Precise Clock Research Articles

GPS satellite inter-frequency clock bias estimation using triple-frequency raw observations

This study proposes a unified uncombined model to estimate GPS satellite inter-frequency clock bias (IFCB) in both triple-frequency code and carrier-phase observations. In the proposed model, the formulae of both phase-based and code-based IFCBs are rigorously derived. Specifically, satellite phase-based IFCB refers to its time-variant part and it is modeled as a periodic function related to the sun–spacecraft–earth angle. A zero-mean condition of all available GPS satellites that support triple-frequency data is introduced to render satellite code-based IFCB estimable. Three months of data from 40 globally distributed stations of the International GNSS Service Multi-GNSS Experiment are used to test our method. The results show that the four-order periodic function is suitable for eliminating the 12-h, 6-h, 4-h, and 3-h periods that exist in the a posteriori phase residuals when no periodic function is used. For comparison, the geometry-free and ionosphere-free (GFIF) phase combination and differential code bias (DCB) products released by DLR (German Aerospace Center) and IGG (Institute of Geodesy and Geophysics, China) are also used to calculate the satellite phase-based and code-based IFCBs, respectively. The results show that (1) the average root mean square (RMS) of the phase-based IFCB difference between the proposed method and the GFIF phase combination is 4.3 mm; (2) the average RMS in the eclipse period increased by 50% compared with the average RMS in the eclipse-free period; (3) the mean monthly STD for code-based IFCB from the proposed method is 0.09 ns; and (4) the average RMS values of code-based IFCB differences between the proposed method and the DCB products released by DLR and IGG are 0.32 and 0.38 ns. This proposed model also provides a general approach for multi-frequency GNSS applications such as precise orbit and clock determination.

Which high-precision clock to choose for high performance and competitive OBN?

Two different high-precision clock technologies are available for OBN manufacturers: OCXO clocks and CSAC clocks. The CSAC clock is being pushed by the oil majors, although it is extremely expensive. Technological progress is being made by the OCXO manufacturers. Their attractive price and their better market availability make them an attractive compromise for the OBN manufacturers who wish to segment their OBN product offerings besides their CSAC-based OBN. OCXO and CSAC clocks’ key parameters and performances are reviewed below. Their advantages and limitations, both technically, economically and strategically, are studied. This article presents the latest advances in the field of OCXO. An effective benchmark between CSAC and OCXO is presented to demonstrate when it may be more advantageous to choose a CSAC or an OCXO as the reference precision clock for OBN.

Interference in a Prototype of a Two-Dimensional Ion Trap Array Quantum Simulator.

Trapped ions are a promising platform for envisioned quantum simulators, with outstanding results in one-dimensional ion crystals. However, theory requires not only interactions at long range, but also higher dimensionality. We operate a basic triangular array of three individually trapped ions based on scalable microfabrication technology. We demonstrate coherent coupling, tunable in real time and enabling interference in 2D, an essential building block for a reconfigurable quantum simulator. Mitigating motional heating will permit accessing the quantum regime and 2D experimental quantum simulations.

