Objectives  Carrier phase is the key to achieve high precision positioning, and its quality determines the reliability of positioning results. Due to the development and needs of society, the data acquisition environment is becoming more and more complex, and the real-time requirements are also constantly improving, which greatly increases the probability of cycle slip and increases the difficulty of cycle slip detection. However, some cycle slip detection algorithms commonly used at present have poor detection effect in such environments as active ionosphere, low elevation angle, occlusion, etc., which lead to false detection and missed detection.

  Methods  In order to solve these problems, firstly, an improved algorithm based on TurboEdit epoch difference model is proposed. The trend terms of ionospheric delay and multipath effect errors are extracted by adding sliding polynomial fitting method to the epoch difference of GF (Geometry-Free), and by choosing appropriate threshold, the detection ability of small cycle slips is enhanced. Then, to solve the problem that epoch difference model can not distinguish cycle slip and gross errors, Score test in statistical diagnosis is introduced and constructed. A cycle slip and gross errors separation model based on Score test is built to avoid the phenomenon of cycle slip detection caused by gross errors. Finally, the improved GF epoch difference model is combined with Melbourne Wübbena(MW) combination to repair cycle slip, and the minimum one norm criterion of detection is used to select the correct repair value of cycle slip. The algorithm is verified by using the GPS un-differenced data of IGS (International GNSS Service) stations.

  Results  The cycle slips obtained by the improved GF epoch difference still have high detection sensitivity for small cycle slips. The simulated small cycle slip, continuous cycle slip and special cycle slip are detected, such as (1, 1), (-1, -1), (5, 4), etc. Two successive abnormal epochs detected by GF epoch difference optimization algorithm have successfully separated the simulated (1, 1), (0, 0.5) small gross errors after a Score test and deviation test.When GF and MW probes are used to calculate cycle slip directly, there are errors in cycle slip calculation due to the excessive noise of MW probe, and the calculation error reaches 3 weeks. By using the improved minimum one norm of GF epoch differential survey and MW survey, the correct cycle slip solution is found successfully.

  Conclusions  In the aspect of cycle slip detection, the improved GF epoch difference method can weaken the influence of ionospheric delay variation and multipath effect, and improve the accuracy of cycle slip detection. At the same time, through the appropriate threshold selection, even in the case of high ionospheric scintillation, small cycle slip and continuous cycle slip can be detected accurately. In the separation of cycle slip and gross errors, the fitting residual is replaced by the prediction residual to improve the Score test, which makes it suitable for anomaly test in real-time situation. Based on this, the separation model of cycle slip and gross errors can separate the gross errors from cycle slip accurately, avoid the misjudgment of cycle slip, and improve the reliability of real-time TurboEdit cycle slip detection method. In the aspect of cycle slip repair, the criterion of cycle slip repair success is to minimize the one norm of the probe change caused by correct cycle slip repair. Compared with solving cycle slip solution directly and rounding, this proposed algorithm can not only verify the correctness of cycle slip solution, but also correct the wrong cycle slip solution in real-time, get the accurate cycle slip value, and repair the subsequent observation value of epoch.