China Satellite Navigation Conference (CSNC 2022) Proceedings

The algorithm, processing strategy and performances of the Global Ionospheric Map (GIM), generated based on the global GNSS tracking network observations by international GNSS Monitoring and Assessment System BAC Analysis Center (BAC), is analyzed in this paper. First, during the “Tianwen-1” Mars Exploring Mission Mars-docking-orbit phase, the comparison among the GIM products of BAC, Center for Orbit Determination in Europe (CODE) and Jet Propulsion Laboratory (JPL) shows that the BAC GIM product performances similar to JPL GIM product and slightly worse than their CODE peer; however, in the middle latitude area where China’s Deep Space Network (DSN) is located, BAC GIM product is the best in model bias. Second, the BAC GIM products are also compared with the ionospheric delay data observed by GNSS receivers mounted at two DSN stations (Kashi and Namibia). It is found that the two data sets show an obvious similarity and the correlation coefficients are within (0.943 – 0.977). Last, the BAC GIM products’ application in the “Tianwen-1” Mars Exploring Mission is also performed. The ionospheric delays in range and rate measurements collected at Jiamusi, Kashi and Argentina DSN stations are corrected; the orbit determination residuals corresponding to the range measurements decrease up to 20% and those corresponding to the rate measurements decrease up to 84%.

The Phase Center Offsets (PCO) of BDS-3 IGSO and MEO satellites are estimated by processing one-year observation data from iGMAS and MGEX ground tracking stations. The variation tendency and contributing factors of PCO daily estimation sequences are analyzed. The estimated PCO values for BDS-3 IGSO and MEO satellites are carried out and compared with the official published values calibrated by satellite manufacturers on the ground. On this basis, the influence of PCO parameters on orbit determination and Precise Point Positioning (PPP) are preliminarily evaluated. The results indicate that the PCO values estimated in this paper are in good agreement with the calibration values from the manufacturers, and the root mean square of the differences between the two are 0.039 m, 0.007 m and 0.063 m in the X axis, Y axis, and Z axis directions of the satellite-fixed coordinate system, respectively. The 3-D orbit overlap accuracy of IGSO and MEO satellites has been improved by using the estimated PCO parameters, achieving an improvement of 17.7% and 20.0%, respectively. In addition, with the estimated PCO parameters, the precision of station coordinates PPP reaches 7.44 mm and 14.01 mm in the horizontal and elevation directions respectively.

The traditional TurboEdit method is not effective in dealing with continuous small cycle slips or specific small cycle slip pairs when utilized to detect and repair cycle slips in dual frequency data. In particular, the detected cycle slip pair cannot be directly separated. An improved TurboEdit cycle slip detection and repair method based on Levenberg Marquardt-Back Propagation (LM-BP) algorithm is proposed in this study. In the proposed method, LM-BP fitting algorithm is utilized to replace the polynomial fitting step in the traditional TurboEdit method, so as to improve the ability of detecting continuous small cycle slips. And it increases LM-BP detection sequence of single difference data to solve the detection failure problem of specific small cycle slip pairs and realize the direct separation of cycle slips. The verification results of measured Beidou Navigation Satellite System (BDS) data show that the improved TurboEdit algorithm based on LM-BP algorithm can detect continuous small cycle slips. And in the case of cycle slip pair with equal cycle slip, it can still effectively detect cycle slips, directly judge the epoch position of cycle slips, and realize the effective separation of cycle slip pair.

In order to take full advantages of the BDS-3 penta-frequency signals in the long-baseline RTK positioning, a long-baseline RTK positioning method based on the BDS-3 penta-frequency ionospheric-reduced (IR) combinations is proposed. First, the low-noise and weak-ionospheric delay characteristics of the multi-frequency combinations of BDS-3 is analyzed. Second, the multi-frequency extra-wide-lane (EWL)/ wide-lane (WL) combinations with long-wavelengths are constructed. Third, the fixed IR EWL combinations are used to constrain the IR WL, of which the ambiguities can be obtained in a single epoch. There is no need to consider the influence of ionospheric parameters in the third step. Compared with the estimated ionospheric model, the proposed method reduces the number of parameters by half, so it is suitable for the use of multi-frequency and multi-system real-time RTK. The results using real data show that stepwise fixed model of the IR EWL/WL combinations can realize long-baseline instantaneous decimeter-level positioning.

The traditional inter-frequency clock bias (IFCB) prediction method based on the harmonic model has large jumps at the junction of prediction arcs. An improved method is proposed for GPS IFCB short-term prediction, which fits linear and sinusoidal terms of the harmonic model adopting epoch-differenced (ED) IFCB and corrects constant term using the precision IFCB with the nearest epoch to the initial prediction epoch. The jumps in adjacent prediction arcs are reduced effectively and the IFCB short-term prediction accuracy is improved. The results illustrate that the average prediction accuracy of the proposed method is improved by 62.5%, 47.1%, 35.5% and 30% for 3, 6, 12 and 24 h, respectively. Meanwhile, the positioning performance of GPS triple-frequency PPP is improved and the accuracy is improved by 5.08%, 2.3% and 5.18% over the traditional prediction method in the three directions of E, N and U, respectively.

In GNSS navigation and positioning, ionospheric delay error is one of the sources of error that cannot be ignored. The BDS Klobuchar (BDSKlob) and BDGIM model parameters are broadcast by the BDS Navigation Satellite System in the broadcast ephemeris to correct for ionospheric delay errors, which can meet the basic navigation and positioning needs of users. However, in the face of the growing demand for autonomous positioning and navigation accuracy, it is necessary to further improve the accuracy of the model and reduce the impact of the space environment on positioning. In this paper, a Back Propagation (BP) neural network optimized by Artificial Bee Colony Algorithm (ABC) is used to compensate for the error prediction of the BDS broadcast ionosphere model from 7 to 13 September 2021. For BDSKlob and BDGIM, a number of grid points in the Chinese region and worldwide are selected for experimental analysis. BDSKlob and BDGIM respectively selected several grid points in China and the world for experimental analysis. The results show that the prediction compensation of the BDS broadcast ionosphere model errors using ABC-BP neural network can achieve better accuracy results. For BDSKlob, the model correction rate improved to 81.66% in China after using the predicted values to compensate for the model values. For BDGIM, the accuracy was significantly improved in the global mid and high latitudes, with model correction rates of 74.25%, 82.05% and 82.13% for the high, mid and low latitudes respectively after compensation.

With the completion of BeiDou Navigation Satellite System (BDS) constellation deployment, the research on improving the service performance of BDS has become the focus. Broadcast ephemeris is a prerequisite for normal navigation in real time navigation and positioning. The real-time performance of broadcast ephemeris results in bad orbit accuracy, and its error variation cannot be accurately described by mathematical model, which has a unignorable impact in positioning and navigation. Based on this research background, we take Multi-GNSS Experiment (MGEX) precision ephemeris as reference and use Back Propagation (BP) Neural Network (NN) and Artificial Bee Colony Algorithm (ABC) optimized BP NN to model the orbit error of broadcast ephemeris to improve the its orbit accuracy. The experimental results show that the two NN models have good modeling effect on broadcast ephemeris orbit error, and the orbit accuracy of broadcast ephemeris of different satellites is improved by 20%–80%. ABC-BP NN has higher accuracy than BP NN, and the results of 3 and 5 days of different orbit types show that it has better ability to control error accumulation, and has better error compensation results for broadcast ephemeris in short and medium term.

