GNSS Measurement Technique in Aerial Navigation

The Global Navigation Satellite System (GNSS) time series non-constructive deformation shows significant seasonal variations, and the study of its periodic term components and possible physical mechanisms has important theoretical significance and application value for the accurate use of the data and more in-depth analysis. In this paper, wavelet transform (WT) is used to extract the seasonal terms of 24 GNSS continuous station time series, Gravity Recovery and Climate Experiment (GRACE) displacement time series and precipitation data in the Sichuan–Yunnan area, and the three data sets are compared and analyzed in terms of amplitude, phase and cross-correlation coefficient (CC), and the results show that the seasonal deformation in the area is strongly related to the precipitation variation. GNSS and GRACE have good consistency in the vertical component, and the seasonal variation is mainly related to the hydrological load; the difference in the horizontal component is obvious, and the amplitude of the seasonal term of GNSS is larger than that of GRACE, indicating that the resolution of GRACE in the horizontal component is lower than that of the vertical component, and the overall estimation accuracy is lower than that of GNSS. There are significant seasonal terms of annual and semi-annual cycles for the three GNSS components, and the vertical component mainly shows the seasonal deformation of the annual cycle with the strongest seasonality; the horizontal component mainly shows the deformation of the semi-annual cycle, and the seasonality of the N component is stronger than that of the E component, and they are negatively correlated with a coefficient of −0.90. Full article

The global navigation satellite system has achieved great success in the civil and military fields and is an important resource for space-time information services. However, spoof interference has always been one of the main threats to the application security of satellite navigation receivers. In order to further improve the application security of satellite navigation receivers, this paper focuses on the application scenarios where narrowband and spoofing interference exist at the same time, studies the problem of spoofing interference detection under mixed interference conditions, then proposes a spoofing interference detection method based on the tracking loop identification curve. This method can effectively deal with the detection of spoofing interference under the conditions of narrowband interference and, at the same time, it can effectively detect the spoofing interference of gradual deviation. Simulation experiments verify the effectiveness of the spoofing interference detection method, based on the tracking loop discrimination curve. In typical jamming and spoofing scenarios, when the spoofing signal is about 7.5 m away from the real signal, the method used in this paper can achieve effective detection. The proposed detection method is of great significance for improving the anti-spoofing capability of satellite navigation receivers. Full article

With the increase in satellites in the medium Earth orbit (MEO) region, there should be a focus on orbit safety in the MEO region. A safe orbit disposal strategy is necessary to maintain the sustainability of the MEO region. This paper focuses on long-term evolution modeling, safety analysis of MEO objects, and different disposal techniques for end-of-life BDS-2 MEO satellites. On the one hand, a long-term numerical evolution model is established, and mean equinoctial elements are adopted to propagate a long-term orbit. Long-term evolution for the MEO region over 100 years is carried out, including the Galileo, BDS, GPS, and GLONASS constellations. The earliest orbit intersection time with other global navigation satellite system (GNSS) constellations is put forward. On the other hand, a dynamic model and an optimization model for disposal orbit are established, which minimize the eccentricity growth within 200 years and the fuel consumption for maneuvering to the disposal orbit. The bounds for the disposal region of BDS MEO satellites are also proposed, which consider the measurement and control error of BDS MEO satellites and the eccentricity bounds for end-of-life BDS MEO satellites. A genetic algorithm is adopted to optimize the orbital elements for end-of-life BDS MEO satellites. In addition, two disposal cases, namely, upraising and reducing the orbit, for end-of-life BDS MEO satellites are simulated. The long-term evolutions for the disposal of orbital elements within 200 years are implemented, and the fuel consumption is calculated. The results show that the current MEO region is relatively safe and that the eccentricity is the most important factor that influences the long-term evolution of safety analysis for BDS MEO disposal orbits. Upraising the orbit is safe for end-of-life BDS MEO satellites. This investigation provides the theoretical foundation for investigating the long-term evolutionary mechanisms of the MEO region and references disposal strategy analysis for decommissioned navigation satellites, and the spent upper stages for other GNSS constellations. Full article