An analysis of inter-system biases in BDS/GPS precise point positioning

The ways of estimating the inter-system bias (ISB) have an important influence on BDS/GPS combined precise point positioning (PPP). Ordinarily, in data processing, the precise ephemeris and clock offset from the Center for Orbit Determination in Europe (CODE), Deutsches GeoForschungsZentrum (GFZ), and Wuhan University (WHU), respectively, are applied to obtain the ISB products ( $${\text{ISB}}_{\text{COD}}$$ , $${\text{ISB}}_{\text{GFZ}}$$ , and $${\text{ISB}}_{\text{WHU}}$$ ). Currently, in the case of BDS/GPS PPP, the ISB is generally considered to be a stable value in a given day and estimated as a constant. To better understand the mechanism underlying the generation of ISB in combined PPP, we deduce and establish the ISB estimation formulas and mathematical models and collect and process data from 19 multi-GNSS experimental stations. The results show that the ranges of $${\text{ISB}}_{\text{COD}}$$ and $${\text{ISB}}_{\text{WHU}}$$ at different times are within 0.3 m, while $${\text{ISB}}_{\text{GFZ}}$$ can change up to 6.5 m. An interesting phenomenon is that the $${\text{ISB}}_{\text{GFZ}}$$ for different stations has a similar variation trend in a day, and in some days, the ISBs of all stations show a linear trend which may mainly be influenced by satellite clock offset. In addition, the temporal stability of ISB is independent of receiver software version number and antenna type, while the receiver type has little influence on the stability of ISB. Therefore, it is reasonable to estimate $${\text{ISB}}_{\text{COD}}$$ and $${\text{ISB}}_{\text{WHU}}$$ as constant in a day and use a random walk to obtain $${\text{ISB}}_{\text{GFZ}}$$ . The results show that the convergence speed and accuracy of BDS/GPS PPP obtained by the random walk method are higher than those using the constant method, no matter whether $${\text{ISB}}_{\text{GFZ}}$$ , $${\text{ISB}}_{\text{COD}}$$ , or $${\text{ISB}}_{\text{WHU}}$$ is used.

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Performance Assessment for Combined GPS and BDS Real-time Precise Point Positioning in the Coastal Region of Bohai Gulf, China

Qu, L.; Huang, H.; Du, M., and Acharya, T.D., 2019. Performance assessment for combined GPS and BDS real-time precise point positioning in the coastal region of Bohai Gulf, China. In: Lee, J.L.; Yoon, J.-S.; Cho, W.C.; Muin, M., and Lee, J. (eds.), The 3rd International Water Safety Symposium. Journal of Coastal Research, Special Issue No. 91, pp. 271-275. Coconut Creek (Florida), ISSN 0749-0208.In this study, we focus on the performance assessment of combined Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS) real-time Precise Point Positioning (PPP) in the coastal region of Bohai Gulf, China. Firstly, 120 Global Navigation Satellite System (GNSS) stations from Multi-GNSS Experiment (MGEX) network of the International GNSS Service (IGS) were processed to generate ultra-rapid precise orbit of both GPS and BDS satellites, updated with the interval of three hours. Secondly, real-time precise satellite clock errors were estimated to compensate the orbit error with 24 regional stations from Crustal Monitor of Network of China (CMONOC) and MGEX networks. Finally, with those products, the performances of GPS-only, BDS-only and combined GPS and BDS real-time PPP were compared and evaluated. The experimental result illustrated that the ultra-rapid orbit accuracy of BDS-2 satellites was still worse than that of GPS satellites which was sub-decimeter level. Among three types of orbital satellites of BDS-2, the orbital accuracy of medium Earth orbit (MEO) and inclined geosynchronous orbit (IGSO) satellites were at decimeter level while for geostationary Earth orbit (GEO) satellites was at meter-level. The MEO satellites had the best accuracy while the GEO satellites performed the worst. In addition, the 3D accuracy of BDS-only real-time PPP was 10 cm better. Although the accuracy of BDS-2 real-time PPP was still worse than that of GPS and more time was taken for convergence. By adding BDS on top of GPS, the accuracy in the east, north and up components improved 40.0%, 33.3% and 18.5%, respectively, and the convergence time reduced 36.3%, 15.4% and 58.3%, respectively compared to the GPS only.

Performance evaluation of real-time global ionospheric maps provided by different IGS analysis centers

