Real-time kinematic positioning over long baselines using triple-frequency BeiDou signals

The BeiDou system is the first global navigation satellite system in which all satellites transmit triple-frequency signals that can provide the positioning, navigation, and timing independently. A benefit of triple-frequency signals is that more useful combinations can be formed, including some extrawide-lane combinations whose ambiguities can generally be instantaneously fixed without distance restriction, although the narrow-lane ambiguity resolution (NL AR) still depends on the interreceiver distance or requires a long time to achieve. In this paper, we synthetically study decimeter and centimeter kinematic positioning using BeiDou triple-frequency signals. It starts with AR of two extrawide-lane signals based on the ionosphere-free or ionosphere-reduced geometry-free model. For decimeter positioning, one can immediately use two ambiguity-fixed extrawide-lane observations without pursuing NL AR. To achieve higher accuracy, NL AR is the necessary next step. Despite the fact that long-baseline NL AR is still challenging, some NL ambiguities can indeed be fixed with high reliability. Partial AR for NL signals is acceptable, because as long as some ambiguities for NL signals are fixed, positioning accuracy will be certainly improved.With accumulation of observations, more and more NL ambiguities are fixed and the positioning accuracy continues to improve. An efficient Kalman-filtering system is established to implement the whole process. The formulated system is flexible, since the additional constraints can be easily applied to enhance the model's strength. Numerical results from a set of real triple-frequency BeiDou data on a 50 km baseline show that decimeter positioning is achievable instantaneously.With only five data epochs, 84% of NL ambiguities can be fixed so that the real-time kinematic accuracies are 4.5, 2.5, and 16 cm for north, east, and height components (respectively), while with 10 data epochs more than 90% of NL ambiguities are fixed, and the rea- -time kinematic solutions are improved to centimeter level for all three coordinate components.

Assessment of code bias variations of BDS triple-frequency signals and their impacts on ambiguity resolution for long baselines

Carrier phase ambiguity resolution over long baselines is challenging in BDS data processing. This is partially due to the variations of the hardware biases in BDS code signals and its dependence on elevation angles. We present an assessment of satellite-induced code bias variations in BDS triple-frequency signals and the ambiguity resolutions procedures involving both geometry-free and geometry-based models. First, since the elevation of a GEO satellite remains unchanged, we propose to model the single-differenced fractional cycle bias with widespread ground stations. Second, the effects of code bias variations induced by GEO, IGSO and MEO satellites on ambiguity resolution of extra-wide-lane, wide-lane and narrow-lane combinations are analyzed. Third, together with the IGSO and MEO code bias variations models, the effects of code bias variations on ambiguity resolution are examined using 30-day data collected over the baselines ranging from 500 to 2600 km in 2014. The results suggest that although the effect of code bias variations on the extra-wide-lane integer solution is almost ignorable due to its long wavelength, the wide-lane integer solutions are rather sensitive to the code bias variations. Wide-lane ambiguity resolution success rates are evidently improved when code bias variations are corrected. However, the improvement of narrow-lane ambiguity resolution is not obvious since it is based on geometry-based model and there is only an indirect impact on the narrow-lane ambiguity solutions.

Geometry-free stochastic analysis of BDS triple frequency signals

The paper presents a geometry-free approach to assess the variation of covariance matrices of undifferenced triple frequency GNSS measurements and its impact on positioning solutions. Four independent geometryfree/ ionosphere-free (GFIF) models formed from original triple-frequency code and phase signals allow for effective computation of variance-covariance matrices using real data. Variance Component Estimation (VCE) algorithms are implemented to obtain the covariance matrices for three pseudorange and three carrier-phase signals epoch-by-epoch. Covariance results from the triple frequency Beidou System (BDS) and GPS data sets demonstrate that the estimated standard deviation varies in consistence with the amplitude of actual GFIF error time series. The single point positioning (SPP) results from BDS ionosphere-free measurements at four MGEX stations demonstrate an improvement of up to about 50% in Up direction relative to the results based on a mean square statistics. Additionally, a more extensive SPP analysis at 95 global MGEX stations based on GPS ionosphere-free measurements shows an average improvement of about 10% relative to the traditional results. This finding provides a preliminary confirmation that adequate consideration of the variation of covariance leads to the improvement of GNSS state solutions.

