Klobuchar, NeQuickG, BDGIM, GLONASS, IRI-2016, IRI-2012, IRI-Plas, NeQuick2, and GEMTEC Ionospheric Models: A Comparison in Total Electron Content and Positioning Domains.

Global navigation satellite systems (GNSS) provide a great data source about the ionosphere state. These data can be used for testing ionosphere models. We studied the performance of nine ionospheric models (Klobuchar, NeQuickG, BDGIM, GLONASS, IRI-2016, IRI-2012, IRI-Plas, NeQuick2, and GEMTEC) both in the total electron content (TEC) domain-i.e., how precise the models calculate TEC-and in the positioning error domain-i.e., how the models improve single frequency positioning. The whole data set covers 20 years (2000-2020) from 13 GNSS stations, but the main analysis involves data during 2014-2020 when calculations are available from all the models. We used single-frequency positioning without ionospheric correction and with correction via global ionospheric maps (IGSG) data as expected limits for errors. Improvements against noncorrected solution were as follows: GIM IGSG-22.0%, BDGIM-15.3%, NeQuick2-13.8%, GEMTEC, NeQuickG and IRI-2016-13.3%, Klobuchar-13.2%, IRI-2012-11.6%, IRI-Plas-8.0%, GLONASS-7.3%. TEC bias and mean absolute TEC errors for the models are as follows: GEMTEC--0.3 and 2.4 TECU, BDGIM--0.7 and 2.9 TECU, NeQuick2--1.2 and 3.5 TECU, IRI-2012--1.5 and 3.2 TECU, NeQuickG--1.5 and 3.5 TECU, IRI-2016--1.8 and 3.2 TECU, Klobuchar-1.2 and 4.9 TECU, GLONASS--1.9 and 4.8 TECU, and IRI-Plas-3.1 and 4.2 TECU. While TEC and positioning domains differ, new-generation operational models (BDGIM and NeQuickG) could overperform or at least be at the same level as classical empirical models.

Constrained L1-Norm Minimization Method for Range-Based Source Localization under Mixed Sparse LOS/NLOS Environments.

Under mixed sparse line-of-sight/non-line-of-sight (LOS/NLOS) conditions, how to quickly achieve high positioning accuracy is still a challenging task and a critical problem in the last dozen years. To settle this problem, we propose a constrained L1 norm minimization method which can reduce the effects of NLOS bias for improve positioning accuracy and speed up calculation via an iterative method. We can transform the TOA-based positioning problem into a sparse optimization one under mixed sparse LOS/NLOS conditions if we consider NLOS bias as outliers. Thus, a relatively good method to deal with sparse localization problem is L1 norm. Compared with some existing methods, the proposed method not only has the advantages of simple and intuitive principle, but also can neglect NLOS status and corresponding NLOS errors. Experimental results show that our algorithm performs well in terms of computational time and positioning accuracy.

A Smart Realtime Service to Broadcast the Precise Orbits of GPS Satellite and Its Performance on Precise Point Positioning.

At present, Global Position System (GPS) navigation ephemeris mainly broadcasts satellite orbits with meter-level precision for standard point positioning and precise relative positioning. With the rapid development of real-time precise point positioning (PPP), the receiver or smartphone has begun to demand more and more convenient, continuous, and reliable access to real-time services of precise orbits. Therefore, this study proposes a solution of utilizing the 18-parameter ephemeris to directly broadcast ultra-rapid precise predicted orbits with centimeter-level precision for real-time PPP. For the first time in GPS, the difference in the PPP results between the precise orbits and the calculated orbits broadcasted from the generated ephemeris parameters is supplied as follows: (1) During the validity period of 2 h, root mean square (RMS) of the relative distance offsets between the results of PPP with the precise orbits and the results of PPP the 18-parameter ephemeris is only 0.0098 m. (2) Within 15 min after the validity period of 2 h, RMS of the relative distance offsets between the results of PPP with the precise orbits and the results of PPP with the predicted orbits by 18-parameter ephemeris is only 0.0057 m. Consequently, the 18-parameter ephemeris is feasible and advisable to broadcast precise predicted orbits for real-time PPP applications. Compared with the classic precise orbits broadcast mode with the orbit corrections defined by the radio technical commission for maritime services standards 10403.2 (RTCM), the mode of broadcasting the precise orbits with the 18-parameter ephemeris achieved the following improvements in convenience, continuity, and reliability: (1) The calculation of satellite position is the same as that of the navigation ephemeris excluding the additional correction operations required to the RTCM; (2) the amount of broadcast parameters was reduced by 20 times; (3) the length of the validity period was expanded 120 times, where the longer valid period helped to overcome the orbit corrections loss caused by RTCM stream failures; and (4) within 15 min after the validity period, the predicted orbits with an accuracy of 2 cm could still be provided by the 18-parameter ephemeris, which can ensure the real-time services of precise orbits in the case of a 15 min communication interruption of the RTCM orbit correction data stream.

A Cycle Slip Repair Method Against Ionospheric Effects and Observational Noises for BDS Triple-Frequency Undifferenced Phases.

