BeiDou Navigation Satellite System Satellites Research Articles

A Study of Solar Radiation Pressure Model in BDS-3 Precise Orbit Determination

For the BDS (BeiDou Navigation Satellite System) satellites, the solar radiation pressure is the major non-gravitational perturbation the satellites suffer. Due to the influence of multiple factors, accurate modeling the solar radiation pressure acting on these satellites is difficult to accomplish. The solar radiation pressure perturbation is an essential source of error in the precise orbit determination (POD) and orbit prediction processes of the BDS satellites. As the ECOMC (Empirical CODE Orbit Model 1 and 2 Combined) model adopts the advantageous features of the ECOM1 (Empirical CODE Orbit Model 1) model and the ECOM2 (Empirical CODE Orbit Model 2) model, a greater number of parameters have been introduced into the model, leading to strong correlation between the ECOMC model parameters. In response to the deficiency of the ECOMC model, the authors collected the BDS-3 satellite precise ephemeris data that were provided by Wuhan University (WHU) from January 2019 to April 2022. And by these ephemeris data, the ECOMC model’s 13 parameters were obtained through the dynamic orbit fitting method. By conducting these time sequence diagrams analysis of the ECOMC model parameters, this thesis affords the selection strategies of the solar radiation pressure parameters of the ECOMC model for BDS-3 inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellite. And the rationality of the selection strategies of the solar radiation pressure parameters for the ECOMC model was verified by orbit fitting and orbit prediction experiments. The results show that using the improved ECOMC model gains the best orbit fitting effects for BDS-3 IGSO and MEO satellite, and can also enhance the accuracy of medium and long-term orbit prediction of BDS-3 IGSO and MEO satellite.

On-orbit BDS signals and transmit antenna gain analysis for a geostationary satellite

A Beidou navigation satellite system (BDS) receiver with high sensitivity is embarked in a geostationary orbit (GEO) spacecraft to demonstrate characteristics of BDS signals tracked. This receiver can be compatible with the regional (BDS-2) and global (BDS-3) systems, which have three orbit types: medium Earth orbit (MEO), inclined geostationary orbit (IGSO), and GEO. The on-orbit BDS signal characteristics, including observations quantity, availability, position dilution of precision (PDOP), and carrier-to-noise ratio (C/N0), are presented according to in-flight data. The observations and distribution of C/N0 with respect to nadir angles were analyzed. The average number of the BDS satellites tracked is 4.4, and the average PDOP is 12.0. PDOP improves when the BDS GEO and IGSO observations are involved. The maximum value of C/N0 of the BDS-3 MEO satellites is approximately 49 dB-Hz, which is roughly 2 dB higher than that of the BDS-2 MEO satellites. Most of the C/N0 of the BDS-3 MEO satellite at nadir angles beyond 26° is in the range of 27–34 dB-Hz. We reconstruct the transmit antenna gain for all observed BDS satellites using C/N0 measurements. Moreover, we investigate the main and side lobe characteristics of the BDS satellites in terms of different orbit types and satellite manufacturers. The side lobe signals of the BDS-3 MEO generally have 20–30 dB lower gain than the peak main lobe gain. The side lobe signal performance of the BDS-2 MEO is evidently better than that of the BDS-3 MEO. We give side lobe characteristics analysis of the BDS-3 MEO satellites from two different manufacturers based on the transmit antenna gain reconstructed.

Three Dual-Frequency Precise Point Positioning Models for the Ionospheric Modeling and Satellite Pseudorange Observable-Specific Signal Bias Estimation

Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) enables the estimation the ionospheric vertical total electron content (VTEC) as well as the by-product of the satellite Pseudorange observable-specific signal bias (OSB). The single-frequency PPP models, with the ionosphere-float and ionosphere-free approaches in ionospheric studies, have recently been discussed by the authors. However, the multi-frequency observations can improve the performances of the ionospheric research compared with the single-frequency approaches. This paper presents three dual-frequency PPP approaches using the BeiDou Navigation Satellite System (BDS) B1I/B3I observations to investigate ionospheric activities. Datasets collected from the globally distributed stations are used to evaluate the performance of the ionospheric modeling with the ionospheric single- and multi-layer mapping functions (MFs), respectively. The characteristics of the estimated ionospheric VTEC and BDS satellite pseudorange OSB are both analyzed. The results indicated that the three dual-frequency PPP models could all be applied to the ionospheric studies, among which the dual-frequency ionosphere-float PPP model exhibits the best performance. The three dual-frequency PPP models all possess the capacity for ionospheric applications in the GNSS community.