In emergency response and disaster rescue, unmanned aerial vehicles (UAVs) onboard thermal infrared (TIR) sensors are an essential means of acquiring ground information in the nighttime working environment. To enable field personnel to make better decisions based on TIR video streams returned from a UAV, the geographic information enhancement of TIR video streams is required. At present, it is difficult for low-cost UAVs to carry high-precision attitude sensors and thus obtain high-precision camera attitude information to meet the enhanced processing requirements of UAV TIR video streams. To this end, this paper proposes an improved Kalman filter algorithm to improve the geographic registration (geo-registration) accuracy by fusing the positioning and heading data from the dual-antenna real-time kinematic global positioning system (RTK-GPS) with onboard internal measurement unit (IMU) data. This method can yield high-precision position and attitude data in real time based on low-cost UAV hardware, based on which high-precision geo-registration results can be obtained. The computational complexity can be reduced compared with video stream feature tracking algorithms. Furthermore, the problem of unstable matching due to the low resolution and texture level of TIR video streams can be avoided. The experimental results prove that the proposed method can reduce the registration error by 66.15%, and significantly improve the geo-registration accuracy of UAV TIR video streams. Thus, it can strongly support the popularization and practicality of the application of augmented reality (AR) technology to low-cost UAV platforms. Full article

High-output-rate relative positions are required for high-speed safety-critical kinematic-to-kinematic applications such as pre-crash sensing and shipboard landing. We propose a real-time, high-output-rate relative positioning method based on the integration of a real time kinematic (RTK) differential global navigation satellite systems (DGNSS) relative positioning algorithm, carrier-phase-based tightly coupled GNSS/Inertial navigation system (TC-GNSS/INS) integration algorithm and polynomial prediction algorithm for position increment. We focus on the rarely studied issue that data broadcast rates and sampling rates have effects on the integrated relative positioning accuracy under different motion states of a moving base. A vehicle-to-vehicle field test with a frequently turning base demonstrates the advantages of the proposed method, such as low bit rate of broadcast data, high output rate of position solutions and excellent real-time tolerance of latency. The results show that compared with the 10-Hz output of sole RTK DGNSS relative positioning, the proposed method can provide centimeter-level-accuracy relative positions at an output rate of 125 Hz with a sampling rate of 1 Hz, and the bit rate can be reduced by 83.12%. A UAV-to-boat field test with straight-line-motion moving base is then carried out to validate the applicability of the proposed system for aircraft applications. The results show that the broadcast rate of position increments of the moving base can be further reduced. Full article

Frequency-domain anti-jamming technology is a common anti-jamming method for satellite navigation receivers. 1/2 overlapping windowing can effectively solve the spectrum leakage in the frequency domain conversion process, but the traditional window function will cause the loss of signal energy. This paper proposes a window function design method with no loss of signal energy, which can effectively solve the signal energy loss caused by the window function. The feasibility of the proposed method is theoretically deduced, and the effectiveness of the proposed method is verified by simulation and measured data. Compared with the traditional window function, the signal-to-noise ratio improvement of the method proposed in this paper is better than 0.5 dB. The frequency domain anti-jamming processing is optimized, the signal-to-noise ratio loss caused by the anti-jamming processing is reduced, and the anti-jamming performance is indirectly improved. This plays an important role in the performance optimization of satellite navigation system links. Full article

A satellite navigation system makes it simple to find and navigate to a specific position. Although a carrier measurement is required to establish a precise position due to the characteristics of the carrier observation, it is difficult to determine a robust position in a poor signal reception environment such as urban areas. Various studies are being carried out to overcome this problem, with cycle slips being the most important factor. With only a single frequency, it is very challenging to detect cycle slips in multiple satellite channels at the same time. A geometry-based technique is proposed in this study as a technical solution for detecting simultaneous cycle slips for multiple channels utilizing only a single-frequency receiver. The method could detect a half-wavelength size of cycle slip for each channel through the geometry information. Full article

