Real-time detection and repair of cycle slips in triple-frequency GNSS measurements

Abstract

Cycle slip detection and repair are prerequisites to the use of the global navigation satellite system (GNSS) carrier phases for precise positioning. Modern GNSS techniques introduce triple- or multi-frequency signals that are beneficial for cycle slip detection and repair. We present a new real-time cycle slip detection and repair method based on the independent linear combinations of undifferenced triple-frequency GNSS observations. The proposed method forms three types of linear combinations based on the original observations. These combinations are called extra-wide lane (EWL), wide lane (WL), and narrow lane (NL). Cycle slips on the combinations are determined sequentially in three cascaded steps. The first step employs the geometry-free and ionosphere-free Hatch–Melbourne–Wübbena combination to determine and repair the EWL cycle slips. The second step subtracts the cycle-slip-repaired EWL combination from the WL combination to eliminate the geometry part of the WL combination. This subtraction results in a new function that contains the WL ambiguity and residual ionospheric delay. This function is differenced at two consecutive epochs to determine the WL cycle slips. The residual ionospheric delay difference is ignored because of its small magnitude relative to WL wavelength. The third step determines the NL cycle slips in the same manner as in the second step. The difference is that the cycle-slip-repaired EWL combination is replaced with the more accurate cycle-slip-repaired WL combination. Moreover, the residual ionospheric delay difference is compensated by the ionospheric delay rate derived from the original carrier phase observations. When the EWL, WL, and NL cycle slips are determined, cycle slips on the original carrier phase observations can be uniquely identified. The proposed approach has been tested on 30-s triple-frequency BeiDou navigation satellite system data under different levels of ionospheric variations, and on 30-s triple-frequency global positioning system and quasi-zenith satellite system data. Results indicate that the approach can effectively detect and correct cycle slips even for one cycle under low sampling rate or active ionospheric conditions on each frequency in real time.