With the development of real-time precise clock and orbit products, high-precision real-time ionospheric products have become one of the most critical resources for real-time single-frequency precise point positioning. Fortunately, there are several international GNSS service (IGS) analysis centers, e.g., UPC, WHU, and CAS, that are providing real-time global ionospheric maps (RT-GIMs). We evaluate these maps in detail over 2 years for different aspects. First, the RT-GIMs and 1-day predicted ionospheric products (C1PG GIM) differenced with the IGS final GIMs (IGSG GIM) are performed. Second, ionospheric vertical total electron content from Jason-2/3 data is set as a reference to evaluate the quality of RT-GIMs over oceanic regions. Third, 22 stations, which are not used in the generation of RT-GIMs, C1PG GIM, and IGSG GIM, are selected and the difference of slant total electron content (dSTEC) method is used to assess the accuracy and consistency of RT-GIMs over continental regions. Finally, the performance of RT-GIMs in the position domain is demonstrated based on SF-PPP solutions. The results show that the accuracy of the RT-GIMs is slightly worse than that of C1PG GIM and IGSG GIM. All RT-GIMs and the C1PG GIM have a smaller mean difference compared to the IGSG GIM by (−0.97, − 0.90, − 0.77, − 0.80) TECU for (UPC RT-GIM, CAS RT-GIM, WHU RT-GIM, C1PG GIM). Over oceanic regions, the RT-GIMs perform nearly the same as the C1PG GIM, but a slightly worse than IGSG GIM. The STDs are (3.96, 3.05, 3.25, 3.12, 2.54) TECU relative to Jason-2 and (4.94, 3.24, 3.38, 3.24, 2.65) TECU relative to Jason-3 for (UPC RT-GIM, CAS RT-GIM, WHU RT-GIM, C1PG GIM, IGSG GIM), respectively. Comparing with dSTEC values observed from the selected ground stations over continental regions, the RMS is (4.02, 2.16, 2.29, 1.86, 1.49) TECU for (UPC RT-GIM, CAS RT-GIM, WHU RT-GIM, C1PG GIM, IGSG GIM). In the position domain, the positioning accuracy of SF-PPP solution corrected by the RT-GIMs and C1PG GIM can reach decimeter level in the horizontal direction and meter level in the vertical direction, which is worse than obtained by IGSG GIM. Meanwhile, the positioning accuracy of SF-PPP corrected by RT-GIMs is almost the same as that obtained using C1PG GIM. For RT-GIMs, the accuracy of the CAS RT-GIM is slightly better than that of the other two RT-GIMs.

An Application-Level Method of Arbitrary Synchronization Failure Detection in TTEthernet Networks

Precise distributed clock synchronization is important for Time-Triggered Ethernet (TTEthernet) in which fail-arbitrary synchronization failure cannot be treated by existed protocols unless every synchronization node is equipped with a dedicated clock monitoring. A novel method was presented to detect arbitrary synchronization failure by some application-level routines which make distributed decisions mainly by monitoring the protocol control frames (PCFs). An arbitrary failure node can be exactly detected and located by the routine resided on each of the Compression Masters based on the concerned accusation messages sent from Synchronization Masters or Synchronization Clients. The proposed method can make up the weak points on the detection of the arbitrary failure node of the existed fault-tolerant synchronization mechanism and enhance the synchronization node to resist the arbitrary failure for TTEthernet. By our SAL-based model checking, this method had been formally verified to have a fail-arbitrary detection capacity even in a standard integration configuration. Simulations imply that the quality of the whole clock synchronization is effectively improved after the failure node has been isolated.

Precise Orbit Determination for GNSS Maneuvering Satellite with the Constraint of a Predicted Clock