In GNSS multi-system fusion positioning, inter-system bias must first be considered. The analysis of the inter-system bias characteristics is helpful for the prediction and modeling of the inter-system basic, improving the precision and convergence speed of precise point positioning. This paper constructes GPS/BDS ionospheric-free combined PPP observation equation by considering ISB parameters. On this basis, the difference between BDS-2/GPS ISB and BDS-3/GPS ISB, the characteristics of BDS-2/BDS-3 ISB and its impact on PPP are analyzed. The results show that GPS/BDS ISB estimation by fusion of BDS-2 and BDS-3 observation data possesses the average characteristics, the estimation process is more stable, the positioning result accuracy is higher, and the convergence speed is faster. In the static state, the positioning accuracy is about 0.6 cm in N direction, about 0.9 cm in E direction, and about 1.4 cm in U direction. The convergence time is about 15 min. The BDS-2/BDS-3 ISB is within ± 10 ns, and the long- and short-term changes are stable, depending on the receiver type. Considering the ISB between BDS-2/BDS-3 systems can help improve positioning accuracy and convergence speed.

The four major satellite navigation suppliers announced by the International Committee on Global Navigation Satellite Systems (ICG) include GPS of the United States, GLONASS of Russia, BDS of China and Galileo of Europe. The development of the four satellite navigation systems not only changes the trajectory of human activities on the earth’s surface, but also provides a cheap and efficient way for the accurate positioning and timing of other aircraft. Due to its low orbit and fast speed, LEO satellite naturally has the characteristics of strong landing power, fast revisit cycle, high ground resolution and fast observation geometry change, which makes it attracted much attention in the fields of mobile communication, remote sensing detection and navigation enhancement, and so on. In addition to the relatively weak irradiation environment, low launch cost and economic advantages, LEO constellation has become a direction that could not be ignored in various fields in recent years. Based on GNSS technology, this paper studied the theoretical method and achievable accuracy of precise orbit determination and time synchronization of LEO constellation. On this basis, the degraded backup effect and application suggestions of LEO constellation under multi-layer architecture including GNSS system were studied.

The inclusion of Low Earth Orbit (LEO) spaceborne GNSS observation or Inter-Satellite Link (ISL) measurement improves strength of normal equation, and then helps to improve ERP accuracy. With a 15-day simulation of BDS-3 ISL measurements and BDS-3 observations from 72 LEO satellites, 10 global stations and 10 Chinese stations, this work studies the impact of LEO satellites and BDS-3 ISL on ERP accuracy. Results show that the introduction of LEO satellites and BDS-3 ISL significantly improves ERP accuracy. Taking the IERS 14 C04 product as a reference, with ground network of 10 global stations, the RMS of polar X, Y coordinate and LOD after introducing 72 LEO satellites are 10.4 μas, 10.8 μas, 3.9 μs, respectively. Compared with ERP accuracy based on solely 10 global stations, the improvement reaches 66.8%, 74.0%, 62.1%, respectively. The accuracy is equivalent to that of using 115 global stations, and the polar coordinate accuracy is better than the case of introducing BDS-3 ISL. Based on 10 Chinese stations, the RMS of polar X, Y coordinate and LOD with BDS-3 ISL are 16.3 μas, 39.8 μas, 7.9 μs, respectively. The contribution of BDS-3 ISL is more pronounced than that of 72 LEO satellites. ERP results based on Chinese stations indicate that the polar Y coordinate accuracy is always worse than the X component, which is not found in results of global stations. Furthermore, analysis of correlation indicates that the inclusion of LEO satellites or BDS-3 ISL reduces correlation between estimated parameters.

BeiDou Navigation Satellite System (BDS) on-orbit satellites contain BDS-2 and BDS-3 satellites. Due to the existence of ISB between BDS-2 and BDS-3 on receiver side, the traditional BDS precise clock estimation (PCE) and precise point positioning (PPP) models for the BDS-2 and BDS-3 combined processing will reduce the accuracy and stability of solutions. To improve the BDS service performance, the ISB between BDS-2 and BDS-3 for both old (B1I/B3I) and new signals (B1C/B2a) and its impact on PCE and PPP are investigated in this contribution. The BDS-2 and BDS-3 integrated PCE and PPP models with and without ISB estimation are presented. The combined processing is comprehensively assessed in terms of the precision of clock offsets and PPP performances. The result demonstrates that the ISB is stable for both old and new signals, and estimating ISB can effectively avoid the confusion of receiver clock datum. The integration of BDS-2 and BDS-3 indeed improves the precision of satellite clock offsets estimations based on the proper PCE models. The average STD for BDS-2 and BDS-3 clock offsets using old signals is improved by 15.8% and 11.1% compared with BDS-2-only and BDS-3-only solutions, respectively. For new signals, the improvement for BDS-3 clock offsets is 14.6% from 0.081 ns to 0.069 ns. The BDS clock offsets estimated by the proposed PCE model with ISB estimation (PCE0) can well support PPP applications. The positioning accuracy for old signals can be improved by 40.4%, 20.0% and 35.4% compared with those of using GFZ rapid products. Similarly, the positioning performance for new signals is slightly better than GFZ PPP. The PCE0 model is the optimal BDS-2 and BDS-3 integrated satellite clock offsets determination model for the server, and the PPP model with ISB estimation (PPP0) is the optimal PPP model for the client. The cooperation between PCE0 and PPP0 can improve the BDS service performance.

The precise orbit determination (POD) of low earth orbit (LEO) satellites is always a hotspot topic in the field of satellite geodesy. Current gravity field determination, satellite altimetry, and remote sensing measurement depend crucially on the precise orbits of the spacecraft. BeiDou global navigation satellite system (BDS-3) is officially completed in 2020 and offers positioning, navigation, and timing (PNT) service for global users. The onboard BDS measurements from LEO satellites can be used for LEO POD and served as an effective supplement for BDS tracking geometry. In this study, the BDS-3 observations with B1C and B2a signals of HY-2D spacecraft are employed for reduced-dynamic POD. For superior orbit quality, the extended analytical model for solar radiation pressure (SRP) is used for LEO POD, and in-flight calibration of the LEO receiver antenna is carried out to improve the orbit precision. Two weeks of onboard BDS-3 observation were used to assess the BDS-based POD performance. For HY-2D satellite based on BDS-3 instruments, the capability of continuous tracking is at the global level, and almost all the epochs can have 5–7 usable BDS satellites. The mean root-mean-squared (RMS) of the phase residual obtained from the reduced-dynamic POD is 6.5 mm, and that of pseudorange residual is 1.28 m. The internal precision for the entire arc is in good agreement. Moreover, an orbit self-consistency of 0.94 cm, 0.76 cm, and 0.49 cm is displayed in the along-track, cross-track, and radial directions, respectively.The 1.33 cm 3D RMS of the internal consistency is achieved for the reduced-dynamic orbits. A better than 2 cm RMS has been achieved in the Satellite Laser Ranging (SLR) validation for BDS-3-based LEO orbit solutions. These results could be used for the Chinese subsequent LEO satellite equipped with a BDS-3 receiver.

