BeiDou Geostationary Satellite Code Bias Modeling Using Fengyun-3C Onboard Measurements

This study validated and investigated elevation- and frequency-dependent systematic biases observed in ground-based code measurements of the Chinese BeiDou navigation satellite system, using the onboard BeiDou code measurement data from the Chinese meteorological satellite Fengyun-3C. Particularly for geostationary earth orbit satellites, sky-view coverage can be achieved over the entire elevation and azimuth angle ranges with the available onboard tracking data, which is more favorable to modeling code biases. Apart from the BeiDou-satellite-induced biases, the onboard BeiDou code multipath effects also indicate pronounced near-field systematic biases that depend only on signal frequency and the line-of-sight directions. To correct these biases, we developed a proposed code correction model by estimating the BeiDou-satellite-induced biases as linear piece-wise functions in different satellite groups and the near-field systematic biases in a grid approach. To validate the code bias model, we carried out orbit determination using single-frequency BeiDou data with and without code bias corrections applied. Orbit precision statistics indicate that those code biases can seriously degrade single-frequency orbit determination. After the correction model was applied, the orbit position errors, 3D root mean square, were reduced from 150.6 to 56.3 cm

DETERMINING THE COMPONENT NUMBER OF LINKS CORRESPONDING TO TRIANGULAR AND HONEYCOMB LATTICES

NSFC [10831001]; Fundamental Research Funds for the Central Universities [2010121007]There is a classical correspondence between edge-signed plane graphs and link diagrams. Determining component number of links corresponding to plane graphs may be one of the first problems in studying links by using graphs. There has been several early studies in this aspect, for example, the component number of links formed from 2-dimensional square lattices (4(4)) has been determined. In this paper, we determine the component number of links corresponding to 2-dimensional triangular (3(6)) and honeycomb (6(3)) lattices with free or cyclic boundary condition

GRACE-FO Antenna Phase Center Modeling and Precise Orbit Determination with Single Receiver Ambiguity Resolution

Precise knowledge of the phase center location of the global navigation satellite system (GNSS) antenna is a prerequisite for precise orbit determination (POD) of the low Earth orbit (LEO) satellite. The phase center offset (PCO) and phase center variation (PCV) values for the LEO antenna obtained from ground calibration cannot reflect the error sources encountered in the actual spacecraft environment. PCV corrections are estimated by ionosphere free (IF) carrier phase post-fit residuals of reduced dynamic orbit determination. Ambiguity resolution (AR) plays a crucial role in achieving the best orbit accuracy. The single receiver AR concept is realized using wide-lane (WL) and narrow-lane (NL) bias products. Single difference (SD) observations between satellites are applied to remove the receiver dependent phase bias. SD AR and traditional double difference (DD) AR methods are applied to fix the ambiguities. The recovered SD and DD IF ambiguities are taken as pseudo-observations to constrain the undifferenced IF ambiguity parameters in the POD process. The LEO orbits based on float ambiguity (FA), SD, AR, and DD AR are investigated. One year’s data collected by the Gravity Recovery And Climate Experiment Follow-On (GRACE-FO) mission and GPS precise products provided by the Center for Orbit Determination in Europe (CODE) were analyzed. Precise orbit generated by the Jet Propulsion Laboratory (JPL), independent satellite laser ranging (SLR), and K-band ranging (KBR) measurements were utilized to assess the orbit accuracy. More than 98% of SD WL and 95% of SD NL ambiguities are fixed, which confirms the good quality of the bias products and correctness of the SD AR method. With PCV corrections, the average phase residuals of DD and SD AR solutions are 0.13 and 0.41 mm, which indicates improved consistency between applied models and observations. Compared with JPL’s orbit, the SD AR orbits achieve the accuracy of 6.0, 6.2, and 5.1 mm in along-track, cross-track, and radial directions. The SD AR solutions show an average improvement of 18.3% related to the FA orbits while 6.3% is gained by the DD AR approach. The root mean squares (RMSs) of SLR residuals for FA, DD AR, and SD AR solutions are 11.5, 10.2, and 9.6 mm, which validate the positive effect of AR on POD. Standard deviation (STD) of KBR residuals for SD AR orbits is 1.8 mm while 0.9 mm is achieved by the DD AR method. The explanation is that the phase bias products used for SD AR are not free of errors and the errors may degrade the KBR validation. In-flight PCV calibration and ambiguity resolution improve the LEO orbit accuracy effectively

Performance Evaluation of Single-Frequency Precise Point Positioning and Its Use in the Android Smartphone