The main purpose of this article is to evaluate the comprehensive performance of two inter-frequency code bias (IFCB) models using undifferenced and uncombined observations. These two IFCB models estimate IFCB parameters for each GLONASS satellite (EG model) and IFCB parameters using a quadratic function of frequency channels K (K = −7…6) (QF model). The data sampled in 30 s from 140 stations of the IGS network on 1–7 September 2021, are used for this study. We analyze all the combinations, including the GLONASS data, from the perspective of positioning accuracy, convergence time, and data utilization. The results show that the positioning accuracy of these two IFCB models for the same combination is comparable in three directions in both static and kinematic modes under long-term observation; the positioning accuracies of each IFCB model for all the combinations are almost the same in three directions in static mode, and the positioning accuracy of the combinations including the GPS data in three directions is better than that of the combinations not including the GPS data for kinematic mode. For some combinations, such as GLONSS-only and GPS/GLONASS, the convergence time of the EG model is better than that of the QF model, but the improvement rate does not exceed 22%. However, for other combinations, such as GLONASS/BDS and GLONASS/BDS/GALILEO, the convergence time of the QF model is better than that of the EG model, and the improvement rate in some directions is more than 50%. For the combinations including GPS data, the data utilization of the EG and QF models are almost the same for both static and kinematic modes; however, for combinations without GPS data, the data utilization of the QF model is better than that of the EG model. For these two IFCB models (EG and QF models), all combinations can achieve the set accuracy thresholds in three directions, but the EG model has more parameters to estimate than the QF model. From the perspectives of positioning accuracy, solution convergence time, data utilization, and the number of estimated parameters for each IFCB model, we suggest that the IFCB should be estimated using the QF model when performing combined PPP for different combinations. Full article

When performing area coverage tasks in some special scenarios, fixed-wing aircraft conventionally adopt the scan-type of path planning, where the distance between two adjacent tracks is usually less than the minimum turning radius of the aircraft. This results in increased energy consumption during turning between adjacent tracks, which means a reduced task execution efficiency. To address this problem, the current paper proposes an area coverage path planning method for a fixed-wing unmanned aerial vehicle (UAV) based on an improved genetic algorithm. The algorithm improves the primary population generation of the traditional genetic algorithm, with the help of better crossover operator and mutation operator for the genetic operation. More specifically, the good point set algorithm (GPSA) is first used to generate a primary population that has a more uniform distribution than that of the random algorithm. Then, the heuristic crossover operator and the random interval inverse mutation operator are employed to reduce the risk of local optimization. The proposed algorithm is verified in tasks with different numbers of paths. A comparison with the conventional genetic algorithm (GA) shows that our algorithm can converge to a better solution. Full article

The integrated navigation system consisting of an inertial navigation system (INS) and Global Navigation Satellite System (GNSS) provides continuous high-accuracy positioning whereas the navigation accuracy during a GNSS outage inevitably degrades owing to INS error divergence. To reduce such degradation, a gated recurrent unit (GRU) and adaptive Kalman filter (AKF)-based hybrid algorithm is proposed. The GRU network, which has advantages of high accuracy and efficiency, is constructed to predict the position variations during GNSS outage. Furthermore, this paper takes the GRU-predicted error accumulation into consideration, and introduces AKF as a supplementary methodology to improve the navigation performance. The proposed hybrid algorithm is trained and tested by practical road datasets and compared with four algorithms, including the standard KF, Multi-Layer Perceptron (MLP)-aided KF, Long Short Time Memory (LSTM) aided KF, and GRU-aided KF. Periods of 180 and 120 s GNSS outage are employed to test the performance of the proposed algorithm in different time scales. The comparison result between the standard KF and neural network-aided KF indicates that the neural network is an effective methodology for bridging GNSS outages. The performance comparison between three kinds of neural networks demonstrate that both recurrent neural networks surpass the MLP in prediction position variation, and the GRU transcends the LSTM in prediction accuracy and training efficiency. Furthermore, it is concluded that the adaptive estimation theory is an effective complement to neural network-aided navigation, as the GRU-aided AKF reduced the horizontal error of GRU-aided KF by 31.71% and 16.12% after 180 and 120 s of GNSS outage, respectively. Full article

The main aim of this paper is to present the results of research on the application of a modified mathematical model to determine the quality parameters of SBAS (Satellite Based Augmentation System) satellite positioning in aviation. The authors developed a new calculation strategy to determine the resultant values of the parameters of accuracy, continuity, availability and integrity of SBAS positioning. To achieve it, a weighted mean model was used for the purposes of developing a mathematical algorithm to determine the resultant values of SBAS positioning. The created algorithm was implemented for two SBAS supporting systems, i.e., EGNOS (European Geostationary Navigation Overlay Service) and SDCM (System of Differential Correction and Monitoring). The algorithm was tested in a flight test conducted with a Diamond DA 20-C airplane in north-eastern Poland in 2020. The conducted research revealed that the resultant error of the position in 3D space determined with use of the proposed weighted mean model improved by, respectively, 1–7% in comparison to the standard arithmetic mean model and by 1–37% in comparison to a single SBAS/EGNOS solution. Moreover, the application of the Multi-SBAS positioning algorithm results in an increase in the nominal results of continuity and availability by 50% in comparison to the arithmetic mean model. Apart from that, the values of the integrity parameters determined with use of the proposed weighted mean model improved by 62–63% in comparison to the standard arithmetic mean model. Full article