Identification of BDS Satellite Clock Periodic Signals Based on Lomb-Scargle Power Spectrum and Continuous Wavelet Transform

Onboard satellite clocks are the basis of Global Navigation Satellite Systems (GNSS) operation, and their revolution periods are at the level of 2 per day (about 12 h) in the case of the Medium Earth Orbit (MEO) satellites. In this work, the authors analysed the entire BeiDou Navigation Satellite System (BDS) space segment (BDS-2 and BDS-3) in terms of the occurrence of periodic, repetitive signals in the clock products, and checked if they coincide with the orbital periods or their multiples. The Lomb-Scargle (L-S) power spectrum was used as a tool to determine the periods present in the BDS clock products, allowing for analyses based on incomplete input data; in this case, the incomplete data were the phase data with jumps and outliers removed. In addition, continuous wavelet transform (CWT) was used to produce a time−frequency representation showing the more complex behaviour of the satellite clock products. As shown in the case of geostationary and geosynchronous inclined orbit satellites, the main period was 23.935 h, while for the Medium Earth Orbit it was 12.887 h, with the BDS satellite orbital period being 12 h 53 m (12.883 h). Some effects connected with reference clock swapping are also visible in the power spectrum. The conducted analyses showed that the BDS-2 satellite clocks have much higher noise than the BDS-3 satellite clocks, meaning that the number of designated periods is greater, but their reliability is significantly lower. BDS-3 satellites have only been in operation for a very short time, thus this is the first analysis to include this type of data. Moreover, such a wide and complex analysis has not been carried out to date.

Recover the abnormal positioning, velocity and timing services caused by BDS satellite orbital maneuvers

The BeiDou Navigation Satellite System (BDS) provides global Positioning, Velocity, And Timing (PVT) services that are widely used in various areas. The BDS satellites frequently need the orbit maneuvers due to various perturbations to keep satellites in their designed positions. During these maneuvers, PVT services may be abnormal if the data from a maneuvering satellite is used. In this paper we developed an approach to recover the abnormal PVT services. By using BDS observations from multiple tracking stations, the orbital errors of a maneuvering satellite can be in real time obtained and corrected, thereby avoiding any influence on the performance of PVT services. The tests show that the average precision of position, velocity and timing services are improved by 0.8 m, 0.1 mm/s and 0.16 ns, respectively, using the developed orbital maneuver recovery approach. In addition, the approach can also be used for the orbital maneuver detection and monitoring.

Comparison and assessment of long-term performance of BDS-2/BDS-3 satellite atomic clocks

Recently, the performance of the new-generation BeiDou Navigation Satellite System (BDS) satellite clocks has attracted considerable attention. There are two types of BDS clocks developed in China—namely, the new rubidium (Rb-II) and passive hydrogen maser (PHM)—and these can affect positioning, navigation and timing (PNT) services. In this paper, to comprehensively evaluate and analyze the performance of BDS satellite atomic clocks, the physical characteristics are exhibited, including phase, frequency, frequency drift and noise. The physical characteristics are applied to detect the switching of satellite clocks. The frequency stability of atomic clocks is assessed by overlapping Allan deviation (ADEV) and overlapping Hadamard deviation (HDEV). The periodic characteristics of satellite clock bias data are studied through spectrum analysis. Based on 550 day precision satellite clock bias data provided by Wuhan University, China, experiments were performed, focusing on the performance of the Rb-II and PHM clocks installed on BDS-3. Some valuable conclusions are obtained: (a) the BDS-3 satellite clocks perform better than BDS-2. The root mean square value of the frequency drift of BDS-3 satellite clocks is enhanced by 41% compared to BDS-2. The noise of BDS-3 is 0.216 ns, which is 55% better than BDS-2. (b) The frequency stability of BDS-2 satellite clocks is worse than that of BDS-3. The mean daily stability of BDS-2 and BDS-3 satellite clocks by ADEV is 5.29 × 10−14 and 5.36 × 10−14, respectively, while that with HDEV is 2.35 × 10−14 and 0.70 × 10−14. For PHM clocks, the stability at 10 000 s with ADEV and HDEV is 2.29 × 10−14 and 2.25 × 10−14, respectively, while the daily stability is 0.77 × 10 −14 and 0.67 × 10−14, respectively. (c) BDS geostationary orbit (GEO) and inclined GEO satellite atomic clocks have multiple significant periodic terms while the medium earth orbit satellite clocks only own one or two, which are related to the corresponding satellite orbital periods.