Wide area kinematic positioning with BeiDou triple frequency signals

A key challenge of wide area kinematic positioning is to overcome the effects of the varying hardware biases in code signals of the BeiDou system. Based on three geometryfree/ionosphere-free combinations, the elevation-dependent code biases are modelled for all BeiDou satellites. Results from the data sets of 30-day for 5 baselines of 533 to 2545 km demonstrate that the wide-lane (WL) integer-fixing success rates of 98% to 100% can be achieved within 25 min. Under the condition of HDOP of less than 2, the overall RMS statistics show that ionospheric-free WL single-epoch solutions achieve 24 to 50 cm in the horizontal direction. Smoothing processing over the moving window of 20 min reduces the RMS values by a factor of about 2. Considering distance-independent nature, the above results show the potential that reliable and high precision positioning services could be provided in a wide area based on a sparsely distributed ground network.

Raman microscopy of formamide-intercalated kaolinites treated by controlled-rate thermal analysis technology

Raman spectroscopy of formamide-intercalated kaolinites treated using controlled-rate thermal analysis technology (CRTA), allowing the separation of adsorbed formamide from intercalated formamide in formamide-intercalated kaolinites, is reported. The Raman spectra of the CRTA-treated formamide-intercalated kaolinites are significantly different from those of the intercalated kaolinites, which display a combination of both intercalated and adsorbed formamide. An intense band is observed at 3629 cm-1, attributed to the inner surface hydroxyls hydrogen bonded to the formamide. Broad bands are observed at 3600 and 3639 cm-1, assigned to the inner surface hydroxyls, which are hydrogen bonded to the adsorbed water molecules. The hydroxyl-stretching band of the inner hydroxyl is observed at 3621 cm-1 in the Raman spectra of the CRTA-treated formamide-intercalated kaolinites. The results of thermal analysis show that the amount of intercalated formamide between the kaolinite layers is independent of the presence of water. Significant differences are observed in the CO stretching region between the adsorbed and intercalated formamide.

Hydrazine-hydrate intercalated halloysite under controlled-rate thermal analysis conditions

The thermal behaviour of halloysite fully expanded with hydrazine-hydrate has been investigated in nitrogen atmosphere under dynamic heating and at a constant, pre-set decomposition rate of 0.15 mg min-1. Under controlled-rate thermal analysis (CRTA) conditions it was possible to resolve the closely overlapping decomposition stages and to distinguish between adsorbed and bonded reagent. Three types of bonded reagent could be identified. The loosely bonded reagent amounting to 0.20 mol hydrazine-hydrate per mol inner surface hydroxyl is connected to the internal and external surfaces of the expanded mineral and is present as a space filler between the sheets of the delaminated mineral. The strongly bonded (intercalated) hydrazine-hydrate is connected to the kaolinite inner surface OH groups by the formation of hydrogen bonds. Based on the thermoanalytical results two different types of bonded reagent could be distinguished in the complex. Type 1 reagent (approx. 0.06 mol hydrazine-hydrate/mol inner surface OH) is liberated between 77 and 103°C. Type 2 reagent is lost between 103 and 227°C, corresponding to a quantity of 0.36 mol hydrazine/mol inner surface OH. When heating the complex to 77°C under CRTA conditions a new reflection appears in the XRD pattern with a d-value of 9.6 Å, in addition to the 10.2 Ĺ reflection. This new reflection disappears in contact with moist air and the complex re-expands to the original d-value of 10.2 Å in a few h. The appearance of the 9.6 Å reflection is interpreted as the expansion of kaolinite with hydrazine alone, while the 10.2 Å one is due to expansion with hydrazine-hydrate. FTIR (DRIFT) spectroscopic results showed that the treated mineral after intercalation/deintercalation and heat treatment to 300°C is slightly more ordered than the original (untreated) clay.