The accuracy of time synchronization can be significantly increased by enhancing the performance of atomic clocks. Future-generation time-frequency loads will be equipped with the latest ultrahigh-precision atomic clocks (with a day stability better than 10⁻¹⁷) and will leverage advantages of the space environment such as microgravity and low interference to operate a new generation of high-performance time-frequency payloads on low-orbit spacecraft. Moreover, using the high-precision time-frequency system of ground stations, low-time-delay high-performance time-frequency transmission networks, which have the potential to achieve ultrahigh-precision time synchronization, will be constructed. By considering full link error terms above the picosecond level, this paper proposes a new space-to-ground microwave two-way time synchronization method for scenarios involving low-orbit spacecraft and ground stations. Using the theoretical principles and practical application scenarios related to this method, a theoretical and simulation verification platform was developed to research the impact of the attitude, phase center calibration, and orbit determination errors on the single-frequency two-way time synchronization method. The effectiveness of this new method was verified. The results showed that when the attitude error is less than 72 arc seconds (0.02°), the phase center calibration error is less than 1 mm, and the precision orbit determination (POD) error is less than 10 cm (three-axis). After disregarding nonlink error terms such as equipment noise, this method can attain a space-to-ground time synchronization accuracy of better than 1.5 ps, and the time deviation (TDEV) of the transfer link is better than 0.7 ps @ 100 s, which results in ultrahigh-precision space-to-ground time synchronization. Full article

Positioning of spacecraft (e.g., geostationary orbit (GEO), high elliptical orbit (HEO), and lunar trajectory) is crucial for mission completion. Instead of using ground control systems, global navigation satellite system (GNSS) can be an effective approach to provide positioning, navigation and timing service for spacecraft. In 2020, China finished the construction of the third generation of BeiDou navigation satellite system (BDS-3); this global coverage system will contribute better sidelobe signal visibility for spacecraft. Meanwhile, with more than 100 GNSS satellites, multi-GNSS navigation performance on the spacecraft is worth studying. In this paper, instead of using signal-in-space ranging errors, we simulate pseudorange observations with measurement noises varying with received signal powers. Navigation performances of BDS-3 and its combinations with other systems were conducted. Results showed that, owing to GEO and inclined geosynchronous orbit (IGSO) satellites, all three types (GEO, HEO, and lunar trajectory) of spacecraft received more signals from BDS-3 than from other navigation systems. Single point positioning (SPP) accuracy of the GEO and HEO spacecraft was 17.7 and 23.1 m, respectively, with BDS-3 data alone. Including the other three systems, i.e., GPS, Galileo, and GLONASS, improved the SPP accuracy by 36.2% and 19.9% for GEO and HEO, respectively. Navigation performance of the lunar probe was significantly improved when receiver sensitivity increased from 20 dB-Hz to 15 dB-Hz. Only dual- (BDS-3/GPS) or multi-GNSS (BDS-3, GPS, Galileo, GLONASS) could provide continuous navigation solutions with a receiver threshold of 15 dB-Hz. Full article

Aiming at the problem of high-precision positioning of mass-pedestrians with low-cost sensors, a robust single-antenna Global Navigation Satellite System (GNSS)/Pedestrian Dead Reckoning (PDR) integration scheme is proposed with Gate Recurrent Unit (GRU)-based zero-velocity detector. Based on the foot-mounted pedestrian navigation system, the error state extended Kalman filter (EKF) framework is used to fuse GNSS position, zero-velocity state, barometer elevation, and other information. The main algorithms include improved carrier phase smoothing pseudo-range GNSS single-point positioning, GRU-based zero-velocity detection, and adaptive fusion algorithm of GNSS and PDR. Finally, the scheme was tested. The root mean square error (RMSE) of the horizontal error in the open and complex environments is lower than 1 m and 1.5 m respectively. In the indoor elevation experiment where the elevation difference of upstairs and downstairs exceeds 25 m, the elevation error is lower than 1 m. This result can provide technical reference for the accurate and continuous acquisition of public pedestrian location information. Full article