The antenna phase center offset and ranging error caused by its variation can reach several cm or even dm level, which is a key error correction term that must be considered for GNSS high-precision applications. China’s independently self-built Beidou navigation satellite system (BDS) has opened global services, but there is no absolute antenna phase center correction model of Beidou-3 in the field of GNSS that is consistent with the definition of IGS. In this paper, based on a high-precision robot, the absolute phase center field calibration method is studied, and the geodetic-grade e antenna of the monitoring station of the international GNSS Monitoring & Assessment Service (iGMAS) is calibrated for the first time based on the absolute antenna correction platform of Wuhan University. The preliminary results show that the antenna phase model has a frequency binning pattern, and the phase model characteristics with similar frequencies are relatively close. The internal conformity accuracy between the calibration results of multiple time periods is better than 1 mm, and the short baseline positioning verification consistency accuracy can reach 1.5–3 mm.

In order to increase the understanding of the positioning performance of BDS in the polar regions, this paper analyzes PPP (precise point positioning) performance under five different combinations which include BDS-3(B1IB3I), BDS(B1CB2a), BDS(B1IB3I), BDS(B1CB2a+B1CB3I) and GPS(L1L2) using the observation data of 15 IGS (International GNSS Service) stations around the world for 30 days. The results show that the accuracy of the static PPP in polar regions in the three directions of NEU is 1.1 cm, 0.7 cm, and 1.7 cm, and the kinematic PPP accuracy is 10 cm, 9 cm, and 20 cm. The time for static PPP in the polar region to converge to within 10 cm in the three directions of NEU is less than 15 min, 11 min, and 19 min, while the time for kinematic PPP to converge within 20 cm is less than 17 min, 16 min, and 23 min.

During the establishment and operation of the space station, rendezvous and docking needs to be carried out. The relative positioning technology based on Beidou can provide highly reliable and high-precision relative position results for the rendezvous and docking of the space station. However, the GNSS receiver is in a high-speed motion state, and the complexity of the space environment, especially the change of the ionosphere, is prone to various faults. For the positioning solution, the faults are manifested as gross pseudorange errors, carrier cycle slips, and even ambiguity. Therefore, this paper carries out a targeted technical design, performs full-cycle quality monitoring of data failures, and designs a real-time carrier phase difference algorithm to speed up the ambiguity. Finally, the simulator in the rendezvous and docking task is used to generate dual-frequency (B1I/B3I) measurement data for testing and analysis. The simulation results show that the adopted technical method has the ability to detect data anomalies and ensures that the relative positioning ambiguity of Beidou is fixed. Compared with the reference baseline value, the relative positioning accuracy of Beidou is 1.96 cm, and the average convergence time is 7.6 s, which verifies the effectiveness of the technical design and meets the requirements of high-precision and high-reliability space rendezvous and docking requirements.

The construction of global high-precision atmospheric delay model is the key and bottleneck problem for global PPP-RTK applications. In order to overcome the problems of large-scale construction of ground stations as well as difficulties in building stations at sea, a global PPP-RTK method based on GRO (GNSS Radio Occultation) and LRO (LEO Radio Occultation) is proposed. Firstly, the mathematical model of occultation events is studied, and then the number distribution and spatio-temporal resolution of GRO and LRO events are analyzed. The proposed LEO constellation can cover the area of 60°S–60°N in real time with the spatio-temporal resolution for GRO and LRO occultation events, and finally the PPP-RTK positioning is verified based on the atmospheric delay model of GRO and LRO, GNSS and GNSS+LEO convergence time are reduced by 58% and 46%, respectively compared with the PPP positioning.

The single-frequency precise point positioning (SFPPP) method has attracted widespread attention for its high precision and low cost, while the time delay caused by the ionosphere is one of the most problematic error sources in its data processing. With the completion of the BeiDou Global Navigation Satellite System (BDS), the users can access BDS positioning, navigation, and timing (PNT) service around the world. It is crucial to generate high-precision ionospheric products to improve the positioning accuracy and accelerate the convergence. However, the existing Global Ionospheric Map (GIM) products cannot satisfy the requirements of regional users for precise positioning, due to its poor spatial and temporal resolution. In this contribution, we estimate the biased slant ionospheric delay (SID) based on GPS dual-frequency (DF) raw observations from 30 stations in Australia and develop the regional ionospheric model (RIM). The performance of SFPPP with ionosphere corrected by RIM is evaluated using the BDS-2/BDS-3 observations from several stations and compared with the corresponding results obtained by CODE-GIM. Accounting for the long convergence time of uncombined (UC) SFPPP, we constrain the ionospheric delay parameter with RIM. And a time-varying weight constraint is attached to weaken the effect of RIM on the positioning accuracy after convergence. The results show that the RMS of the VTEC difference between RIM and CODE-GIM is better than 2 TECU. The RMS of BDS SFPPP with ionosphere corrected by RIM is better than 0.4 m and 0.3 m in north and east directions, respectively, and the average vertical accuracy is 0.53 m. The ionosphere-weighted (IW) SFPPP with RIM can significantly improve the convergence speed compared to the UC-SFPPP.

The Fengyun-3E satellite (FY-3E) is the world's first civilian weather satellite in the twilight orbit, which enables the solar panel to be designed with a larger size and vertically upwards to absorb more energy. In order to solve the problem of obstructing the observation field of the GNSS positioning antenna, the GNOS positioning antenna on the FY3E is designed as a dual-antenna combination cooperative observation method. Therefore, the precise orbit determination (POD) solution mainly needs to solve two problems: (1) the problem of inconsistent phase centres; (2) the problem of inconsistent hardware delay parameters. This article is aimed at the design structure of FY-3E satellite GNOS dual positioning antenna, uses the simplified dynamics non-differenced low-orbit satellite POD method and least squares quadratic (LSQ) recursive batch processing, subsequently to calculate the satellite's precise orbit, and at the end evaluates the POD precision with the overlapping arc inspection method. The results show that the satellite-borne GNSS low-orbit satellite with dual-antenna can observe more GNSS data, while the position accuracy of POD is centimetre level, and the speed accuracy is micrometres per second, finally the orbit accuracy is equivalent to that of the traditional unobstructed single positioning antenna for POD.

When the observation value is abnormal, the traditional robust estimation method only reduces the weight of the abnormal observation value, but does not repair the abnormal residual, and the abnormal residual statistics seriously limit the accuracy of noise variance estimation. Aiming at the above problems, this paper proposes an adaptive observation noise variance algorithm based on innovation repair. First, use the IGG III method to construct an equivalent weight function to reduce or give up weight from abnormal observations. Secondly, considering that abnormal observed values will lead to abnormal innovation, this paper uses the zero-mean constraint of innovation to estimate the sum of abnormal innovation, and then distributes it according to the ratio of abnormal innovation variance, to reduce the influence of abnormal innovation on statistical information. At the same time, considering that the innovation will approach the real situation gradually with the convergence of filtering, the innovation variance is calculated by combining the forgetting factor function to improve the accuracy of its statistical information. Finally, the observation noise variance is estimated in real-time by the function relationship between the innovation variance and the observation value variance. Simulation results show that the proposed method can guarantee the accuracy of noise variance estimation even with gross error and prior observation noise deviation. The accuracy of the filtering result is improved.

