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Ion-mediated interaction between DNAs is essential for DNA condensation, and it is generally believed that monovalent and nonspecifically binding divalent cations cannot induce the aggregation of double-stranded (ds) DNAs. Interestingly, recent experiments found that alkaline earth metal ions such as Mg can induce the aggregation of triple-stranded (ts) DNAs, although there is still a lack of deep understanding of the surprising findings at the microscopic level. In this work, we employed all-atom dynamic simulations to directly calculate the potentials of mean force (PMFs) between tsDNAs, between dsDNAs, and between tsDNA and dsDNA in Mg solutions. Our calculations show that the PMF between tsDNAs is apparently attractive and becomes more strongly attractive at higher [Mg], although the PMF between dsDNAs cannot become apparently attractive even at high [Mg]. Our analyses show that Mg internally binds into grooves and externally binds to phosphate groups for both tsDNA and dsDNA, whereas the external binding of Mg is much stronger for tsDNA. Such stronger external binding of Mg for tsDNA favors more apparent ion-bridging between helices than for dsDNA. Furthermore, our analyses illustrate that bridging ions, as a special part of external binding ions, are tightly and positively coupled to ion-mediated attraction between DNAs.

Satellite remote sensing systems require accurate, autonomous and real-time orbit determinations (RTOD) for geo-referencing. Onboard Global Positioning System (GPS) has widely been used to undertake such tasks. In this paper, a novel RTOD method achieving decimeter precision using GPS carrier phases, required by China’s HY2A and ZY3 missions, is presented. A key to the algorithm success is the introduction of a new parameter, termed pseudo-ambiguity. This parameter combines the phase ambiguity, the orbit, and clock offset errors of the GPS broadcast ephemeris together to absorb a large part of the combined error. Based on the analysis of the characteristics of the orbit and clock offset errors, the pseudo-ambiguity can be modeled as a random walk, and estimated in an extended Kalman filter. Experiments of processing real data from HY2A and ZY3, simulating onboard operational scenarios of these two missions, are performed using the developed software SATODS. Results have demonstrated that the position and velocity accuracy (3D RMS) of 0.2–0.4 m and 0.2–0.4 mm/s, respectively, are achieved using dual-frequency carrier phases for HY2A, and slightly worse results for ZY3. These results show it is feasible to obtain orbit accuracy at decimeter level of 3–5 dm for position and 0.3–0.5 mm/s for velocity with this RTOD method.

Achieving continuous and high-precision positioning services via smartphone under a Global Navigation Satellite System (GNSS)-degraded environment is urgently demanded by the mass market. In 2018, Xiaomi launched the world’s first dual-frequency GNSS smartphone, Xiaomi Mi 8. The newly added L5/E5 signals are more precise and less prone to distortions from multipath reflections. This paper discusses the characteristics of raw dual-frequency GNSS observations from Xiaomi Mi 8 in urban environments; they are characterized by high pseudorange noise and frequent signal interruption. The traditional dual-frequency ionosphere-free combination is not suitable for Xiaomi Mi 8 raw GNSS data processing, since the noise of the combined measurements is much larger than the influence of the ionospheric delay. Therefore, in order to reasonably utilize the high precision carrier phase observations, a time differenced positioning filter is presented in this paper to deliver continuous and smooth navigation results in urban environments. The filter first estimates the inter-epoch position variation (IEPV) with time differenced uncombined L1/E1 and L5/E5 carrier phase observations and constructs the state equation with IEPV to accurately describe the user’s movement. Secondly, the observation equations are formed with uncombined L1/E1 and L5/E5 pseudorange observations. Then, kinematic experiments in open-sky and GNSS-degraded environments are carried out, and the proposed filter is assessed in terms of the positioning accuracy and solution availability. The result in an open-sky environment shows that, assisted with L5/E5 observations, the root mean square (RMS) of the stand-alone horizontal and vertical positioning errors are about 1.22 m and 1.94 m, respectively, with a 97.8% navigation availability. Encouragingly, even in a GNSS-degraded environment, smooth navigation services with accuracies of 1.61 m and 2.16 m in the horizontal and vertical directions are obtained by using multi-GNSS and L5/E5 observations.

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