Cycle slip detection is one of the essential steps for high-precision GNSS data processing when carrier phase observations are involved, such as in precise point positioning (PPP) and precise orbit determination (POD). A number of algorithms have been developed since the 1980s and are effective for processing dual-frequency GPS. However, the emerging BeiDou navigation satellite system in China brings some new challenges for these existing algorithms, especially when small cycle slips occur more frequently. In this study, a large number of 1-cycle slips have been found in low-elevation BeiDou GEO carrier phase observations, which are collected by receivers of the IGS multi-GNSS experiment. Such small cycle slips should be identified and repaired, if possible, before PPP and POD processing. We propose an enhanced cycle slip detection method based on the series of dual-frequency phase geometry-free combinations. A robust polynomial fit algorithm and a general autoregressive conditional heteroskedastic modeling technique is employed to provide an adaptive detection threshold, which allows identification of such small cycle slips with high reliability. Simulated and real data tests reveal that the proposed method has both high sensitivity and low false-alarm rate even in the case of ionospheric scintillation.

The increasing use of mathematical techniques in scientific research leads to the interdisciplinarity of applied mathematics. This viewpoint is validated quantitatively here by statistical and network analysis on the corpus PNAS 1999–2013. A network describing the interdisciplinary relationships between disciplines in a panoramic view is built based on the corpus. Specific network indicators show the hub role of applied mathematics in interdisciplinary research. The statistical analysis on the corpus content finds that algorithms, a primary topic of applied mathematics, positively correlates, increasingly co-occurs, and has an equilibrium relationship in the long-run with certain typical research paradigms and methodologies. The finding can be understood as an intrinsic cause of the interdisciplinarity of applied mathematics.

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