Due to different designs of receiver correlators and front ends, receiver-related pseudorange biases, called signal distortion biases (SDBs), exist. Ignoring SDBs that can reach up to 0.66 cycles and 10 ns in Melbourne-Wübbena (MW) and ionosphere-free (IF) combinations can negatively affect phase bias estimation. In this contribution, we investigate the SDBs and evaluate the impacts on wide-lane (WL) and narrow-lane (NL) phase bias estimations, and further propose an approach to eliminating these SDBs to improve phase bias estimation. Based on a large data set of 302 multi-global navigation satellite system (GNSS) experiment (MGEX) stations, including 5 receiver brands, we analyze the characteristics of these SDBs The SDB characteristics of different receiver types for different GNSS systems differ from each other. Compared to the global positioning system (GPS) and BeiDou navigation satellite system (BDS), SDBs of Galileo are not significant; those of BDS-3 are significantly superior to BDS-2; Septentrio (SEPT) receivers show the most excellent consistency among all receiver types. Then, we apply the corresponding corrections to phase bias estimation for GPS, Galileo and BDS. The experimental results reveal that the calibration can greatly improve the performance of phase bias estimation. For WL phase biases estimation, the consistencies of WL phase biases among different networks for GPS, Galileo, BDS-2 and BDS-3 improve by 89%, 77%, 76% and 78%, respectively. There are scarcely any improvements of the fixing rates for Galileo due to its significantly small SDBs, while for GPS, BDS-2 and BDS-3, the WL ambiguity fixing rates can improve greatly by 13%, 27% and 14% after SDB calibrations with improvements of WL ambiguity fixing rates, the corresponding NL ambiguity fixing rates can further increase greatly, which can reach approximately 16%, 27% and 22%, respectively. Additionally, after the calibration, both WL and NL phase bias series become more stable. The standard deviations (STDs) of WL phase bias series for GPS and BDS can improve by more than 46%, while those of NL phase bias series can yield improvements of more than 13%. Ultimately, the calibration can make more WL and NL ambiguity residuals concentrated in ranges within ±0.02 cycles. All these results demonstrate that SDBs for phase bias estimation cannot be ignored and must be considered when inhomogeneous receivers are used. Full article

At present, the design and manufacturing technology of mechanically dithered ring laser gyroscope (MDRLG) have matured, the strapdown inertial navigation systems (SINS) with MDRLG have been widely used in military and business scope. When the MDRLG is working, high-frequency dithering is introduced, which will cause the size effect error of the accelerometer. The accelerometer signal has a time delay relative to the system, which will cause the accelerometer time delay error. In this article, in order to solve the above-mentioned problem: (1) we model the size effect error of the mechanically dithering of the MDRLG and perform an error analysis for the size effect error of the mechanically dithering of the MDRLG; (2) we model the time delay error of accelerometer and perform an error analysis for the time delay error of accelerometer; (3) we derive a continuous linear 43-D SINS error model considering the above-mentioned two error parameters and expand the temperature coefficients of accelerometers, inner lever arm error, outer lever arm error parameters to achieve high-precision calibration of SINS. We use the piecewise linear constant system (PWCS) method during the calibration process to prove that all calibration parameters are observable. Finally, the SINS with MDRLG is used in laboratory conditions to test the validity of the calibration method. Full article

Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) is an attractive positioning technology due to its high precision and flexibility. However, the vulnerability of PPP brings a safety risk to its application in the field of life safety, which must be evaluated quantitatively to provide integrity for PPP users. Generally, PPP solutions are processed recursively based on the extended Kalman filter (EKF) estimator, utilizing both the previous and current measurements. Therefore, the integrity risk should be qualified considering the effects of all the potential observation faults in history. However, this will cause the calculation load to explode over time, which is impractical for long-time missions. This study used the innovations in a time window to detect the faults in the measurements, quantifying the integrity risk by traversing the fault modes in the window to maintain a stable computation cost. A non-zero bias was conservatively introduced to encapsulate the effect of the faults before the window. Coping with the multiple simultaneous faults, the worst-case integrity risk was calculated to overbound the real risk in the multiple fault modes. In order to verify the proposed method, simulation and experimental tests were carried out in this study. The results showed that the fixed and hold mode adopted for ambiguity resolution is critical to an integrity risk evaluation, which can improve the observation redundancy and remove the influence of the biased predicted ambiguities on the integrity risk. Increasing the length of the window can weaken the impact of the conservative assumption on the integrity risk due to the smoothing effect of the EKF estimator. In addition, improving the accuracy of observations can also reduce the integrity risk, which indicates that establishing a refined PPP random model can improve the integrity performance. Full article

Adaptive filtering algorithms can be used on the time-domain processing of navigation receivers to suppress interference and maintain the navigation and positioning function. The filter length can affect the interference suppression performance and hardware utilization simultaneously. In practical engineering, the filter length is usually set to a large number to guarantee anti-jamming performance, which means a high-performance receiver requires a high-complexity anti-jamming filter. The study aims at solving the problem by presenting a design method for the optimal filter order in the time-domain anti-jamming receiver, with no need for detailed interference information. According to interference bandwidth and jam-to-signal ratio (JSR), the approach designed a band-stop filter by Kaiser window for calculating the optimal filter order to meet interference suppression requirements. The experimental results show that the time-domain filtering processing has achieved good interference suppression performance for engineering requirements with optimal filter order in satellite navigation receivers. Full article

To satisfy the demands of civil aviation organizations and other users of satellite navigation systems for high-precision and high-integrity service performance, many countries and regions have established satellite-based augmentation systems (SBAS) referring to the Radio Technical Commission for Aeronautics (RTCA) service standards and agreements. The BeiDou SBAS (BDSBAS) provides both single-frequency service, which augments Global Positioning System (GPS) L1 C/A signal, and dual-frequency multi-constellation (DFMC) service, which augments BeiDou Navigation Satellite System (BDS) B1C and B2a dual frequency signals presently, meeting the requirements of the RTCA DO-229D protocol and the SBAS L5 DFMC protocol requirements, respectively. As one of the main error sources, the pseudorange bias errors of BDSBAS monitoring receivers were estimated and their effect on the performance of the BDSBAS service was analyzed. Based on the user algorithms of SBAS differential corrections and integrity information, the service accuracy, integrity, and availability of the BDSBAS were evaluated using real observation data. The results show that the maximum of monitoring receiver pseudorange bias errors between L1P and L1P/L2P can reach 1.57 m, which become the most important errors affecting the performance of the BDSBAS service. In addition, the results show that the pseudorange bias of GPS BlockIII is the smallest, while that of GPS BlockIIR is the largest. Compared with the positioning accuracy of the open service of the core constellation, the positioning accuracy of the BDSBAS service can be improved by approximately 47% and 36% for the RTCA service and DFMC service, respectively. For RTCA services, the protection limit (PL) calculated with the integrity information can 100% envelop the positioning error (PE) and no integrity risk event is detected. The service availability of BDSBAS for APV-I approach is approximately 98.8%, which is mainly affected by the availability of ionospheric grid corrections in the service marginal area. For DFMC service, the integrity risk is not detected either. The service availability for CAT-I approach is 100%. Improving the availability of ionospheric grid corrections is one of the important factors to improve service performance of BDSBAS RTCA service. Full article

With the rapid development and gradual perfection of GNSS in recent years, improving the real-time service performance of GNSS has become a research hotspot. In GNSS single-point positioning, broadcast ephemeris is used to provide a space–time reference. However, the orbit parameters of broadcast ephemeris have meter-level errors, and no mathematical model can simulate the variation of this, which restricts the real-time positioning accuracy of GNSS. Based on this research background, this paper uses a BP (Back Propagation) neural network and a PSO (Particle Swarm Optimization)–BP neural network to model the variation in the orbit error of GPS and BDS broadcast ephemeris to improve the accuracy of broadcast ephemeris. The experimental results showed that the two neural network models in GPS can model the broadcast ephemeris orbit errors, and the results of the two models were roughly the same. The one-day and three-day improvement rates of RMS(3D) were 30–50%, but the PSO–BP neural network model was better able to model the trend of errors and effectively improve the broadcast ephemeris orbit accuracy. In BDS, both of the neural network models were able to model the broadcast ephemeris orbit errors; however, the PSO–BP neural network model results were better than those of the BP neural network. In the GEO satellite outcome of the PSO–BP neural network, the STD and RMS of the orbit error in three directions were reduced by 20–70%, with a 20–30% improvement over the BP neural network results. The IGSO satellite results showed that the PSO–BP neural network model output accuracy of the along- and radial-track directions experienced a 70–80% improvement in one and three days. The one- and three-day RMS(3D) of the MEO satellites showed that the PSO–BP neural network has a greater ability to resist gross errors than that of the BP neural network for modeling the changing trend of the broadcast ephemeris orbit errors. These results demonstrate that using neural networks to model the orbit error of broadcast ephemeris is of great significance to improving the orbit accuracy of broadcast ephemeris. Full article

