A Cycle Slip Repair Method Against Ionospheric Effects and Observational Noises for BDS Triple-Frequency Undifferenced Phases.

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.