Algorithm for Real-Time Cycle Slip Detection and Repair for Low Elevation GPS Undifferenced Data in Different Environments

Real-time cycle slip detection and repair is one of the key issues in global positioning system (GPS) high precision data processing and application. In particular, when GPS stations are in special environments, such as strong ionospheric disturbance, sea, and high-voltage transmission line interference, cycle slip detection and repair in low elevation GPS observation data are more complicated than those in normal environments. For low elevation GPS undifferenced carrier phase data in different environments, a combined cycle slip detection algorithm is proposed. This method uses the first-order Gauss–Markov stochastic process to model the pseudorange multipath in the wide-lane phase minus narrow-lane pseudorange observation equation, and establishes the state equation of the wide-lane ambiguity with the pseudorange multipath as a parameter, and it uses the Kalman filter for real-time estimation and detects cycle slips based on statistical hypothesis testing with a predicted residual sequence. Meanwhile, considering there are certain correlations among low elevation, observation epoch interval, and ionospheric delay error, a second-order difference geometry-free combination cycle slip test is constructed that takes into account the elevation. By combining the two methods, real-time cycle slip detection for GPS low elevation satellite undifferenced data is achieved. A cycle slip repair method based on spatial search and objective function minimization criterion is further proposed to determine the correct solution of the cycle slips after they are detected. The whole algorithm is experimentally verified using the static and kinematic measured data of low elevation satellites under four different environments: normal condition, high-voltage transmission lines, dynamic condition in the sea, and ionospheric disturbances. The experimental results show that the algorithm can detect and repair cycle slips accurately for low elevation GPS undifferenced data, the difference between the float solution and the true value for the cycle slip does not exceed 0.5 cycle, and the differences obey the normal distribution overall. At the same time, the wide-lane ambiguity and second-order difference GF combination sequence calculated by the algorithm is smoother, which give further evidence that the algorithm for cycle slip detection and repair is feasible and effective, and has the advantage of being immune to the special observation environments.

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

In advance of precise positioning with phase data, cycle slip detection (CSD) is a basic work that should be implemented in phase data possessing. When the cycle slip occurred, cycle slip repair (CSR) can be taken to rebuild the continuity of phase data. Unfortunately, the large pseudorange errors can contaminate the combinations with the pseudoranges and phases such as the Hatch–Melbourne–Wubbena combination (HMW) and cause false CSD or wrong CSR results. On the other hand, the severe ionospheric time variation can deteriorate the epoch-difference geometry-free phase (GF), and tremendously interfere with the performances of CSD and CSR. To handle the aforementioned limitations, a global position system (GPS) triple-frequency CSR method (GTCSR) is proposed with two efficient treatments: (1) the significant ionospheric variations are corrected, and the influences from the residual ionospheric effects are minimized along with the observational noises; and (2) the impacts of large pseudorange errors are refrained by designing a discrimination function with a geometry-free and ionosphere-free phase to identify the correct cycle slip values. Consequently, CSR tests were conducted with three monitoring stations at different regions. First, during a strong geomagnetic storm, without correcting the ionospheric variation of CSR (WICSR) displayed obvious failures, and many epochs of cycle slip values from WICSR deviated from the known values. However, the results of the GTCSR were correct, and GTCSR presented a higher success rate than that of WICSR. Furthermore, for the real triple-frequency data, by adding gross errors of 2.5 m on all epoch-difference pseudoranges epoch by epoch, the conventional triple-frequency CSR with the optimized combinations (CTCSR) and the CSD with HMW (HMWCSD) showed many mistakes, where the results of CTCSR and HMWCSD on numerous epochs were inconsistent with the actual situations, but the success rate of GTCSR was significantly higher than those of CTCSR and HMWCSD. In summary, in the condition of the cutoff elevation being larger than 10 degrees, improved performances and higher success rates were achieved from GTCSR under environments of large pseudorange errors and severe ionospheric variations.

Optimization and selection of Galileo triple-frequency carrier linear combination

The triple-frequency linear combination with a low noise, a long wavelength, and a weak ionosphere is beneficial to effectively eliminate or weaken the common errors, advance the reliability of cycle slip detection and repair, and speed up the convergence time of fixed ambiguity. By establishing the Galileo triple-frequency carrier linear combination model, three types of linear combinations are derived: Geometry-free (GF) combinations, minimum noise (MN) combinations, and ionosphere-free (IF) combinations. The geometric relationships of these linear combinations are displayed in the form of image. The results indicate that the angle formed by the IF combinations and the MN combinations is between 75.02° and 86.01°, which also illustrates that it is more difficult to meet the carrier phase combinations with a low noise and a weak ionosphere. Moreover, to guarantee the integer cycle characteristics of ambiguity, the combination coefficient must be an integer. Galileo triple-frequency linear combination is solved utilizing the extremum method. To sum up, the sum of the coefficients of the extra wide lane (EWL) combinations and wide lane (WL) combinations is zero, and the sum of the coefficients of the narrow lane (NL) combinations is one. (0, 1, −1) is the optimal triple-frequency linear combination in Galileo. Three independent linear combinations are selected separately from the EWL, WL, and NL to jointly solve the integer ambiguity. Further, it creates a prerequisite for high-precision and real-time kinematic positioning.