒定IFPB标定和实时IFPB标定，以满足不同的定位要求。结果表明，恒定 IFPB 速率与实时 IFPB 速率的平均值仅相差 2 mm。该算法估计的IFPB速率和IFCB具有很好的稳定性，参考卫星的变化不会影响IFPB速率的结果和IFCB的稳定性。采用两种标定方法可以获得厘米级的定位结果，实时标定方法的定位结果比恒定标定方法好10%~20%。在无卫星环境下，