The opening access of global navigation satellite system (GNSS) raw data in Android smart devices has led to numerous studies on precise point positioning on mobile phones, among which single-frequency precise point positioning (SF-PPP) has become popular because smartphone-based dual-frequency data still suffer from poor observational quality. As the ionospheric delay is a dominant factor in SF-PPP, we first evaluated two SF-PPP approaches with the MGEX (Multi-GNSS Experiment) stations, the Group and Phase Ionospheric Correction (GRAPHIC) approach and the uncombined approach, and then applied them to a Huawei P40 smartphone. For MGEX stations, both approaches achieved less than 0.1 m and 0.2 m accuracy in horizontal and vertical components, respectively. Uncombined SF-PPP manifested a significant decrease in the convergence time by 40.7%, 20.0%, and 13.8% in the east, north, and up components, respectively. For P40 data, the SF-PPP performance was analyzed using data collected with both a built-in antenna and an external geodetic antenna. The P40 data collected with the built-in antenna showed lower carrier-to-noise ratio (C/N0) values, and the pseudorange noise reached 0.67 m, which is about 67% larger than that with a geodetic antenna. Because the P40 pseudorange noise presented a strong correlation with C/N0, a C/N0-dependent weight model was constructed and used for the P40 data with the built-in antenna. The convergence of uncombined SF-PPP approach was faster than the GRAPHIC model for both the internal and external antenna datasets. The root mean square (RMS) errors for the uncombined SF-PPP solutions of P40 with an external antenna were 0.14 m, 0.15 m, and 0.33 m in the east, north, and up directions, respectively. In contrast, the P40 with an embedded antenna could only reach 0.72 m, 0.51 m, and 0.66 m, respectively, indicating severe positioning degradation due to antenna issues. The results indicate that the two SF-PPP models both can achieve sub-meter level positioning accuracy utilizing multi-GNSS single-frequency observations from mobile smartphones

Reduced-Dynamic Precise Orbit Determination of Haiyang-2B Altimetry Satellite Using a Refined Empirical Acceleration Model

The Haiyang 2B (HY-2B) satellite requires precise orbit determination (POD) products for geodetic remote sensing techniques. An improved set of reduced-dynamic (RD) orbit solutions was generated from the onboard Global Positioning System (GPS) measurements over a 14-month period using refined strategies and processing techniques. The key POD strategies include a refined empirical acceleration model, in-flight calibration of the GPS antenna, and the resolution of single-receiver carrier-phase ambiguities. In this study, the potential periodicity of empirical acceleration in the HY-2B POD was identified by spectral analysis. In the along-track direction, a noticeable signal with four cycles per revolution (CPR) was significant. A mixed spectrum was observed for the cross-track direction. To better understand the real in-flight environment, a refined empirical acceleration model was used to cope with the time variability of empirical accelerations in HY-2B POD. Three POD strategies were used for the reprocessing for superior orbit quality. Validation using over one year of satellite laser ranging (SLR) measurements demonstrated a 5.2% improvement in the orbit solution of the refined model. Reliable correction for the GPS antenna phase center was obtained from an over-420-day dataset, and a trend in radial offset change was observed. After application of the in-flight calibration of the GPS antenna, a 26% reduction in the RMS SLR residuals was achieved for the RD orbit solution, and the carrier phase residuals were clearly reduced. The integer ambiguity resolution of HY-2B led to strong geometric constraints for the estimated parameters, and a 15% improvement in the SLR residuals could be inferred compared with the float solution

Thiacalix[4]arene-Supported Kite-Like Heterometallic Tetranuclear Zn^IILn^III₃ (Ln = Gd, Tb, Dy, Ho) Complexes

Four kite-like tetranuclear Zn^IILn^III₃ (Ln= Gd <b>1</b>, Tb <b>2</b>, Dy <b>3</b>, Ho <b>4</b>) clusters supported by <i>p</i>-<i>tert</i>-butylthiacalix­[4]­arene (H₄BTC4A) have been prepared under solvothermal conditions and structurally characterized by single crystal X-ray diffraction and powder X-ray diffraction (PXRD). In the structures of these four complexes, each of them is capped by two tail-to-tail <i>p</i>-<i>tert</i>-butylthiacalix­[4]­arene molecules to form a bent sandwich-like unit. The photoluminescent analyses reveal that the H₄BTC4A is an efficient sensitizer for Tb³⁺ ions in <b>2</b>. The magnetic properties of complexes <b>1</b>–<b>4</b> are also investigated, in which complex <b>3</b> exhibits slow magnetization relaxation typical for single molecule magnets

Thiacalix[4]arene-Supported Kite-Like Heterometallic Tetranuclear Zn^IILn^III₃ (Ln = Gd, Tb, Dy, Ho) Complexes