Global Positioning System (GPS) is a global navigation satellite system and the most common satellite system used in navigation and tracking devices. The phenomenon of week number rollover happened recently—a year ago—due to a design limitation in the week number variable that counting weeks which causes vast losses. As many fleet management systems depend on GPS raw data, such systems stopped working due to inaccurate data provided by GPS receivers. In this paper, we propose a technical and mathematical analysis for the GPS week number rollover phenomenon and suggest a solution to avoid the resulting damage to other subsystems that depend on the GPS device’s raw data. In addition, this paper seeks to provide precautionary measures to deal with the problem proactively. The Open Systems Interconnection model (OSI) and transport layer level solution that has been suggested depends on a TCP packet reforming tool that re-formats the value of the week number according to a mathematical model based on a timestamp complement. At the level of the database, a solution is also suggested which uses triggers. A hardware-level solution is suggested by applying a timestamp complement over the GPS internal controller. Complete testing is applied for all suggested solutions using actual data provided by Traklink—a leading company in navigation and fleet management solutions. After testing, it is evident that the transport layer level solution was the most effective in terms of speed, efficiency, accuracy, cost, and complexity. Applying a transport layer level complement mathematical model can fix the consequences of GPS week number rollover and provide stability to all subsystems that used GPS data from infected devices. Full article

Paving thickness and evenness are two key factors that affect the paving operation quality of earth-rock dams. However, in the recent study, both of the key factors characterising the paving quality were measured using finite point random sampling, which resulted in subjectivity in the detection and a lag in the feedback control. At the same time, the on-site control of the paving operation quality based on experience results in a poor and unreliable paving quality. To address the above issues, in this study, a novel assessment and feedback control framework for the paving operation quality based on the observe–orient–decide–act (OODA) loop is presented. First, in the observation module, a cellular automaton is used to convert the location of the bulldozer obtained by monitoring devices into the paving thickness of the levelling layer. Second, in the orient module, the learning automaton is used to update the state of the corresponding and surrounding cells. Third, in the decision module, an overall path planning method is developed to realise feedback control of the paving thickness and evenness. Finally, in the act module, the paving thickness and evenness of the entire work unit are calculated and compared to their control thresholds to determine whether to proceed with the next OODA loop. The experiments show that the proposed method can maintain the paving thickness less than the designed standard value and effectively prevent the occurrence of ultra-thick or ultra-thin phenomena. Furthermore, the paving evenness is improved by 21.5% as compared to that obtained with the conventional paving quality control method. The framework of the paving quality assessment and feedback control proposed in this paper has extensive popularisation and application value for the same paving construction scene. Full article

Aircraft flying the trans-arctic routes usually apply inertial navigation mechanization in two different navigation frames, e.g., the local geographic frame and the grid frame. However, this change of navigation frame will cause filter overshoot and error discontinuity. To solve this problem, taking the inertial navigation system/global navigation satellite system (INS/GNSS) integrated navigation system as an example, an integrated navigation method based on covariance transformation is proposed. The relationship of the system error state between different navigation frames is deduced as a means to accurately convert the Kalman filter’s covariance matrix. The experiment and semi-physical simulation results show that the presented covariance transformation algorithm can effectively solve the filter overshoot and error discontinuity caused by the change of navigation frame. Compared with non-covariance transformation, the system state error is thereby reduced significantly. Full article