Analysis of BDS/GPS Signals’ Characteristics and Navigation Accuracy for a Geostationary Satellite

The utilization of Global Navigation Satellite System (GNSS) is becoming an attractive navigation approach for geostationary orbit (GEO) satellites. A high-sensitivity receiver compatible with Global Position System (GPS) developed by the United States and BeiDou Navigation Satellite System (BDS) developed by China has been used in a GEO satellite named TJS-5 to demonstrate feasibility of real-time navigation. According to inflight data, the GNSS signal characteristics including availability, position dilution of precision (PDOP), carrier-to-noise ratio (C/N0), observations quantity and accuracy are analyzed. The mean number of GPS and GPS + BDS satellites tracked are 7.4 and 11.7 and the mean PDOP of GPS and GPS + BDS are 10.24 and 3.91, respectively. The use of BDS significantly increases the number of available navigation satellites and improves the PDOP. The number of observations with respect to C/N0 is illustrated in detail. The standard deviation of the pseudorange noises are less than 4 m, and the corresponding carrier phase noises are mostly less than 8 mm. We present the navigation performance using only GPS observations and GPS + BDS observations combination at different weights through comparisons with the precision reference orbits. When GPS combined with BDS observations, the root mean square (RMS) of the single-epoch least square position accuracy can improve from 32.1 m to 16.5 m and the corresponding velocity accuracy can improve from 0.238 m/s to 0.165 m/s. The RMS of real-time orbit determination position accuracy is 5.55 m and the corresponding velocity accuracy is 0.697 mm/s when using GPS and BDS combinations. Especially, the position accuracy in x-axis direction reduced from 7.24 m to 4.09 m when combined GPS with BDS observations.

The improvement of BDS Observation Geometry with LEO constellations in Orbit Determination

The ability of low earth orbit (LEO) satellites with space-borne global navigation satellite system (GNSS) to improve the accuracy of GNSS satellite orbit determinations has been demonstrated. In this paper, the ability of LEO satellites to improve the observation geometry in the process of the determination of BeiDou Navigation Satellite System (BDS) satellite orbits is the focus. First, the visible BDS satellite model with ground stations and LEO satellites is derived, and the definition of the position dilution of precision (PDOP) is proposed for assessing the observation geometries of BDS satellite orbit determination. Then, the observation geometry of BDS geosynchronous earth orbit (GEO), inclined geosynchronous satellite orbit (IGSO) and medium earth orbit (MEO) satellites are individually analysed by regional ground stations. By designing LEO satellites with different inclinations, altitudes and right ascensions of ascending nodes (RAANs), the PDOP improvements achieved through combinations with different orbital LEO satellites are calculated. Finally, the PDOP improvements caused by incorporating different numbers of LEO constellations are compared. The results show that LEO satellites can improve the observation geometries of BDS satellites, especially when the monitoring of observation configurations by only ground stations is very poor. The PDOP improvements of BDS GEO satellites caused by LEO satellites are more significant than those of IGSO or MEO satellites; i.e., the improvement percentage of C04 is better than 60%. Generally, LEO satellites with high altitudes are more suitable for PDOP improvements to BDS satellites than are LEO satellites with low altitudes; moreover, LEO satellites with high inclinations are more suitable for PDOP improvements to BDS GEO satellites than LEO satellites with low inclinations are. The influence of the RAAN on the PDOP improvements of IGSO and MEO satellites is relatively larger than its influence on the PDOP improvement of GEO satellites. The PDOP improvement percentage and stability of BDS satellites, especially GEO satellites, increase with the number of incorporated LEO satellites. When incorporating the LEO constellation 16/4/1:1000 km, 70°, the maximum improvements of the GEO and IGSO satellites are above 84% and 77%. The improvements of the GEO, IGSO and MEO satellites are above 81%, 42% and 58% respectively.