Four kite-like tetranuclear Zn^IILn^III₃ (Ln= Gd <b>1</b>, Tb <b>2</b>, Dy <b>3</b>, Ho <b>4</b>) clusters supported by <i>p</i>-<i>tert</i>-butylthiacalix­[4]­arene (H₄BTC4A) have been prepared under solvothermal conditions and structurally characterized by single crystal X-ray diffraction and powder X-ray diffraction (PXRD). In the structures of these four complexes, each of them is capped by two tail-to-tail <i>p</i>-<i>tert</i>-butylthiacalix­[4]­arene molecules to form a bent sandwich-like unit. The photoluminescent analyses reveal that the H₄BTC4A is an efficient sensitizer for Tb³⁺ ions in <b>2</b>. The magnetic properties of complexes <b>1</b>–<b>4</b> are also investigated, in which complex <b>3</b> exhibits slow magnetization relaxation typical for single molecule magnets

Thiacalix[4]arene-Supported Kite-Like Heterometallic Tetranuclear Zn^IILn^III₃ (Ln = Gd, Tb, Dy, Ho) Complexes

Four kite-like tetranuclear Zn^IILn^III₃ (Ln= Gd <b>1</b>, Tb <b>2</b>, Dy <b>3</b>, Ho <b>4</b>) clusters supported by <i>p</i>-<i>tert</i>-butylthiacalix­[4]­arene (H₄BTC4A) have been prepared under solvothermal conditions and structurally characterized by single crystal X-ray diffraction and powder X-ray diffraction (PXRD). In the structures of these four complexes, each of them is capped by two tail-to-tail <i>p</i>-<i>tert</i>-butylthiacalix­[4]­arene molecules to form a bent sandwich-like unit. The photoluminescent analyses reveal that the H₄BTC4A is an efficient sensitizer for Tb³⁺ ions in <b>2</b>. The magnetic properties of complexes <b>1</b>–<b>4</b> are also investigated, in which complex <b>3</b> exhibits slow magnetization relaxation typical for single molecule magnets

Self-Assembly of Thiacalix[4]arene-Supported Nickel(II)/Cobalt(II) Complexes Sustained by in Situ Generated 5-Methyltetrazolate Ligand

Solvothermal reactions of thiacalix[4]­arene, NaN₃, and acetonitrile in the presence of nickel­(II)/cobalt­(II) salts yielded four discrete complexes sustained by the in situ generated 5-methyltetrazolate ligand, [Ni^II₁₂(PTC4A)₃(μ₆-CO₃)₂(μ-Mtta)₂(μ-Mtta)₄ (μ₄-Mtta)₂(Py)₄]·7DMF·2Py·dma (<b>1</b>), [Co^II₁₂(PTC4A)₃(HCOO)₃(μ₆-CO₃)₂ (μ-Mtta)­(μ-Mtta)₂(μ₄-Mtta)₂(Py)₄]·5DMF·dma (<b>2</b>), [Co^II₁₂(BTC4A)₃(HCOO)₂ (μ₆-CO₃)₂(μ-Mtta)₄(μ₄-Mtta)₂(dma)₂(Pz)₂]·2DMF·3dma (<b>3</b>), and [Co^II₁₆(BTC4A)₄(μ₄-Cl)₄ (HCOO)₂(μ-Mtta)₆(μ-Mtta)₈]·10DMF·6CH₃CN·4Hdma (<b>4</b>) (H₄PTC4A = <i>p</i>-phenylthiacalix­[4]­arene; H₄BTC4A = <i>p</i>-tert-butylthiacalix­[4]­arene; HMtta = 5-methyl tetrazolate). Crystal structural analyses revealed that complexes <b>1</b>–<b>3</b> are stacked by pseudotrigonal planar entities, which consist of three metal^II₄-thiacalix­[4]­arene subunits including two shuttlecock-like and one cylinder-like ones. These subunits are connected in an up-to-down-to-up fashion through six different 5-methyl tetrazolate anions. Both the in situ generated 5-methyl tetrazolate anion and carbonato anion play an important role in constructing these high-nuclearity clusters. When the corresponding chloride salt was used as precursors in the synthesis, complex <b>4</b> was obtained, which is stacked by wheel-like entities possessing four shuttlecock-like building blocks linked by eight in situ generated 5-methyl tetrazolate ligands in an up-to-up fashion. The differences in the structures of complexes <b>3</b> and <b>4</b> indicate that the geometry and size of the corresponding anions together with their coordinating properties are essential in determining the final structures. The magnetic properties of complexes <b>1</b>–<b>4</b> were examined, indicating strong antiferromagnetic interactions between the nickel­(II)/cobalt­(II) ions in the temperature range of 50–300 K