The purpose of this study is to verify the rationality and validity of directly adopting segmental modeling prediction of single-station regional scatter data by considering space environment information comprehensively. First, a single-station regional ionospheric model is constructed and predicted by the long short-term memory neural network (LSTM) method based on the single-station global positioning system total electron content (GPS-TEC) data of different regions (low-, mid-, and high latitude regions) and the space environment data. Then, the prediction results are compared and analyzed with the international reference ionosphere 2016 (IRI2016) model, CMONOC Regional Ionosphere Maps (RIM) data, and GPS measurement data. The results show that: i) the LSTM model forecasts are consistent with GPS-TEC observations at high, mid and low latitudes, and the forecast error is less than 3 TECu. The forecast accuracy is much better than that of the IRI2016 model and RIM TEC, and is less susceptible to anomalies. Geographically, the forecast MAE and RMSE of LSTM model decreases with increasing latitude. Among them, the relative accuracy of LSTM forecasts in low and mid latitudes is high, up to 82% or more; ii) the RIM data as a whole are more consistent with the measured data, but the RIM TEC is overestimated during the daytime, a phenomenon related to the discrete anomalies; iii) the IRI2016 model only captures the general trend of TEC. The IRI model forecast values are poor in daytime forecasting, and its overestimation becomes more obvious as the latitude increases, while the forecast performance is better in the evening. This study is a foundation for subsequent regional modeling and forecasting of the ionosphere, and can provide ionospheric constraints to support navigation positioning.

The whole Beidou Global Navigation Satellite System (BDS-3) constellation was completed and officially announced to provide global service on July 31, 2020. Apart from the global positioning, navigation and timing (PNT) service, BDS-3 also broadcasts real-time precise point positioning (PPP) corrections by 3 Geostationary Orbit satellites (GEOs) via PPP-B2b signal. At present, the PPP-B2b service for GPS/BDS-3 satellites is available for users in China and the surrounding area. In this paper, we conduct the PPP-B2b static and kinematic tests to evaluate the positioning performance of the BDS-3 new PPP-B2b service. Regarding PPP-B2b static positioning performance, the average positioning accuracy are 4.1 cm, 1.8 cm, and 5.2 cm in the east-, north-, and up-components, respectively. Additionally, the average horizontal and 3-dimensional positioning accuracy is about 4.5 cm and 6.9 cm. As to PPP-B2b kinematic positioning performance, the vehicle test results show that the overall positioning accuracy is 25.7 cm and 40.1 cm in horizontal and vertical components. It could be concluded that centimeter-level positioning accuracy is reached in static scenario, and decimeter-level positioning accuracy can be achieved in kinematic scenario.

BDS-3 provides signals on six frequencies nowadays. In this contribution, five groups of geometry-free phase combinations and one group of geometry-free pseudo range phase combinations are combined to detect BDS-3 ultra-multi-frequency cycle slips. Considering the ill-conditioned problem of cycle-slip estimation equations, a condition-number principle for optimizing coefficient combinations is presented. Combined with the condition-number principle, final coefficient combinations with long combination wavelength, small ionospheric delay amplification factor and small standard deviation are determined, which consider both cycle-slip detection and repair performance. Nevertheless, it often causes a failed cycle-slip repair due to the poor accuracy of float estimates on some frequencies. Therefore, a partial cycle slip repair method based on the LAMBDA algorithm is presented. Firstly, the LAMBDA algorithm with a threshold of 3.0 for the ratio test is performed. If the ratio test fails, the variances of all cycle-slip estimates are sorted from the largest to smallest, then the cycle-slip float estimates corresponding to the maximum variance and its variance are removed and the LAMBDA algorithm is performed again. Subsequently, the above steps are repeated until the ratio test passes. Noted that the number of remaining frequencies must be larger than 2, otherwise, stop the algorithm. The ultra-multi-frequency observations provide more iterative redundancy, making the partial cycle-slip repair method more reasonable. The algorithm is verified by BDS-3 observations. The statistical results show that the averaged success rates of the rounding method, LAMBDA method and our method are 78.37%, 88.65% and 98.70%. The average improvements of our method are 20.33% and 10.38% respectively.

Real-time precise point positioning (RTPPP) is a preferred method for ocean high-precision location services, but its positioning performance depends on high-precision state space representation (SSR) corrections. At present, Inmarsat are used to transmit SSR corrections in areas with poor Internet such as the open sea, but the communication cost is extremely expensive. Therefore, this study proposes a strategy of SSR encode and Beidou short-message broadcast for ocean RTPPP. On the one hand, for the limitation of the narrow bandwidth of Beidou short-message, a coding strategy combining difference and non-difference between epochs is adopted to make full use of visible satellites, and the resolution is readjusted so that a Beidou card can broadcast the number of satellites from 2 to 19. On the other hand, in order to overcome the limitation of low broadcast frequency of short-message, two Beidou cards are used to broadcast the SSR corrections of visible satellites at equal intervals within one minute, which can effectively reduce the data delay and enable RTPPP. The experimental results show that the three-dimensional positioning accuracy of the BDS/GPS combination is better than 0.35 m, and the horizontal positioning accuracy is better than 0.25 m.

Prediction of GNSS vertical coordinate time series is helpful to monitor crustal plate movement, dam or bridge deformation monitoring, global or regional coordinate system maintenance and so on. Machine learning is an effective method for time series prediction by manually inputting features, and its prediction results have strong interpretability. XGBoost algorithm is a machine learning algorithm that can evaluate features. It has good potential and stability for long-span time series prediction. By analyzing the applicability of XGBoost algorithm, a multi-station time series prediction model is proposed. Firstly, the model learns the characteristics of multi-station data in the data set, and then predicts the stations set as the target. The time series data of U direction from 2013 to 2015 at six stations such as BJYQ, BJSH and BJGB were selected for the experiment. The experimental results show that XGBoost algorithm has small prediction error and high prediction accuracy, and has strong generalization ability. It can be applied to GNSS time series prediction.

At present, the Beidou-3 global satellite navigation system (BDS-3) has been fully completed, which can provide the broadcast of four-frequency signals (BIC, B1I, B3I and B2a). Compared with triple-frequency or dual-frequency signals, four-frequency signals can form more extra-wide-lane/wide-lane (EWL/WL) combinations, which helps to the rapid resolution of ambiguity and the improvement of positioning performance. However, most of the current research on four frequency signals focuses on baseline solutions, and research in dynamic environments is not yet available. Therefore, the single epoch positioning performance of the BDS-3 four-frequency EWL/WL observation in the dynamic environment is studied in this paper. First, the BDS-3 four-frequency linear combination observation equation is given, the optimal linear combination is selected through certain criteria, and four linear combination schemes are analyzed. Then, the stepwise ambiguity fixing method of EWL/WL is used to obtain stable WL observation for positioning. Finally, the influence of the four linear combination schemes on the single-epoch dynamic positioning performance of the BDS-3 four-frequency EWL/WL observation are analyzed through vehicular experiment. The experimental results show that the dynamic positioning accuracy of schemes 1 and 3 are basically the same in the horizontal and vertical directions, both reaching the decimeter level. Therefore, the EWL/WL combination of scheme 1 and scheme 3 is better for dynamic positioning.

Low-orbiting satellites have the advantages of rapid geometric configuration changes and strong ground receiving signals, which have a significant effect on accelerating the convergence speed of precise single-point positioning. During the operation of the satellite, it is affected by many complex perturbation forces such as sunlight pressure, atmospheric resistance and empirical force, and its orbital changes are complex. At the same time, due to cost and weight constraints, high-precision atomic clocks are generally not equipped, and the long-term stability performance is poor. The accuracy of satellite orbit and clock error estimation has become the most important source of error affecting precision single-point positioning services. Therefore, it is necessary to realize the high-precision calculation of the low-orbit satellite orbit and clock error in real time. Estimating the solar pressure, atmospheric resistance and empirical power of low-orbit satellites requires a huge amount of observational data to participate in the calculation. This paper proposes a method to determine and predict the high-precision orbits and clock errors of navigation satellites and low-orbit satellites on the monitoring data of medium-high orbit satellites by global stations and low-orbit satellites, and use clock-error reduction algorithms to speed up the solution. Based on the data of IGS, the performance analysis of orbit and clock error estimation was carried out, and the estimation and forecast accuracy were obtained. On this basis, the simulation and analysis of the influence of orbit error and clock error error on the performance of precision single-point positioning. The methods and analysis results presented in this paper can provide a basis for the design of low-orbit navigation enhancement systems.