Precision and Characteristics Analysis of Precise Satellite Clock Bias Data of BDS

High-precision satellite clock bias (SCB) data is a critical product for satellite navigation systems to realize accurate navigation, positioning and timing. Unlike other satellite navigation systems, the precise SCB data for the BeiDou Navigation Satellite System (BDS) are mainly determined by two methods, the Two-Way Time Transfer (TWTT) method and the Orbit Determination and Time Synchronization (ODTS) method. Awareness of the data variations obtained from different methods can be used to improve clock modeling performance, and be beneficial to higher-rate GNSS positioning and for predictions in real-time applications. We describe a comprehensive method to analyze the systematic and random characteristics of BDS SCB data obtained from TWTT and ODTS and discuss possible causes of observed variations. Some new conclusions are drawn: the data continuity of TWTT is highly related to satellite orbit types; affected by orbit error and other factors, the fitting residuals (RMS) of ODTS is 0.2 ns worse than that of TWTT on average, while the fitting precision of TWTT is 0.49 ns. There are up to 8ns periodic fluctuations in the mutual agreement between TWTT and ODTS data. The stability result shows a remarkable effect of flicker phase modulation (FLPM) noise can be seen in the period of 300-1000 s in TWTT data. All the BDS satellites display more complex, nonpower law behavior due to the effects of periodic clock variations.

Decoding PPP Corrections From BDS B2b Signals Using a Software-Defined Receiver: An Initial Performance Evaluation

With the rapid development of China's BeiDou Navigation Satellite System (BDS), the application of real-time precise point positioning (RTPPP) based on BDS has become an active research area in the field of Global Navigation Satellite Systems (GNSS). BDS has provided the service of broadcasting RTPPP information. It indicates that BDS has become the second satellite system that provides RTPPP services, following Galileo among the GNSS, but work based on this direction has yet to be explored. Therefore, this paper evaluates the performance of precise point positioning (PPP) service using a software-defined receiver (SDR). An experiment was carried out to verify the feasibility of the SDR. The PPP-B2b signal was processed to obtain PPP service information, including orbit corrections, clock corrections, and differential code bias corrections. The time-varying attributes of these corrections of BDS and GPS are evaluated, and the integrity and stability of the PPP service were analyzed. The results show the PPP-B2b signal can stably provide PPP services for satellites in the Asia-Pacific region, including centimeter to decimeter-level orbit corrections and meter-level clock corrections for BDS satellites. At the same time, PPP services provide decimeter to meter-level orbit correction and meter-level clock correction for GPS satellites. Finally, detection tip for bitstream availability in SDR is proposed. Some content which is not defined in the official document, such as the PPP-B2b frame arrangement, various correction update cycles and the progress of PPP service are discussed.

An Improved Multi-Satellite Method for Evaluating Real-Time BDS Satellite Clock Offset Products

Two methods are widely used for evaluating the precision of satellite clock products, namely the single-satellite method (SSM) and the multi-satellite method (MSM). In the satellite clock product evaluation, an important issue is how to eliminate the timescale difference. The SSM selects a reference satellite to eliminate the timescale difference by between-satellite differencing, but its evaluation results are susceptible to the gross errors in the referenced satellite clock offsets. In the MSM, the timescale difference is first estimated and then removed. Unlike the GPS, the BeiDou Navigation Satellite System (BDS) consists of three types of satellites, namely geosynchronous earth orbit (GEO), inclined geosynchronous orbit (IGSO), and medium earth orbit (MEO) satellites. The three types of satellites have uneven orbital accuracy. In the generation of satellite clock products, the orbital errors are partly assimilated into the clock offsets. If neglecting the orbital accuracy difference of the three types of BeiDou satellites, the MSM will obtain biased estimates of the timescale difference and finally affect the clock product evaluation. In this study, an improved multi-satellite method (IMSM) is proposed for evaluating the real-time BDS clock products by removing the assimilated orbital errors of the three types of BDS satellites when estimating the timescale difference. Three real-time BDS clock products disseminated by three different International GNSS Service (IGS) analysis centers, namely CLK16, CLK20, and CLK93, over a period of two months are used to validate this method. The results indicate that the assimilated orbital errors have a significant impact on the estimation of the timescale difference. Subsequently, the IMSM is compared with the SSM in which the referenced satellite is rigorously chosen, and their RMS difference is only 0.08 ns, which suggests that the evaluation results obtained by the IMSM are accurate. Compared with the traditional MSM, the IMSM improves the RMS by 0.16, 0.11, and 0.07 ns for CLK16, CLK20, and CLK93, respectively. Finally, three real-time BDS clock products are evaluated using the proposed method, and results reveal a significant precision difference among them.