The cycle slip detection (CSD) and cycle slip repair (CSR) are easily affected by ionospheric delay and observational noise. Aiming at mitigating the above disadvantage, a new BeiDou navigation satellite system (BDS) triple-frequency CSR method (BTCSR) is proposed for the undifferenced phase. BTCSR learns from the classic triple-frequency CSR (CTCSR), with combinations of phases and pseudoranges in correcting ionospheric delay and optimizing observational noise. Different from CTCSR, though, BTCSR has made the following improvements: (1) An optimal model of calculating cycle slip combination is established, which further takes into account the minimization of the effect of residual ionospheric error after the correction. The calculation of cycle slip combination is obtained with the root mean squared errors (0.0646, 0.1261, 0.1069) of cycles, resulting in CSR success rate of 99.9927%, and the wavelengths (4.8842,3.5738,8.1403) of m. (2) A discriminant function is added to guarantee the CSR correctness. This function utilizes epoch-difference value of the ionosphere-free and geometry-free phase to select the correct cycle slip value, which eliminates the interference of large pseudorange errors in determining the final cycle slip. Consequently, the performances of BTCSR and CTCSR have been compared. For the real BDS pseudorange observation with additional 1.5 m errors, which can cover situations of 99.96% pseudorange noise, results of CTCSR show failure, but results of BTCSR keep correct. Moreover, BTCSR has made the following improvements relative to the geometry-free cycle slip detection method (GFCSD) and Melboune-Wubbena cycle slip combination detection method (MWCSD): (1) During a moderate magnetic storm of level 6, CSR testing, with the BDS monitoring station in a low latitude region, showed that some failures occur in GFCSD because of severe ionospheric variation, but BTCSR could correctly identify and fix cycle slips. (2) For the BDS observation data with an additional 1.5 m error on the actual pseudoranges, MWCSD exhibited failures, but the repair results of BTCSR were correct and reliable. (3) For the special slips of (0,59,62) cycles, and equal slips of (1,1,1) cycles on (B1,B2,B3), that are hard to detect by GFCSD and MWCSD, respectively, BTCSR could repair these correctly. Finally, BTCSR obtains reliable repair results under large pseudorange errors and severe ionospheric variations, and the cut-off elevation larger than 10 degrees is the suggested background.

Research on Attitude Models and Antenna Phase Center Correction for Jason-3 Satellite Orbit Determination.

We focused on the researches of two models used for Jason-3 precise orbit determination (POD)-Jason-3 attitude modes and receiver phase center variation (PCV) model. A combined attitude mode for the Jason-3 satellite is designed based on experimental analysis used in some special cases, such as in the absence of quaternions or when inconvenient to use. We researched the linking of satellite attitude with antenna phase center. Specially, to verify the validity of the combined attitude, we analyzed the effects of different attitude modes on receiver phase center offset (PCO) estimation, PCO correction and POD. Meanwhile, the difference analysis of PCO correction based on attitude modes also contains the combined attitude modeling processes. The POD results showed that the orbital accuracies with the combined attitude are slightly more stable than those with attitude event file. By introducing receiver PCVs into POD, the mean residuals root-mean-square (RMS) is reduced by 1.9 mm and orbital 3D-RMS position difference is improved by 5.7 mm. The eight schemes were designed to integratedly verify the effectiveness of different attitude modes and receiver PCVs model. The results conclude that the accuracy using the combined attitude is higher than that of event file, which also prove the feasibility of the combined attitude in integrated POD and it can be as a revision of attitude event file. Using all mentioned attitude modes, the orbital accuracy by introducing PCVs can be improved by the millimeter level. The integrated effects of attitude modes and receiver PCVs on POD are almost consistent with the effects of a single variable. The optimal results of Jason-3 POD indicate that orbital mean radial RMS is close to 1 cm, and the 3D-RMS position difference is within 3 cm.

Real-Time Monitoring for BDS Signal-In-Space Anomalies Using Ground Observation Data.

Signal-in-space (SIS) User Range Error (URE) is one of the major error sources for BeiDou Navigation Satellite System (BDS) applications and can reach tens of meters or even more. Therefore, real-time monitoring of SIS anomalies has a great realistic significance to guarantee the safety of users. According to an analysis of the BDS navigation messages, it showed that the User Range Accuracy (URA) index could not reflect the change of URE when it was abnormal. The conventional models using the relationship between URA and URE to monitor SIS anomalies are not suitable to the present BDS. Therefore, we use a prior information of SIS URE derived from ground observational data instead of URA to monitor BDS SIS anomalies. In order to realize the corresponding functions, we analysed the distribution of SIS UREs and obtained their prior models. Then, the monitoring threshold is determined using the prior models and a confidence interval instead of URA. The scheme was tested by applying to BDS SIS anomalies monitoring based on 13 ground tracking stations. The performance of this method was assessed by comparison with the satellite-health indicators from broadcast ephemeris. The results confirm that the method developed in this paper can rightly and timely detect abnormal SIS.

A Robust Method to Detect BeiDou Navigation Satellite System Orbit Maneuvering/Anomalies and Its Applications to Precise Orbit Determination.