Two-way ranging and communication between satellites by inter-satellite link (ISL) is an important innovative design of BDS-3, which can make up for the disadvantage of regionally distributed network and realize the tracking and measurement for the whole arc of navigation satellites. By introducing ISL measurements into orbit determination processing, the orbit accuracy can be effectively improved. The influence of ISL measurement geometry on satellite orbit determination accuracy is evaluated. Taking the post-processed satellite orbit solutions provided by IGS as references, the orbit accuracy of BeiDou satellites under different conditions is evaluated. The results show that in the case no ISL measurements, the user ranging error (URE) of satellite orbit is about 0.3 m. With all ISLs used, the orbital URE is below 0.08 m. Then, the influence of the number of the ISLs on orbit determination accuracy is further investigated. The results show that when the number of ISLs between satellites is reduced by 17%, 24% and 40%, respectively, the accuracy loss of orbit in radial component is only at millimeter level, and the loss in tangential and normal component is at centimeter level, thus the accuracy loss can be neglected. Even if a satellite has only two ISLs, the orbital URE is only increased to 12 cm, which indicates that the satellite orbit can still maintain relatively high accuracy in the case of only a few links. This provides a reference for the operator to formulate the plan of ISL.

A new precise point positioning (PPP) service has been provided by BeiDou global navigation satellite system (BDS-3). The correction parameters are broadcasted by PPP-B2b signal of GEO satellites in real time, including precision orbit correction, clock difference correction and et al. for BDS-3 and other GNSS. The PPP service can be realized with dynamic decimeter level and static centimeter level at China and surrounding areas. Firstly, the area of PPP-B2b service is analyzed based on the threshold of DOP value, and the concerned problems are also pointed out in use, such as the matching problem between correction parameters. Then the evaluation is conducted for three types of correction parameters broadcasted by PPP-B2b. Lastly, the performance of static PPP and kinematic PPP is also evaluated comprehensive, and suggestions is also gave for the PPP-B2b applications.

The earth orientation parameters (EOP) who connect the earth-fixed coordinate frame and celestial coordinate frame are the important input parameters for GNSS precise orbit determination (POD). The earth rotation parameters are also one of the core products of GNSS service. The third generation Beidou Global Navigation Satellite System (BDS-3) provides global high-accuracy service because of the benefit from Inter-satellite link measurement. It is of great significance to study the enhancement of inter-satellite link measurement on ERP products. This paper analyzes the mathematical relationship between ISL measurement and ERP, designs the experiment, and analyzes and summarizes the results. For BDS-3 constellation POD based on regional stations, the ISL measurement has improved the accuracy of orbit radial, along and cross directions by 97%, 60% and 46% respectively. xp accuracy of ERP pole motion improved by 69%, the length of day (LOD) accuracy improved by 69%. The results show that, in the integrated processing of BDS-3 POD and ERP, the ISL measurement has a significant enhancement on orbit and ERP accuracy based on regional stations. The experiment and conclusions in this paper are significant for high-precision ERP product solution with regional stations, which is applied to BDS-3 operation control system.

Mercury ion microwave clock has great prospect in timekeeping and space applications for its excellent frequency stability and very low drift rate. In recent years, we have been studying the method to maintain the sealed vacuum system with getters for mercury ion microwave clock. This technology, which can reduce the size, weight and power consumption (SWaP) and greatly improve the reliability of the vacuum system, plays the key role in developing the mercury ion microwave clock from laboratory to practical application. In this letter, we present a multipole trap mercury ion clock developed for ground timekeeping applications using sealed vacuum system. Based on the ion shuttling between the quadrupole and 12-pole trap, the sensitivity of ion number dependence effect and external magnetic field could be effectively suppressed, which promising a better long-term stability than conventional single quadrupole trap system. The optical system is also optimized to enhance the signal to noise ratio (SNR) of the clock spectral line. To date, the ion clock physical package has been built. The clock transition spectral is measured in quadrupole trap region firstly. That shows a stability limit of 7.29  × 10–14 at 1s according to the shot noise. The signal of ions shuttling between the two traps is also observed. The near 100% shuttling efficiency has been demonstrated even after 50 times ion shuttling.

Compact cesium beam clocks play significant roles in navigation, time-keeping and precision measurements. In comparison to the traditional detection method using inhomogeneous magnetic fields, ionizers and electron multipliers, the optical detection method avoids complicated structures. In consequence of introducing laser to the system, the light shift influences the clock’s long-term stability. We present a new method to suppress the light shift by using pulsed light instead of continuous light. The method only detects part of the atoms which do not interact with light and microwave simultaneously therefore reduces the light shift. We demonstrate the validity and the results correspond to our expectation in different pulse duty cycles and pulse frequencies. We test this method on a clock which adopts the optically detected magnetic-state-selection scheme. Under optimum value conditions light shift coefficient is reduced from (1.63 ± 0.04)E–12/mW to (1.15 ± 0.03)E–13/mW. The method can be used to optimize the long-term frequency stability of cesium beam clocks.

To improve the accuracy of the satellite rapid clock bias, a modified Elman neural network clock bias prediction method based on particle swarm optimization (PSO) algorithm is proposed. The Elman recurrent neural network is introduced to predict the clock bias, its weights and thresholds are improved by PSO algorithm to improve the training speed and prediction accuracy. Then, the optimization method is applied to the rapid clock bias prediction, and the steps of using this method for the rapid clock bias prediction are given. Finally, the optimization method is compared with common quadratic polynomial model, gray model and ultra rapid clock bias product IGU-P. The results show that the PSO-Elman model achieves high accuracy and stability for four different types of GPS satellite clock, and its prediction accuracy and stability improved by 85%, 74%, 89% and 71%, 53%, 28% compared with QPM, GM(1,1) and IGU- P products, respectively.

After officially announced the service of BDS-3 system, the promotion and industrial application of BDS-3 is a new highland for BeiDou innovation and development. Satellites’ performances are one of prerequisite for high-accuracy and high-reliability location-based services, in which the atomic clock is playing an important role as the main technology advantage. In order to evaluate the reliability of GNSS and BDS-3 on-orbit atomic clock, this paper compared and analyzed the main technical indicators of the on-board atomic clock based on the GNSS satellite product sequence accumulated by iGMAS Analysis Center. Firstly, using GNSS and BDS-3 satellite clock offset products of 5 years and 2 years respectively, the clock offset performance of each system is analyzed from the aspects of phase, frequency, frequency drift and fitting residuals. Then, the overlapping Hadamard variance is used to evaluate the stability of the atomic clocks. The results indicate that: 1) the continuities of GPS, GLONASS, Galileo and BDS-2 on-board are poor during 2015–2017, in which the phase jumps are relatively obvious. After 2008, the qualities of phase data are improved with fewer modulation operations. Meanwhile, BDS-3 presents a better continuous and high-quality clock for 2019–2020 with less phase-modulation operation. 2) the frequency drift values of GPS, GLONASS, Galileo and BDS-3 satellite clocks are all in the order of 10–19, while the frequency drift values of BDS-2 satellite clocks are in the order of 10–18. In terms of the overall variation trend, the frequency drift of GPS, GLONASS and BDS-2 systems is relatively stable, while the frequency drift of Galileo and BDS-3 systems presents an obvious segmentation phenomenon. The frequency drift of satellite clock of BDS-3 system will increase by one order in 2020 compared with that of 2019, reaching the order of 10−20. 3) the RMS of fitting clock models for GPS, GLONASS, Galileo, BDS-2 (GEO/IGSO/MEO) and BDS-3 are 0.62 ns, 0.72 ns, 0.99 ns, 1.97/1.61/1.45 ns and 0.85 ns, respectively. 4) The stability of GPS, GLONASS and BDS-2 atomic clocks is maintained at the same order of magnitude, namely 10−13 and 10−14 for integration time of 1000 s and 10000 s, respectively. Some of the Galileo and BDS-3 satellites are equipped with high-precision hydrogen clocks, both of which have stability in the integration time of 10000 s with order of 10−14.

