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

Abstract

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.

A Novel Ionospheric Disturbance Index to Evaluate the Global Effect on BeiDou Navigation Satellite System Signal Caused by the Moderate Geomagnetic Storm on May 12, 2021

“…Since the BDS heterogeneous constellation includes Geosynchronous Earth Orbit (GEO) satellites, Inclined Geosynchronous Satellite Orbit (IGSO) satellites, and Middle Earth Orbit (MEO) satellites, using the same threshold for different types of satellites will result in missing or misjudging the number of anomaly satellite signals. It is recommended that the detection threshold could be selected between 0.01 and 0.02 m during moderate geomagnetic storms [ 32 , 33 , 34 , 35 , 36 ]. Then, we calculated the PAS index for all the BDS stations globally.…”

Improved Cycle Slip Repair with GPS Triple-Frequency Measurements by Minifying the Influences of Ionospheric Variation and Pseudorange Errors

“…Under the environments of strong geomagnetic storm and adding gross errors on the pseudoranges of the real GPS triple-frequency data, the performance of GTCSR was verified through a comparison with the conventional CSR with the GPS triple-frequency combinations, the traditional CSD with GF, and HMW. Although many studies have been conducted on BDS triple-frequency CSR [28,29], it should be stressed that there are some noticeable differences between triple-frequency GPS and triple-frequency BDS [30]. Results of the optimized CSR in this study are suitable for GPS signals only.…”

“…Finally, GTCSR builds a cycle slip discrimination function to eliminate the adverse influence of large pseudorange errors on the fixation of the cycle slip combination. The epochdifference, ionosphere-free, and geometry-free phase under GPS triple-frequency condition are designed as the discrimination function [28,29]. In this discrimination function, the pseudoranges are uninvolved; the ionospheric delay, geometric terms, and hardware biases are offset; and only the influence of cycle slips is retained.…”