Precise orbit products are essential and a prerequisite for global navigation satellite system (GNSS) applications, which, however, are unavailable or unusable when satellites are undertaking maneuvers. We propose a clock-constrained reverse precise point positioning (RPPP) method to generate the rather precise orbits for GNSS maneuvering satellites. In this method, the precise clock estimates generated by the dynamic precise orbit determination (POD) processing before maneuvering are modeled and predicted to the maneuvering periods and they constrain the RPPP POD during maneuvering. The prediction model is developed according to different clock types, of which the 2-h prediction error is 0.31 ns and 1.07 ns for global positioning system (GPS) Rubidium (Rb) and Cesium (Cs) clocks, and 0.45 ns and 0.60 ns for the Beidou navigation satellite system (BDS) geostationary orbit (GEO) and inclined geosynchronous orbit (IGSO)/Median Earth orbit (MEO) satellite clocks, respectively. The performance of this proposed method is first evaluated using the normal observations without maneuvers. Experiment results show that, without clock-constraint, the average root mean square (RMS) of RPPP orbit solutions in the radial, cross-track and along-track directions is 69.3 cm, 5.4 cm and 5.7 cm for GPS satellites and 153.9 cm, 12.8 cm and 10.0 cm for BDS satellites. When the constraint of predicted satellite clocks is introduced, the average RMS is dramatically reduced in the radial direction by a factor of 7–11, with the value of 9.7 cm and 13.4 cm for GPS and BDS satellites. At last, the proposed method is further tested on the actual GPS and BDS maneuver events. The clock-constrained RPPP POD solution is compared to the forward and backward integration orbits of the dynamic POD solution. The resulting orbit differences are less than 20 cm in all three directions for GPS satellite, and less than 30 cm in the radial and cross-track directions and up to 100 cm in the along-track direction for BDS satellites. From the orbit differences, the maneuver start and end time is detected, which reveals that the maneuver duration of GPS satellites is less than 2 min, and the maneuver events last from 22.5 min to 107 min for different BDS satellites.

Assessment of L5 frequency on real-time GPS orbit and clock estimation

Real-time precise Global Navigation Satellite System (GNSS) satellite orbit and clock products are the prerequisite of real-time GNSS-based applications. With the modernization of Global Positioning System (GPS) constellation and construction of other GNSS constellations, the number of GNSS satellites transmitting multi-frequency signals is increasing rapidly. While the benefit of multi-frequency to Precise Point Positioning (PPP) and Precise Clock Estimation (PCE) has been evaluated by many researchers, the impact of multi-frequency on orbit and clock estimation is still limited, especially in real-time mode. Different from the dual-frequency model, the Inter-Frequency Clock Bias (IFCB) must be treated carefully in the triple-frequency model. In this contribution, the triple-frequency model for real-time GPS satellite orbit and clock estimation is derived and the influence of L5 frequency observations on real-time GPS satellite orbit and clock are analyzed. With observation data from globally distributed stations spanning January 1 to 14 of 2018, real-time GPS orbit and clock are estimated with both dual-frequency and triple-frequency observations. Numerical experiments indicate that, compared to the International GNSS Service (IGS) final orbit, the L5 frequency observations improve the consistency of the normal component with about 0.2 cm, however lead to a decrease of consistency in the radial component with about 0.6 cm; the influence on the tangential direction varies with different number of stations. The potential reason for this phenomenon may partly be attributed to the absence of accurate antenna information for L5 frequency. However, due to the tight constraint of dynamic force model on orbit, the overall differences for each component is less than 1.0 cm, which means the contribution of the third frequency observation on the orbit is limited.

Initial assessment of BeiDou-3 global navigation satellite system: signal quality, RTK and PPP

China has recently established the primary constellation of BeiDou-3 global navigation satellite system (BDS-3). It is necessary to conduct a comprehensive assessment about its performance. The signal quality, ambiguity resolution efficiency and real-time kinematic (RTK) performance are assessed based on the datasets collected with two Trimble Alloy receivers that can track all open signals of BDS-3. Then, the precise point positioning (PPP) using combined BDS-2 and BDS-3 measurements is compared with the PPP using BDS-2 only, where the precise satellite orbits and clocks are determined using 116 globally distributed monitor stations. The results show that the signal quality of BDS-3 is generally better than that of BDS-2. Also, the ambiguity resolution efficiency of RTK is improved by incorporating the BDS-3 measurements with success rate improving from 88.5 to 91.4%. Regarding PPP, the convergence time is shortened from about an hour to less than half an hour, while the positioning accuracy is also improved significantly.

Roles of Direct Photoreception and the Internal Circadian Oscillator in the Regulation of Melatonin Secretion in the Pineal Organ of the Domestic Turkey: A Novel In Vitro Clock and Calendar Model.