Real‐time detection of BDS orbit manoeuvres based on the combination of GPS and BDS observations

The construction of the third generation of the Chinese BeiDou navigation satellite system (BDS), which provides global positioning, navigation, and timing (PNT) services, will be completed in 2020. As BDS satellites contain the geostationary orbit (GEO), inclined geosynchronous (IGSO), and medium earth orbit (MEO), orbital manoeuvres occur more frequently. Thus, orbit manoeuvre detection is important for continuous and reliable PNT services. A BDS orbit manoeuvre detection method based on the combination of global positioning system (GPS) and BDS observations is proposed in this study. The standard deviations of the observation residuals of the epoch-differenced velocity estimation of the single BDS system and combined GPS + BDS system were compared to determine the beginning and end of the orbit manoeuvre. The results show that the orbital manoeuvre leads to a position, velocity, and receiver clock error bias of approximately tens to hundreds of metres, several centimetres per second, and tens to hundreds of metres, respectively. Based on the proposed method, the start and end times can be detected in real time and the usable observation time can be extended by >157 min.

Evaluation of Inter-System Bias between BDS-2 and BDS-3 Satellites and Its Impact on Precise Point Positioning

The BeiDou navigation satellite system (BDS) currently has 41 satellites in orbits and will reach its full constellation following the launch of the last BDS satellite in June 2020 to provide navigation, positioning, and timing (PNT) services for global users. In this contribution, we investigate the characteristics of inter-system bias (ISB) between BDS-2 and BDS-3 and verify whether an additional ISB parameter should be introduced for the BDS-2 and BDS-3 precise point positioning (PPP). The results reveal that because of different clock references applied for BDS-2 and BDS-3 in the International GNSS Service (IGS) precise satellites clock products and the inconsistent code hardware delays of BDS-2 and BDS-3 for some receiver types, an ISB parameter needs to be introduced for BDS-2 and BDS-3 PPP. Further, the results show that the ISB can be regarded as a constant within a day, the value of which is closely related to the receiver type. The ISB values of the stations with the same receiver type are similar to each other, but a great difference may be presented for different receiver types, up to several meters. In addition, the impact of ISB on PPP has also been studied, which demonstrates that the performance of kinematic PPP could be improved when ISB is introduced.

Evaluation of GBAS flight trials based on BDS and GPS

Ground-based augmentation systems (GBASs) are widely used augmentation systems using satellite navigation. GBAS can improve the performance of BeiDou navigation satellite system (BDS) in civil aviation application. Evaluation is necessary before using a GBAS. On the basis of the flight trials conducted at the Dongying airport, evaluation results show that based on both the global positioning system (GPS) L1 signal and BDS B1I signal, ground accuracy designators (GADs) of four reference receivers are consistent with GAD-C levels. The improvement in accuracy obtained with GBAS differential process is ∼60%, and the differential position error based on the BDS B1I signal is 40% greater than that of the GPS L1 signal, because currently incomplete BDS satellites distribution is worse than that of GPS. Airborne protection levels assessments show that the approach trials based on the BDS B1I signal exhibit several false alarm events. Further analysis indicates that BDS vertical protection levels were larger because of larger pseudoinverse S result from low elevation angle and unsatisfactory geometric distribution of BDS satellites. Besides, monitors show that BDS B1I signal is more affected by ionospheric delay than GPS L1 signal, which can also contribute to false alarm events.

Initial analysis for characterizing and mitigating the pseudorange biases of BeiDou navigation satellite system

Pseudorange bias has become a practical obstacle in the field of high-precision global navigation satellite system (GNSS) applications, which greatly restricts the further development of high-precision applications. Unfortunately, no studies have been conducted on the pseudorange biases of the BeiDou navigation satellite system (BDS). To mitigate the effects of pseudorange biases on the BDS performance to the greatest extent possible, the origin of such BDS pseudorange biases are first thoroughly illustrated, based upon which the dependency of the biases on the receiver configurations are studied in detail. Owing to the limitations regarding the parameter re-settings for hardware receivers, software receiver technology was used to achieve the ergodicity of the receiver parameters, such as the correlator spacing and front-end bandwidth, using high-fidelity signal observations collected by a 40-m-high gain dish antenna at Haoping Observatory. Based on this, the pseudorange biases of the BDS B1I and B3I signals and their dependency on different correlator spacings and front-end bandwidths were adequately provided. Finally, herein, the suggested settings of the correlator spacing and front-end bandwidth for BDS receivers are in detail proposed for the first time. As a result, the pseudorange biases of the BDS signals will be less than 20 cm, reaching even under 10 cm, under this condition. This study will provide special attention to GNSS pseudorange biases, and will significantly promote a clear definition of the appropriate receiver parameter settings in the interface control documents of BDS and other individual satellite systems.