RNSS timing is one of the basic services of BDS, it is of great significance to monitor the timing accuracy and integrity. Aiming at the problems of current RNSS timing monitoring methods and taking advantage of BDS-3 PPP service, this paper designs a timing monitoring method based on B2b signal called B2b-TM. Firstly, the BDS-3 PPP service was introduced. Then, the specific implementation process and key algorithm of B2b-TM method was discussed in detail. The data of several iGMAS stations were used to verify the feasibility of B2b-TM method, experiment result shows that the BDS-3 RNSS timing accuracy is 9.0 ns using B1C frequency and 15.8 ns using B2a frequency. There are great differences in timing service at different areas and different periods, which reveals the necessity of distributed timing monitoring nationwide.

A low temperature-sensitive microwave-vacuum integrated Ramsey cavity (MVIC) used for Rb fountain clocks is proposed to solve the problems that the clocks have a small operating-temperature range and are sensitive to the ambient temperature changes. This cavity mainly consists of a tube made of titanium (Ti) and two end caps made of oxygen-free copper (OFC), forming a cylindrical microwave resonator (CMwR) working at TE011 mode. Utilizing the different thermal expansion of the tube and the end caps, the change of the cavity resonance frequency (ReF) to temperature can be self-compensated. To improve this cavity quality factor Q, the tube inner surface is coated by a thin copper film fist and then by a thin gold film on the top. There are two coupling holes (C-holes) face to face on the tube wall for microwave coupling. Each C-hole is vacuum-sealed with a ceramic window (CW) first. And then it is covered by a rectangular waveguide. Two microwaves are fed into the waveguides then coupled into the CMwR through the CWs, respectively. For the prepared MVIC for Rb fountain clocks, its Q-factor is measured to be 11500 and its ReF matches the Rb clock frequency within −49 kHz. And its ReF thermal-coefficient is measured to be −16.3 kHz/℃, which is 7.1 times lower than that of a commonly used OFC Ramsey cavity with the same sizes in the temperature range of 22.48 ℃–34.48 ℃. Additionally, this cavity ReF can be tuned about 130 kHz after performing a further bake-out for the fully assembling clock physical package.

This article introduces the development status of an ultra high-performance physics package (PP) for rubidium atomic clock. In order to increase the number of atoms participating in the resonance transition and enhance the atomic transition signal, we have appropriately increased the size of the PP. At the same time, we also have improved and optimized the microwave cavity, spectral lamp, filter components and the overall PP structure. And a new physics package with a Φ40 mm microwave cavity has been designed. We have conducted a comprehensive experimental research and theoretical analysis on the PP. Based on the measured PP parameters, we have evaluated that the contribution of the shot noise of the PP to frequency stability is 5.1 × 10−14τ−1/2. Preliminary test results suggest that the rubidium atomic clock with this new PP can reach the short-term frequency stability of 1.5 × 10−13τ−1/2 (1–100 s). This is the best short-term frequency stability of the lamp pumped vapor-cell rubidium atomic clock reported at home and abroad up to now, and the result is equivalent to the performance of the highest level laser pumped rubidium clock.

With the successive large-scale launches of low-earth orbit satellites (LEOs), satellite-based augmentation systems (SBAS) have become an important supplementary part of the GNSS system. However, the emergence of new concepts such as B5G/6G, national integrated positioning, navigation and timing systems (PNTs), has brought new challenges to the integration of navigation and communication (NavCom), but the core issue is still the challenge of the signal system. This paper proposes a new signal scheme. Through preliminary research on the same frequency band or adjacent frequency bands, it is found that this scheme is more suitable for S-band and has a wider normalized power spectral density (PSD) and peak sidelobe ratio (PSR). And the multi-peak characteristics of autocorrelation. Through the analysis of simulation performance evaluation, it is found that the proposed scheme has high potential positioning accuracy. The code tracking accuracy can reach 0.85 m and the carrier-to-noise ratio (CNR) is 20 dB⋅Hz. The proposed signal has less mutual influence with other candidate signals, and has better anti-multipath ability. At the same time, it is in terms of code tracking anti-matching spectrum interference factor, demodulation anti-matching spectrum interference factor, and demodulation anti-narrowband interference factor, the proposed signal also has excellent performance. Therefore, from the perspective of technical feasibility and theoretical evaluation, the signal proposed in this paper is superior to other candidate signals. And from an application point of view, the solution we propose can be used as a competitive potential signal solution for BDS in the future, and it is also B5G/6G foundation and PNT.

Pulsar navigation technology is an important technology in the construction of national integrated positioning and navigation timing (PNT) system. It can provide high-precision autonomous navigation service and high stable time-frequency reference. High precision pulsar signal propagation model is the prerequisite for realizing high-precision navigation and high stability pulsar time. In view of the inconsistency of existing pulsar observation models and the need to expand the application scope of pulsar navigation and time service to deep space, under the framework of general relativity, through the geometric. The gravitational delay formula of pulsar signal under the second-order post Newton effect in the solar system is analyzed and deduced, and a universal pulsar observation model in the solar system is established. According to the influence magnitude of various time delays, a simplified observation model in near earth space with accuracy better than 1ns is obtained.

With the rapid development of wireless communication technology, people have higher and higher requirements for positioning and navigation services. However, due to the existence of non-line-of-sight in the complex indoor environment, the accuracy and robustness of TDOA-based positioning methods are drastically reduced. In order to reduce the distance error in TDOA positioning, this paper proposes a TDOA positioning algorithm based on adaptive threshold function wavelet transform, which uses the low-pass filtering characteristics of discrete wavelet transform and multi-resolution analysis capabilities to perform multi-scale decomposition of positioning signals. The wavelet coefficients obtained by the decomposition are processed, and the pre-processed signal is finally reconstructed to achieve the effect of suppressing the Non Line of Sight (NLOS) error. The experimental results prove that in non-line-of-sight environments, the improved algorithm improves the positioning accuracy, reduces the computational complexity, and has better performance than the traditional wavelet transform-based TDOA algorithm.