The regulation of melatonin secretion in the avian pineal organ is highly complex and shows prominent interspecies differences. The aim of this study was to determine the roles of direct photoreception and the internal oscillator in the regulation of melatonin secretion in the pineal organ of the domestic turkey. The pineal organs were collected from 12-, 13- and 14-week-old female turkeys reared under a 12 L:12 D cycle with the photophase from 07.00 to 19.00, and were incubated in superfusion culture for 3–6 days. The cultures were subjected to different light conditions including 12 L:12 D cycles with photophases between 07.00 and 19.00, 13.00 and 01.00 or 01.00 and 13.00, a reversed cycle 12 D:12 L, cycles with long (16 L:8 D) and short (8 L:16 D) photophases, and continuous darkness or illumination. The pineal organs were also exposed to light pulses of variable duration during incubation in darkness or to periods of darkness during the photophase. The secretion of melatonin was determined by direct radioimmunoassay. The turkey pineal organs secreted melatonin in a well-entrained diurnal rhythm with a very high amplitude. Direct photoreception as an independently acting mechanism was able to ensure quick and precise adaptation of the melatonin secretion rhythm to changes in light-dark conditions. The pineal organs secreted melatonin in circadian rhythms during incubation in continuous darkness or illumination. The endogenous oscillator of turkey pinealocytes was able to acquire and store information about the light-dark cycle and then to generate the circadian rhythm of melatonin secretion in continuous darkness according to the stored data. The obtained data suggest that the turkey pineal gland is highly autonomous in the generation and regulation of the melatonin secretion rhythm. They also demonstrate that the turkey pineal organ in superfusion culture is a valuable model for chronobiological studies, providing a highly precise clock and calendar. This system has several features which make it an attractive alternative to other avian pineal glands for circadian studies.

Development of a Highly Flexible and High-Resolution Deep-Towed Streamer

We have developed new a deep-towed seismic streamer for sub-bottom profiling. To obtain a high-resolution seismic signal, this streamer can be operated at depths of up to 2000 m, and state-of-the-art technology is adopted with electronics circuits, that can withstand high pressures of up to 22 MPa. The streamer houses an ultra-low noise pre-amplifier, micro-processor, AD convertor, high precision clock, gain controller, and other circuitry in an oil-filled vessel. The high S/N ratio gives us high-resolution seismic images. The streamer comprises several catenated single modules and the recorded acoustic data are transmitted to the control computer with the Ethernet protocol. This makes the length of the streamer cable, and the number of hydrophones, flexible. For instance, we can use both single-channel and multi-channel streamers in the same system. Up to 24-channels can be catenated.

Demonstration of 4.8 × 10−17 stability at 1 s for two independent optical clocks

Improvements in atom-light coherence are foundational to progress in quantum information science, quantum optics, and precision metrology. Optical atomic clocks require local oscillators with exceptional optical coherence due to the challenge of performing spectroscopy on their ultra-narrow linewidth clock transitions. Advances in laser stabilization have thus enabled rapid progress in clock precision. A new class of ultrastable lasers based on cryogenic silicon reference cavities has recently demonstrated the longest optical coherence times to date. In this work we utilize such a local oscillator, along with a state-of-the-art frequency comb for coherence transfer, with two Sr optical lattice clocks to achieve an unprecedented level of clock stability. Through an anti-synchronous comparison, the fractional instability of both clocks is assessed to be $4.8\times 10^{-17}/\sqrt{\tau}$ for an averaging time $\tau$ in seconds. Synchronous interrogation reveals a quantum projection noise dominated instability of $3.5(2)\times10^{-17}/\sqrt{\tau}$, resulting in a precision of $5.8(3)\times 10^{-19}$ after a single hour of averaging. The ability to measure sub-$10^{-18}$ level frequency shifts in such short timescales will impact a wide range of applications for clocks in quantum sensing and fundamental physics. For example, this precision allows one to resolve the gravitational red shift from a 1 cm elevation change in only 20 minutes.