Fractal behavior of BDS-2 satellite clock offsets and its application to real-time clock offsets prediction

The satellite clocks of the BeiDou Navigation Satellite System (BDS) have characteristic differences compared to those of the global positioning system and Galileo. Therefore, the satellite clock offsets prediction method of BDS is different from those of these two systems. The basis for establishing a more appropriate prediction model is to clarify the statistical characteristics of the BDS satellite clock offsets, which can be reflected by fitting residuals of precise clock errors. Fractal behavior is generally not considered in existing studies. In this study, the rescaled range analysis method is improved by using the moving-average method in order to verify the fractal behavior of the BDS clock offsets. The computation results of the Hurst exponent show that the BDS clock offsets are fractal series with long-term memory, and the memory spans are obtained by V-statistic calculation. The quadratic polynomial fitting residuals of BDS clock offsets are fitted by using the periodic model and fractal interpolation model, where the latter approach has a higher accuracy. In the predictive modeling process, the quadratic polynomial forecasting model is improved by using the memory span, so that the forecasting model not only inherits the overall clock offsets trend but also considers the local memory trend. The fractal interpolation prediction model of the clock offsets is established by using the extension method of the affine iteration function system. The experimental results show that the average prediction accuracy of the fractal model in 3, 6, 12, and 24 h can reach 1.4890, 2.0222, 3.1609, and 4.9278 ns, which is 57.74%, 50.20%, 52.66%, and 49.42% higher than the products from the China iGMAS ultra-rapid prediction, respectively.

Cycle Slips Detection for Triple-Frequency Signals of BDS by Combining Carrier Phase and Doppler Measurements

A new model is presented to resolve cycle slips detection for triple-frequency observations of BeiDou navigation satellite system (BDS) in this article when pseudorange observations are missing or insufficiently accurate under harsh or special situations. Based on the first-order time-difference geometry-free (GF) pseudorange-phase combination model, the new cycle slips detection and correction method based on the triple-frequency carrier phase and Doppler observations is proposed. With analyses on the two common sampling intervals (30 s and 1 s), it can be concluded that the optimal combination coefficients of the proposed model relate to sampling intervals. Combinations [4, −2, −3], [−1, −5,6], and [−3,6, −2] are selected to detect and correct cycle slips for 30 s sampling interval, while combinations [0, −1,1], [1,0, −1], and [−3,2,2] are selected for 1 s sampling interval. The validity of the phase-Doppler combination model under the static condition and the steady ionosphere with 30 s sampling interval and 1 s sampling interval is verified by two static experiments. Results show that the phase-Doppler combination model can achieve the same performance as the pseudorange-phase combination model. All the small, insensitive, and large cycle slips added to the three types of BDS satellites which separately belong to Geostationary Earth Orbit (GEO), Inclined Geosynchronous Orbit (IGSO), and Medium Earth Orbit (MEO) are detected and corrected successfully by the proposed model.

A Strategy to Mitigate the Ionospheric Scintillation Effects on BDS Precise Point Positioning: Cycle-Slip Threshold Model

Because of the special design of BeiDou navigation satellite system (BDS) constellation, the effects of ionospheric scintillation on operational BDS generally are more serious than on the global positioning system (GPS). As BDS is currently providing global services, it is increasingly important to seek strategies to mitigate the scintillation effects on BDS navigation and positioning services. In this study, an improved cycle-slip threshold model is proposed to decrease the high false-alarm rate of cycle-slips under scintillation conditions, thus avoiding the frequent unnecessary ambiguity resets in BDS precise point positioning (PPP) solution. We use one-year (from 23 March 2015 to 23 March 2016) BDS dataset from Hong Kong Sha Tin (HKST) station (22.4°N, 114.2°E; geomagnetic latitude: 15.4°N) to model the cycle-slip threshold and try to make it suitable for three types of BDS satellites and multiple scintillation levels. The availability of our mitigation strategy is validated by using three months (from 1 September 2015 to 30 November 2015) BDS dataset collected at 10 global navigation satellite system (GNSS) stations in Hong Kong. Positioning results demonstrate that our mitigated BDS PPP can prevent the sudden fluctuations of positioning errors induced by the ionospheric scintillation. Statistical results of BDS PPP experiments show that the mitigated solution can maintain an accuracy of about 0.08 m and 0.10 m in the horizontal and vertical components, respectively. Compared with standard BDS PPP, the accuracy of mitigated PPP can be improved by approximately 24.1%, 38.2%, and 47.9% in the east, north, and up directions, respectively. Our study demonstrates that considering different scintillation levels to establish appropriate cycle-slip threshold model in PPP processing can efficiently mitigate the ionospheric scintillation effects on BDS PPP.