Gravity matching aided navigation is an important technical means for the underwater passive navigation system. Accurate and stable matching navigation algorithm is the key factor determined the underwater gravity navigation performance. However, the matching navigation performance of current algorithms would be significantly reduced by short gravity sampling length, large measurement noise, or the flat gravity change in the matching area. In this paper, a matching algorithm combining fast search strategy and spatial feature matching for underwater gravity navigation is proposed. The proposed algorithm integrates the numerical values and spatial structure of gravity sequences to evaluate the correlation between real-time maps and reference maps. In addition, a multi-scale search strategy based on contour constraints was added in gravity matching search process to improve the matching efficiency, which effectively dwindled the number of search points in the matching area. Multiple matching areas located in the South China Sea were selected to conduct gravity matching navigation simulation experiments. Three sets of experiments were designed based on different gravity sampling lengths, gravity measurement accuracy, and gravity matching areas. Furthermore, some matching algorithms such as MSD, MAD, NCC, NCCDM, NMSD were selected for comparative analysis. Simulation results showed that under the same measurement conditions, compared with the existing algorithms, the new fast spatial feature matching algorithm proposed in this paper could obtain a significantly better positioning accuracy, matching success rate, and matching efficiency than others. Moreover, the proposed method was more flexible in practical application with lower requirements for sampling length, gravity measurement accuracy, and gravity matching area, and other environmental conditions. This algorithm provides a novel technical means for marine experiments of gravity matching aided navigation, underwater integrated navigation, and future practical underwater PNT.

The rapid deployment of 5G systems and the new communication technologies adopted in system design make “5G positioning” a new direction to the problem of high-precision positioning. This paper studies the opportunistic navigation method using 5G downlink cellular signals. Then proposes a software-defined receiver (SDR) that extracts navigation observations from 5G cellular signals and completes the signal acquisition and tracking. In view of the intermittent broadcast characteristics of 5G reference signals, the traditional Delay Locked Loop (DLL) tracking loop cannot perform long-term coherent integration of this type of signal, the tracking accuracy is limited and the loop robustness is poor. This paper proposes a method of intermittent signal tracking combined with DLL and Kalman Filter (KF), derives a signal model based on the 5G intermittent signal tracking loop, and modifies the traditional DLL code phase discrimination function. The output of the discriminator is used as the KF filter observation. At the same time, this paper proposes for the first time to compensate residual frequency offset on different subcarriers of OFDM signals to reduce the influence of frequency offset on code phase estimation. Further, from the perspective of multi-dimensional resource joint optimization in time domain, frequency domain and space, A Signal tracking scheme of Positioning Reference Signal (PRS) and Channel State Information Reference Signal (CSIRS) is proposed. Estimation and correction of the observed noise in the tracking process are carried out in the iterative process. Experimental results show that compared with the traditional DLL tracking results, the tracking loop processing method proposed in this paper can effectively improve the code phase tracking accuracy.

Most of the existing indoor visual positioning of smartphone are depending on pure vision methods. The sparse feature point clouds are obtained by 3D reconstruction of image sequences, and then the query image is matched with the point clouds. This method has a problem of poor robustness in practical application, and is very vulnerable to the environment, resulting in large positioning errors. In this paper, lasers and RGB images data of the mobile measurement system are used to generate the RGBD images. A new indoor vision positioning method based on location recognition and geometric solution is proposed and implemented based on the RGBD images; Aiming at the influence of the distribution of image feature points on the positioning results, a representation method of the number of effective feature points is proposed to avoid the large positioning error caused by the excessive concentration of feature points; According to the characteristics of smartphone indoor visual positioning, this paper explains the necessity of output-ting positioning confidence from visual positioning results, and analyzes the feasibility of judging positioning confidence by using elevation difference and PDOP value of spatial feature point distribution. The experimental results demonstrate that the 3D positioning error of this method is 0.43 m (1σ) and 3.07 M (2σ). It has the advantages of high precision and good robustness, which meets the accuracy requirements of smartphone indoor positioning. It provides a novel idea for the practical promotion of smartphone indoor positioning based on vision.

The measurement noise in underwater SINS/USBL integrated navigation is often non-Gaussian due to the influence of the multipath effect. In this case, applying traditional filter algorithms will result in reduced accuracy. To solve this problem, this paper combines the maximum correntropy criterion with Kalman filter, proposes a robust Kalman filter algorithm based on MCC, which can adjust the kernel bandwidth adaptively. Finally, Kalman filter (KF), Huber-KF, MCC-KF, and the proposed algorithm are applied to the SINS/USBL integrated navigation for comparative analysis. The results of the simulated experiment verify that the proposed algorithm can improve navigation accuracy significantly under the environment of non-Gaussian measurement noise.

The carrier phase has a higher positioning accuracy than the pseudorange measurement value, and the dual-frequency combined observation is an effective method to eliminate the observation error and fix the carrier ambiguity. However, in the base station positioning scenario, the accuracy of clock synchronization between base stations is not high, and there is a strong correlation between clock deviation and carrier phase ambiguity, which limits the convergence speed and success rate of traditional ambiguity fixed methods. For this reason, this paper proposes a center iterative optimization (CIO) ambiguity fixed algorithm based on dual-frequency combination, which eliminates the influence of base station and receiver clock deviation through dual-frequency combination of carrier phase observations. The dual-frequency ambiguity mapping relationship is established, and the objective function is determined according to the posterior probability of the ambiguity and the center distance weighting matrix, and finally the optimal value of the ambiguity is obtained by searching within the constraint condition. The simulation results show that the ambiguity fixed speed and the fixed success rate of the algorithm proposed in this paper are increased by more than 33.3% and 6.3%, respectively, compared with the traditional Bootstrapping algorithm and the LAMBDA algorithm.

In underwater acoustic long baseline navigation, the motion state of underwater vehicle is changeable and there are abnormal observations, which reduces the navigation accuracy of traditional filtering algorithm and cannot meet the demand of high precision underwater navigation. To solve this problem, this paper proposes an improved robust interacting multiple model algorithm. Firstly, the robust estimation of each model is carried out, and the equivalent variance and model probability of each model are obtained. The weight of equivalent variance is determined according to the model probability, and the mixed equivalent variance is obtained by weighted summation of equivalent variance. The mixed equivalent variance is used to replace the measurement noise variance in each model for state estimation, and the interacting robust estimation is realized. Then the model probability is updated, and the power function with faster growth rate is used to replace the matching model probability to realize the model probability correction. Finally, the final state estimation value and its covariance matrix are obtained by weighted summation of the results of the interacting robust estimation of each model according to the revised model probability, so as to improve the navigation accuracy and stability of underwater vehicles. By processing simulation and measured data, the results show that compared with Kalman filter, interactive multi-model and robust interactive multi-model, in the simulation data, the navigation error of the proposed method is reduced by 64.18%, 26.35% and 10.61%, respectively; in the measured data, the navigation accuracy of this method is improved by 31.79%, 14.76% and 14.93% respectively, and the navigation accuracy reaches 3.7687 m in 3 km × 3 km. Compared with the traditional filtering algorithm, the improved robust interacting multiple model algorithm can significantly improve the navigation accuracy and stability of underwater vehicles.

We present a node layout algorithm based on NSGA-II for Communication and Navigation Fusion System (CNFS), to address the issue that the impact on communication service should be considered jointly in positioning network planning. CNFS mostly adopts co-site deployment scheme to reduce deployment and maintenance costs, and node layout has a significant impact on network performance. This paper employs ray tracing technique to accurately predict indoor signal propagation path, develops a set of network performance evaluation criteria, and then determines the layout scheme using RSRP, SINR and average positioning error as the objective functions of the multi-objective optimization algorithm. This algorithm can reduce the negative effects of multipath and NLOS propagation on positioning while maintaining communication performance. The simulation results show that the proposed algorithm outperforms the random layout algorithm in terms of communication and positioning network performance, with the communication performance improving by 23.5% when compared to the existing location network planning algorithm.