A comparison of interferometric and single-dish methods to measure distances to pulsar scattering screens

Abstract Investigations of small-scale structure in the interstellar medium through pulsar scintillation and the use of scattering screens as interferometers to resolve pulsar emission regions rely on reconstructions of the spatial distributions of scattered pulsar flux and the distances to scattering screens. In many cases, a single, highly anisotropic scattering screen is responsible for pulsar scintillation. This leads to a sparsity of information in the secondary spectrum which can be leveraged to measure the scattering geometry and map the distribution of scattered images of the pulsar using Very Long Baseline Interferometry. It is also possible to make these same measurements using only the autocorrelations from simultaneous observations at multiple stations. We compare the results from these two methods applied to PSR B0834+06, and find that the two main measurables, the effective distance and velocity, obtained from these two analyses agree to within ∼10 per cent. The relative ease of using autocorrelations from simultaneous single-dish measurements, where the data rates are much lower, only millisecond clock precision is required and the results are less sensitive to the calibration of the data, means that this method opens up a more observationally accessible route for mapping pulsar scattering screens. Since this method does not require the recording and storage of baseband data, it can be applied to ultrawide-band observations, which typically have unmanageable baseband data rates but are vital for testing theoretical models of pulsar scintillation.

A BDS-2/BDS-3 Integrated Method for Ultra-Rapid Orbit Determination with the Aid of Precise Satellite Clock Offsets

The accuracy of ultra-rapid orbits is a key parameter for the performance of GNSS (Global Navigation Satellite System) real-time or near real-time precise positioning applications. The quality of the current BeiDou demonstration system (BDS) ultra-rapid orbits is lower than that of GPS, especially for the new generational BDS-3 satellites due to the fact that the availability of the number of ground tracking stations is limited, the geographic distribution of these stations is poor, and the data processing strategies adopted are not optimal. In this study, improved data processing strategies for the generation of ultra-rapid orbits of BDS-2/BDS-3 satellites are investigated. This includes both observed and predicted parts of the orbit. First, the predicted clock offsets are taken as constraints in the estimation process to reduce the number of the unknown parameters and improve the accuracy of the parameter estimates of the orbit. To obtain more accurate predicted clock offsets for the BDS’ orbit determination, a denoising method (also called the Tikhonov regularization algorithm), inter-satellite correlation, and the partial least squares method are all incorporated into the clock offsets prediction model. Then, the Akaike information criterion (AIC) is used to determine the arc length in the estimation models by taking the optimal arc length in the estimation of the initial orbit states into consideration. Finally, a number of experiments were conducted to evaluate the performance of the ultra-rapid orbits resulting from the proposed methods. Results showed that: (1) Compared with traditional models, the accuracy improvement of the predicted clock offsets from the proposed methods were 40.5% and 26.1% for BDS-2 and BDS-3, respectively; (2) the observed part of the orbits can be improved 9.2% and 5.0% for BDS-2 and BDS-3, respectively, by using the predicted clock offsets as constraints; (3) the accuracy of the predicted part of the orbits showed a high correlation with the AIC value, and the accuracy of the predicted orbits could be improved up to 82.2%. These results suggest that the approaches proposed in this study can significantly enhance the accuracy of the ultra-rapid orbits of BDS-2/BDS-3 satellites.

Precise Point Positioning (PPP): Method and its Geodetic Usage

Combining the precise satellite positions and clocks correction with dual-frequency GNSS receiver, PPP is able to provide position solutions at centimeter- decimeter level. PPP can be regarded as a global positioning approach because its position solutions referred to a global reference frame. As a result, PPP provides much greater positioning consistency than the differential approach in which position solutions are relative to the local base station or stations. Due to this, today PPP has been the demand of large number of market.

