The Global Navigation Satellite System (GNSS) traditional dual‐frequency cycle slip detection and repair methods such as the TurboEdit algorithm are restricted by the availability and accuracy of pseudorange observations. Doppler observations represent the instantaneous variation of the carrier phase during the integration time, which are immune to cycle slips. They are less affected by multipath effects compared with the pseudorange observations. Hence, a real‐time cycle slip detection and repair approach for the BeiDou Navigation Satellite System (BDS) dual‐frequency signals is proposed by combining the carrier phase and Doppler observations. The proposed method adopts the phase‐Doppler combination and the geometry‐free combination to detect cycle slips, and uses the simple rounding method or the dual‐frequency least‐square ambiguity decorrelation adjustment (LAMBDA) method to repair cycle slips. The validity of the proposed method is verified by the static and kinematic observation data under 1 s sampling interval and steady ionosphere. The results show that the new method can successfully detect all the small, insensitive, and large cycle slips. Moreover, the fixing rates of the simple rounding method under static and kinematic conditions are above 94% and 83%, respectively, while those of the dual‐frequency LAMBDA method are both 100%.

A new model is presented to resolve cycle slips detection for triple-frequency observations of BeiDou navigation satellite system (BDS) in this paper when pseudorange observations are missing or insufficiently accurate under harsh or special situations. Based on the first-order time-difference geometry-free (GF) pseudorange-phase combination model, the new cycle slips detection and correction method based on the triple-frequency carrier phase and Doppler observations is proposed. With analyses on the two common sampling intervals (30 s and 1 s), it can be concluded that the optimal combination coefficients of the proposed model relate to sampling intervals. Combinations [4,-2,-3], [-1,-5,6], and [-3,6,-2] are selected to detect and correct cycle slips for 30 s sampling interval, while combinations [0,-1,1], [1,0,-1], and [-3,2,2] are selected for 1 s sampling interval. The validity of the phase-Doppler combination model under the static condition and the steady ionosphere with 30 s sampling interval and 1 s sampling interval is verified by two static experiments. Results show that the phase-Doppler combination model can achieve the same performance as the pseudorange-phase combination model. All the small, insensitive, and large cycle slips added to the three types of BDS satellites which separately belong to Geostationary Earth Orbit (GEO), Inclined Geosynchronous Orbit (IGSO), and Medium Earth Orbit (MEO) are detected and corrected successfully by the proposed model.

The triple-frequency linear combination method can provide combinations with different characteristics and is one of the important methods to improve the performance of navigation services. Due to the large number of combinations and different combination performances, combinatorial clustering optimization is very important, and the efficiency of manual screening is very low. Firstly, based on the basic model, the objective equations are derived. Secondly, based on the fuzzy c-means (FCM) algorithm, three improved PSO-FCM algorithms are proposed, namely the S-PSO-FCM algorithm, L-PSO-FCM algorithm, and LOG-PSO-FCM algorithm. Thirdly, according to the different combination characteristics, the two datasets whose combined coefficients sum to 0 and 1 are emphatically discussed. Finally, the effectiveness of the improved PSO-FCM algorithms is studied based on the public dataset and the measured BeiDou-3 navigation satellite system (BDS-3) data of short baseline, long baseline, and ultra-long baseline. The results show that the performance of the proposed algorithm is better than that of the FCM algorithm, especially in short baseline and long baseline cases.