Li Dehai, Mi Jinzhong, Cheng Pengfei, Yuan Yunbin, Gan Xingli
Chinese Academy of Surveying and Mapping, No.28, Lianhuachi West Road, Beijing 100830, China.
Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Science, Xiaohongshan West Road, Wuhan 430071, China.
Sensors (Basel). 2020 May 15;20(10):2819. doi: 10.3390/s20102819.
The cycle slip detection (CSD) and cycle slip repair (CSR) are easily affected by ionospheric delay and observational noise. Aiming at mitigating the above disadvantage, a new BeiDou navigation satellite system (BDS) triple-frequency CSR method (BTCSR) is proposed for the undifferenced phase. BTCSR learns from the classic triple-frequency CSR (CTCSR), with combinations of phases and pseudoranges in correcting ionospheric delay and optimizing observational noise. Different from CTCSR, though, BTCSR has made the following improvements: (1) An optimal model of calculating cycle slip combination is established, which further takes into account the minimization of the effect of residual ionospheric error after the correction. The calculation of cycle slip combination is obtained with the root mean squared errors (0.0646, 0.1261, 0.1069) of cycles, resulting in CSR success rate of 99.9927%, and the wavelengths (4.8842,3.5738,8.1403) of m. (2) A discriminant function is added to guarantee the CSR correctness. This function utilizes epoch-difference value of the ionosphere-free and geometry-free phase to select the correct cycle slip value, which eliminates the interference of large pseudorange errors in determining the final cycle slip. Consequently, the performances of BTCSR and CTCSR have been compared. For the real BDS pseudorange observation with additional 1.5 m errors, which can cover situations of 99.96% pseudorange noise, results of CTCSR show failure, but results of BTCSR keep correct. Moreover, BTCSR has made the following improvements relative to the geometry-free cycle slip detection method (GFCSD) and Melboune-Wubbena cycle slip combination detection method (MWCSD): (1) During a moderate magnetic storm of level 6, CSR testing, with the BDS monitoring station in a low latitude region, showed that some failures occur in GFCSD because of severe ionospheric variation, but BTCSR could correctly identify and fix cycle slips. (2) For the BDS observation data with an additional 1.5 m error on the actual pseudoranges, MWCSD exhibited failures, but the repair results of BTCSR were correct and reliable. (3) For the special slips of (0,59,62) cycles, and equal slips of (1,1,1) cycles on (B1,B2,B3), that are hard to detect by GFCSD and MWCSD, respectively, BTCSR could repair these correctly. Finally, BTCSR obtains reliable repair results under large pseudorange errors and severe ionospheric variations, and the cut-off elevation larger than 10 degrees is the suggested background.
周跳检测（CSD）和周跳修复（CSR）很容易受到电离层延迟和观测噪声的影响。针对这一缺点，提出了一种用于非差相位的北斗导航卫星系统（BDS）三频周跳修复方法（BTCSR）。BTCSR借鉴了经典三频周跳修复方法（CTCSR），通过相位和伪距组合来校正电离层延迟并优化观测噪声。然而，与CTCSR不同的是，BTCSR有以下改进：（1）建立了一个计算周跳组合的最优模型，该模型进一步考虑了校正后残余电离层误差影响的最小化。周跳组合的计算结果为周期的均方根误差（0.0646、0.1261、0.1069），周跳修复成功率为99.9927%，波长为4.8842、3.5738、8.1403米。（2）增加了一个判别函数以确保周跳修复的正确性。该函数利用无电离层和无几何相位的历元差值来选择正确的周跳值，消除了在确定最终周跳时大伪距误差的干扰。因此，对BTCSR和CTCSR的性能进行了比较。对于实际BDS伪距观测中附加1.5米误差（可覆盖99.96%伪距噪声情况），CTCSR的结果显示失败，但BTCSR的结果保持正确。此外，相对于无几何周跳检测方法（GFCSD）和墨尔本 - 武贝纳周跳组合检测方法（MWCSD），BTCSR有以下改进：（1）在6级中等磁暴期间，对低纬度地区的BDS监测站进行周跳修复测试表明，由于电离层剧烈变化，GFCSD出现了一些失败情况，但BTCSR能够正确识别并修复周跳。（2）对于实际伪距上附加1.5米误差的BDS观测数据，MWCSD出现了失败情况，但BTCSR的修复结果正确且可靠。（3）对于GFCSD和MWCSD分别难以检测到的（0,59,62）周期的特殊周跳以及（B1,B2,B3）上（1,1,1）周期的相等周跳，BTCSR能够正确修复。最后，BTCSR在大伪距误差和严重电离层变化情况下获得了可靠的修复结果，建议截止高度大于10度作为背景条件。