Mitigation of Unmodeled Error to Improve the Accuracy of Multi-GNSS PPP for Crustal Deformation Monitoring

High-rate multi-constellation global navigation satellite system (GNSS) precise point positioning (PPP) has been recognized as an efficient and reliable technique for large earthquake monitoring. However, the displacements derived from PPP are often overwhelmed by the centimeter-level noise, therefore they are usually unable to detect slight deformations which could provide new findings for geophysics. In this paper, Global Positioning System (GPS), GLObalnaya NAvigatsionnaya Sputnikovaya Sistema (GLONASS), and BeiDou navigation satellite system (BDS) data collected during the 2017 Mw 6.5 Jiuzhaigou earthquake were used to further exploit the capability of BDS-only and multi-GNSS PPP in deformation monitoring by applying sidereal filtering (SF) in the observation domain. The equation that unifies the residuals for the uncombined and undifferenced (UCUD) PPP solution on different frequencies was derived, which could greatly reduce the complexity of data processing. An unanticipated long-term periodic error term of up to ± 3 cm was found in the phase residuals associated with BDS satellites in geostationary Earth orbit (GEO), which is not due to multipath originated from the ground but is in fact satellite dependent. The period of this error is mainly longer than 2000 s and cannot be alleviated by using multi-GNSS. Compared with solutions without sidereal filtering, the application of the SF approach dramatically improves the positioning precision with respect to the weekly averaged positioning solution, by 75.2%, 42.8%, and 56.7% to 2.00, 2.23, and 5.58 cm in the case of BDS-only PPP in the east, north, and up components, respectively, and 71.2%, 27.7%, and 37.9% to 1.25, 0.81, and 3.79 cm in the case of GPS/GLONASS/BDS combined PPP, respectively. The GPS/GLONASS/BDS combined solutions augmented by the SF successfully suppress the GNSS noise, which contributes to the detection of the true seismic signal and is beneficial to the pre- and post-seismic signal analysis.

An improved method for detecting BeiDou signal-in-space anomalies from precise ephemerides

The signal-in-space (SIS) anomalies caused by satellites and control segments can greatly affect the reliability and safety of navigation and positioning users. The prior information associated with the failure of the Advanced Receiver Autonomous Integrity Monitoring (ARAIM) algorithm were obtained by the evaluation of SIS failure rates broadcasted with navigation ephemeris to investigate the integrity of navigation and positioning. For the existing ARAIM algorithm, the failure rate of satellites in the BeiDou Navigation Satellite System (BDS) is a conservative estimate, which is inconsistent with the actual SIS performance of BDS. Only the accurate detection of the SIS anomalies of BDS satellites can provide an effective reference to associate with failure. Therefore, to improve the accuracy of SIS anomaly detection for BDS satellites, and to provide higher integrity services for users, this study presents an improved method of SIS anomaly detection with precise ephemeris. The median method was used to detect a gross error in clock data before the calculation of clock datum, and the combination of an experience threshold and trimmed mean was used to determine the anomaly detection threshold. The feasibility and efficiency of the proposed method were also analyzed using data collected between 2015 and 2016. The detection results show that the constellation fault caused by erroneous clock data can be avoided, and the SIS anomalies can also be detected using the proposed method. Additionally, through the comprehensive tests performed in this study, it was found that from 2015 to 2016, the average accumulated duration of anomalies for BDS satellites was 10 h for geostationary orbit (GEO) and incline geosynchronous orbit (IGSO) and 55 h for medium earth orbit (MEO), respectively. These anomalies were primarily caused by the satellite clock.