The failure to detect anomalies and maneuvering of the orbits of navigation satellite sensors will deteriorate the performance of positioning and orbit determination. Motivated by the influence of the frequent maneuvering of BDS GEO and IGSO satellites, this paper analyzes the limitations of existing methods, where BDS orbit maneuvering and anomalies can be detected, and develops a method to solve this problem based on the RMS model of orbit mutual differences proposed in this paper. The performance of this method was assessed by comparison with the health flag of broadcast ephemeris, precise orbit products of GFZ, the O-C values of a GNSS station and a conventional method. The results show that the performance of the method developed in this paper is better than that of the conventional method when the periodicity and trend items are obvious. Meanwhile, three additional verification results show that the method developed in this paper can find error information in the merged broadcast ephemeris provided by iGMAS. Furthermore, from the testing results, it can be seen that the detection of anomaly and maneuvering items do not affect each other based on the robust thresholds constructed in this paper. In addition, the precise orbit of the maneuvering satellites can be determined under the circumstances that the maneuver information detected in this paper is used, and the root mean square (RMS) of orbit overlap comparison for GEO-03/IGSO-03 in Radial, Along, Cross, 1D-RMS are 0.7614/0.4460 m, 1.8901/0.3687 m, 0.3392/0.2069 m, 2.0657/0.6145 m, respectively.

A new analytical solar radiation pressure model for current BeiDou satellites: IGGBSPM.

An analytical solar radiation pressure (SRP) model, IGGBSPM (an abbreviation for Institute of Geodesy and Geophysics BeiDou Solar Pressure Model), has been developed for three BeiDou satellite types, namely, geostationary orbit (GEO), inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO), based on a ray-tracing method. The performance of IGGBSPM was assessed based on numerical integration, SLR residuals and analyses of empirical SRP parameters (except overlap computations). The numerical results show that the integrated orbit resulting from IGGBSPM differs from the precise ephemerides by approximately 5 m and 2 m for GEO and non-GEO satellites, respectively. Moreover, when IGGBSPM is used as an a priori model to enhance the ECOM (5-parameter) model with stochastic pulses, named ECOM + APR, for precise orbit determination, the SLR RMS residual improves by approximately 20-25 percent over the ECOM-only solution during the yaw-steering period and by approximately 40 percent during the yaw-fixed period. For the BeiDou GEO01 satellite, improvements of 18 and 32 percent can be achieved during the out-of-eclipse season and during the eclipse season, respectively. An investigation of the estimated ECOM D0 parameters indicated that the ß-angle dependence that is evident in the ECOM-only solution is no longer present in the ECOM + APR solution.

Analysis of the Bias on the Beidou GEO Multipath Combinations.

The Beidou navigation satellite system is a very important sensor for positioning in the Asia-Pacific region. The Beidou inclined geosynchronous orbit (IGSO) and medium Earth orbit (MEO) satellites have been analysed in some studies previously conducted by other researchers; this paper seeks to gain more insight regarding the geostationary earth orbit (GEO) satellites. Employing correlation analysis, Fourier transformation and wavelet decomposition, we validate whether there is a systematic bias in their multipath combinations. These biases can be observed clearly in satellites C01, C02 and C04 and have a great correlation with time series instead of elevation, being significantly different from those of the Beidou IGSO and MEO satellites. We propose a correction model to mitigate this bias based on its daily periodicity characteristic. After the model has been applied, the performance of the positioning estimations of the eight stations distributed in the Asia-Pacific region is evaluated and compared. The results show that residuals of multipath series behaves random noise; for the single point positioning (SPP) and precise point positioning (PPP) approaches, the positioning accuracy in the upward direction can be improved by 8 cm and 6 mm, respectively, and by 2 cm and 4 mm, respectively, for the horizontal component.

Assessment of Three Tropospheric Delay Models (IGGtrop, EGNOS and UNB3m) Based on Precise Point Positioning in the Chinese Region.

Tropospheric delays are one of the main sources of errors in the Global Navigation Satellite System (GNSS). They are usually corrected by using tropospheric delay models, which makes the accuracy of the models rather critical for accurate positioning. To provide references for suitable models to be chosen for GNSS users in China, we conduct herein a comprehensive study of the performances of the IGGtrop, EGNOS and UNB3m models in China. Firstly, we assess the models using 5 years' Global Positioning System (GPS) derived Zenith Tropospheric Delay (ZTD) series from 25 stations of the Crustal Movement Observation Network of China (CMONOC). Then we study the effects of the models on satellite positioning by using various Precise Point Positioning (PPP) cases with different tropospheric delay resolutions, the observation data processed in PPP is from 21 base stations of CMONOC for a whole year of 2012. The results show that: (1) the Root Mean Square (RMS) of the IGGtrop model is about 4.4 cm, which improves the accuracy of ZTD estimations by about 24% for EGNOS and 19% for UNB3m; (2) The positioning error in the vertical component of the PPP solution obtained by using the IGGtrop model is about 15.0 cm, which is about 30% and 21% smaller than those of the EGNOS and UNB3m models, respectively. In summary, the IGGtrop model achieves the best performance among the three models in the Chinese region.