Aiming at the problem of cross-correlation interference in a terrestrial code division multiple access (CDMA) positioning system, this paper proposes a Pseudo-code Generation with Transform Coefficient (PGTC) model. When the receiver is trying to capture the weak signal, the working signal channel extracts code phase, Doppler frequency and other parameters from the strong signal tracking loop. By calculating the cross-correlation value of the strong and weak signals in the next cycle, the working signal channel can determine the local pseudo-code transform coefficient. The pseudo-code generator generates a new local replica pseudo-code, which tends to be orthogonal to the strong signal pseudo-code in the received signal, thereby suppressing cross-correlation interference, and the receiver can capture and track weak signal. This model comprehensively considers the working mechanism of the receiver code loop, and can simultaneously reduce the cross-correlation interference of the early, prompt and late codes of the code loop. Data bit transition will cause a non-linear change of the pseudo-code. With the assistance of AGPS providing navigation message data bits, PGTC model is suitable for the situation of data bit transition. The tracking effect of weak signal is evaluated through simulation, which shows that PGTC model can effectively suppress the cross-correlation interference.

The robot realizes the perception of its own location through the fusion of multiple navigation sources. However, there are limits in application scenarios and cost for various navigation sources such as vision, laser, and inertial measurement unit. Therefore, a robust magnetic field loop closure detection for low-cost robot’s localization and mapping method is proposed in this paper. In front-end, The MEMS inertial measurement unit and wheel odometer are fused to estimate the pose state of the robot, andmagnetic field sequence loop closure is detected in DTW algorithm, and a general graph optimization method is applied to optimize the pose in back-end. Experiments show that this method can effectively detect the magnetic sequence loop closures and eliminate the cumulative error in inertial recurrence, realize the long-time continuous indoor positioning of the robot.

The application of differential navigation technology can eliminate the influence of pulse ephemeris error, which can improve navigation accuracy. The paper proposes a differential X-ray pulsar navigation method, which is based on the time difference of pulse arrival. The method firstly uses the photon arrival sequence to get the pulse arrival time difference (TOA), then difference the current moment from the previous moment TOA, which constructs the navigation measurement equation. In this paper, robust unscented Kalman filter is used to solve the uncertainty of measurement model. The paper analyses the influence of ephemeris error on photon TOA correction and observation equation, infer the differential navigation measurement model and measurement noise covariance matrix. Simulate and verify three Mars orbits at different altitudes at different observation time. The simulation results show that the navigation accuracy of the standard X-ray pulsar navigation method decreases by about 60% when the error is $$0.007^{\prime\prime}$$ 0 . 007 ″ . The proposed differential navigation method can improve the navigation accuracy by 24%–31%.

With the continuous development of the lunar exploration mission, it is very important to obtain the real-time and accurate position, speed, and time information of the spacecraft near the moon. However, with the increase of distance, the GNSS signal becomes weaker and weaker, and it becomes very difficult to use GNSS to realize navigation and positioning near the moon. In this paper, the GNSS signal power, the number of visible satellites, and the geometric distribution near the lunar orbit are analyzed. This paper proposes a method of using ground station for GNSS navigation enhancement to realize lunar GNSS navigation and positioning. By setting up a ground station on the earth, the navigation enhancement signal pointing to the moon is broadcast. This can enhance the information of lunar orbit GNSS receiver and improve the signal acquisition sensitivity of lunar orbit GNSS receiver. It can also provide its own ephemeris information, improve the visible navigation satellite geometry, and improve positioning accuracy. Simulation results show that this method can realize GNSS navigation and positioning near the moon.

Simultaneous localization and mapping (SLAM) are playing an increasingly important role in the field of robotics and autonomous driving. However, when mapping indoor and outdoor large-scale scenes, due to the sparseness of multi-line lidar point clouds, it is difficult to extract features in some scenes, which seriously affects the accuracy and robustness of lidar odometry. Aiming at this problem, this paper proposes an accurate localization algorithm for 3D lidar based on image semantic information constraints. Firstly, the lidar and camera timestamps are synchronized, then the point cloud is projected to the image coordinate system through the transformation matrix; Secondly, the static target semantic information is extracted through the SFSegNets network, and the depth value of the pixels in the area is obtained by interpolation according to the depth information of the point cloud, so as to realize the calculation of the semantic 3D position; Finally, the extracted semantic information of the image is used as landmarks to form constraints with the point clouds at the back end of the lidar odometry for localization optimization. In order to verify the performance of the algorithm proposed in this paper, experimental tests are carried out on the KITTI dataset and the actual campus scene, which both show that loop closures can be effectively detected after adding semantic information constraints. In the KITTI data set experiment with evo evaluation, the absolute error of the odometry has an average improvement of 1.64% after adding image semantic constraints.

The time difference RTK (TDRTK) of GNSS can obtain high-precision relative position information, which can be used to constrain the cumulative error of positioning methods such as inertial navigation system. However, with the increase of time interval, the cumulative error over time seriously affects the fixed success rate of differential ambiguity and relative positioning accuracy. Through in-depth analysis of the factors affecting TDRTK, it is found that the epoch difference of broadcast ephemeris error can reach the decimeter level, which is the main factor affecting the fixed success rate of differential ambiguity. In this paper, the influence of ephemeris error on the positioning is weakened by three carrier ambiguity resolution and robust M-estimation, and the quality of positioning accuracy con-trolled by the isotropy-based protection level. Experimental results show that this method can effectively improve the fixed success rate of differential ambiguity and positioning accuracy.

Global Satellite Navigation System (GNSS) can provide accurate time and space information for Space-Ground Integrated Network (SGIN) to support the application in various fields. However, GNSS has inherent vulnerability and cannot provide continuous and reliable positioning and timing services for SGIN users. The quasi-GNSS augment system (QGAS) is used to provide positioning and timing enhancement services for SGIN. QGAS distributes over a wide area, and the heterogeneity of the network poses a significant risk to the security management of the system. The traditional centralized network security technology is not suitable for QGAS. In view of the network spoofing threat of QGAS, a novel security management technology based on consortium blockchain for QGAS is proposed. The architecture and the workflow of the system are given. Security analysis show that the proposed framework can be used as an efficient way to ensure the reliability of PT information, supporting QGAS as a supplement and backup to GNSS. Together, they can provide SGIN with accurate time and space information

BeiDou Navigation Satellite System (BDS) can provide positioning, navigation and timing (PNT) service with high-precision and wide-coverage. However, in special scenarios such as urban-canyons and indoor areas, the positioning performance will degrade caused by the limitation of signal transmission. To solve this problem, a new communication and navigation integration (CNI) technology based on Open Radio Access Network (OpenRAN) architecture is proposed. This new architecture, using a new 5G white-box basestation (WBBS), has better compatibility than the classical architecture. And an integrated positioning protocol is implemented on WBBS to meet the communication service and support the real-time broadcasting of Beidou’s auxiliary enhancement information. Furthermore, a new integrated positioning scheme of outdoor “WBBS + A-RTK” and indoor “WBBS + Beidou pseudolite basestation” are suggested to satisfy the specific scenario using cases. In the end, the test results showed that the outdoor “WBBS + A-RTK “ system can provide real-time positioning services with centimeter-level accuracy, and the indoor “WBBS + Beidou pseudolite basestation” system can provide real-time positioning services with sub-meter-level accuracy.