Instantaneous cycle slip detection and repair for a standalone triple-frequency GPS receiver

An instantaneous cycle-slip detection and fix method for a standalone triple-frequency GPS receiver is developed based on a dual-frequency method. By jointly using the ionospheric total electron contents (TEC) rate (TECR) and extra-wide-lane (EWL) linear combination, we can detect and fix cycle slips on the three frequencies L1, L2 and L5. The detection is achieved by time-differencing the TECR and EWL combination ambiguity between current epoch when cycle slips occur and previous epoch, and the cycle slip will cause a significant change in TECR and EWL combination ambiguity. As for the determination of cycle slips, two algorithms are explored, one using TECR and EWL cycle-slip terms, the other using uncombined triple-frequency cycle-slip terms. Float cycle-slip values are obtained according to least-squares principle using the two algorithms. Next, integer values can be approached either by simply rounding or by the LAMBDA algorithm, depending on the severity of noise. Measurements from both satellite data and simulated data are used to test the detection method and compare the two algorithms for cycle slip determination. The results confirm the efficiency of the detection method and show that the uncombined algorithm slightly outperforms the other one in terms of the accuracy of obtained float cycle-slip values.