Implementation of quasi-real-time estimation of BDS clock

To obtain high reliability and accuracy of the zenith tropospheric delay more quickly, this study describes a parameter estimation method that uses an epoch-differenced and undifferenced function model to estimate the clock of the BeiDou navigation satellite system (BDS)/global positioning system (GPS) satellites using a quasi-real-time process. Forty-five MGEX tracking stations distributed globally were selected for study. The initial orbit information of the clock estimation used the ultra-rapid orbit products released by the German Research Center for Geosciences and post-products as reference values. The experimental results showed that the accuracy of the GPS satellite clock was better than 0.06 ns. The precision of clock for three kinds of BDS satellites was between 0.04 and 0.08 ns, slightly worse than the GPS. The estimated BDS clock appears to meet the demands for computing the quasi-real-time zenith tropospheric delay.

Gravity Field Model Determination Based on GOCE Satellite Point-Wise Accelerations Estimated from Onboard Carrier Phase Observations

GPS-based, satellite-to-satellite tracking observations have been extensively used to elaborate the long-scale features of the Earth’s gravity field from dedicated satellite gravity missions. We proposed compiling a satellite gravity field model from Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite accelerations directly estimated from the onboard GPS data using the point-wise acceleration approach, known as the carrier phase differentiation method. First, we composed the phase accelerations from the onboard carrier phase observations based on the sixth-order seven-point differentiator, which can eliminate the carrier phase ambiguity for Low Earth Orbiter (LEO). Next, the three-dimensional (3D) accelerations of the GOCE satellite were estimated from the derived phase accelerations as well as GPS satellite ephemeris and precise clock products. Finally, a global gravity field model up to the degree and order (d/o) 130 was compiled from the 71 days and nearly 2.5 years of 3D satellite accelerations. We also recovered three gravity field models up to d/o 130 from the accelerations derived by differentiating the kinematic orbits of European Space Agency (ESA), Graz, and School of Geodesy and Geomatics (SGG), which was the orbit differentiation method. We analyzed the accuracies of the derived accelerations and the recovered gravity field models based on the carrier phase differentiation method and orbit differentiation method in time, frequency, and spatial domain. The results showed that the carrier phase derived acceleration observations had better accuracy than those derived from kinematic orbits. The accuracy of the recovered gravity field model based on the carrier phase differentiation method using 2.5 years observations was higher than that of the orbit differentiation solutions for degrees greater than 70, and worse than Graz-orbit solution for degrees less than 70. The cumulative geoid height errors of carrier phase, ESA-orbit, and Graz-orbit solutions up to degree and order 130 were 17.70cm, 21.43 cm, and 22.11 cm, respectively.

A Method to Determine BeiDou GEO/IGSO Orbital Maneuver Time Periods.

Because there are different types of BeiDou constellations with participating geostationary orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites, the maneuvering frequency of BeiDou satellites is higher than that of other navigation systems. The satellite orbital maneuvers lead to orbital parameter failure for several hours from broadcast ephemeris. Due to the missing initial orbit, the maneuvering thrust, and the period of orbital maneuvering, the orbit products of maneuvering satellites cannot be provided by the International Global Navigation Satellite System (GNSS) Service (IGS) and International GNSS Monitoring and Assessment System (iGMAS). In addition, the period of unhealthy status and the orbital parameters of maneuvering satellites in broadcast ephemeris are unreliable, making the detection of orbital maneuver periods more difficult. Here, we develop a method to detect orbital maneuver periods involving two key steps. The first step is orbit prediction of maneuvering satellites based on precise orbit products. The second step is time period detection of orbit maneuvering. The start time detection factor is calculated by backward prediction orbit and pseudo-range observations, and the end time detection factor is calculated by forward prediction orbit and pseudo-range observations. Data of stations from the Multi-GNSS Experiment (MGEX) and iGMAS were analyzed. The results show that the period of orbit maneuvering could be detected accurately for BeiDou GEO and IGSO satellites. In addition, the orbital maneuver period of other GNSS medium Earth orbit (MEO) satellites could also be determined by this method. The results of period detection for orbit maneuvering provide important reference information for precision orbit and clock offset determination during satellite maneuvers.