For the tracking of high-dynamic satellite navigation signals, the conventional scalar tracking loop (STL) is vulnerable. Frequent signal-tracking interruption affects the continuity of navigation. The vector tracking loop (VTL) can overcome this disadvantage. However, there are some difficulties in implementing existing vector tracking methods on a real-time hardware receiver, such as the synchronization problem and computation load. This paper proposes an implementation framework of VTL based on a partial open-loop numerically controlled oscillator (NCO) control mode that can be implemented with minor modifications on an existing receiver platform. The structure of VTL, the design of the navigation filter, and the key points of hardware implementation are introduced in detail. Lastly, the VTL performance was verified by a GPS simulator test. The results show that the proposed VTL can run in real-time and be significantly improved in the tracking continuity of high-dynamic signals, tracking sensitivity, positioning accuracy, and recovery time for interrupted signals compared with those of STL. Full article

Suffering from hardware phase biases originating from satellites and the receiver, precise point positioning (PPP) requires a long convergence time to reach centimeter coordinate accuracy, which is a major drawback of this technique and limits its application in time-critical applications. Ambiguity resolution (AR) is the key to a fast convergence time and a high-precision solution for PPP technology and PPP AR products are critical to implement PPP AR. Nowadays, various institutions provide PPP AR products in different forms with different strategies, which allow to enable PPP AR for Global Positioning System (GPS) and Galileo or BeiDou Navigation System (BDS). To give a full evaluation of PPP AR performance with various products, this work comprehensively investigates the positioning performance of GPS-only and multi-GNSS (Global Navigation Satellite System) combination PPP AR with the precise products from CNES, SGG, CODE, and PRIDE Lab using our in-house software. The positioning performance in terms of positioning accuracy, convergence time and fixing rate (FR) as well as time to first fix (TTFF), was assessed by static and kinematic PPP AR models. For GPS-only, combined GPS and Galileo PPP AR with different products, the positioning performances were all comparable with each other. Concretely, the static positioning errors can be reduced by 21.0% (to 0.46 cm), 52.5% (to 0.45 cm), 10.0% (to 1.33 cm) and 21.7% (to 0.33 cm), 47.4% (to 0.34 cm), 9.5% (to 1.16 cm) for GPS-only and GE combination in north, east, up component, respectively, while the reductions are 20.8% (to 1.13 cm), 42.9% (to 1.15 cm), 19.9% (to 3.4 cm) and 20.4% (to 0.72 cm), 44.1% (to 0.66 cm), 10.1% (to 2.44 cm) for kinematic PPP AR. Overall, the positioning performance with CODE products was superior to the others. Furthermore, multi-GNSS observations had significant improvements in PPP performance with float solutions and the TTFF as well as the FR of GPS PPP AR could be improved by adding observations from other GNSS. Additionally, we have released the source code for multi-GNSS PPP AR, anyone can freely access the code and example data from GitHub. Full article

Data collected from a moving lidar sensor can produce an accurate digital representation of the physical environment that is scanned, provided the time-dependent positions and orientations of the lidar sensor can be determined. The most widely used approach to determining these positions and orientations is to collect data with a GNSS/INS sensor. The use of dual-antenna GNSS/INS sensors within commercial UAS-lidar systems is uncommon due to the higher cost and more complex installation of the GNSS antennas. This study investigates the impacts of using a single-antenna and dual-antenna GNSS/INS MEMS-based sensor on the positional precision of a UAS-lidar generated point cloud, with an emphasis on the different heading determination techniques employed by each type of GNSS/INS sensor. Specifically, the impacts that sensor velocity and acceleration (single-antenna), and a GNSS compass (dual-antenna) have on heading precision are investigated. Results indicate that at the slower flying speeds often used by UAS (≤5 m/s), a dual-antenna GNSS/INS sensor can improve heading precision by up to a factor of five relative to a single-antenna GNSS/INS sensor, and that a point of diminishing returns for the improvement of heading precision exists at a flying speed of approximately 15 m/s for single-antenna GNSS/INS sensors. Additionally, a simple estimator for the expected heading precision of a single-antenna GNSS/INS sensor based on flying speed is presented. Utilizing UAS-lidar mapping systems with dual-antenna GNSS/INS sensors provides reliable, robust, and higher precision heading estimates, resulting in point clouds with higher accuracy and precision. Full article

Aiming to improve the positioning accuracy of an unmanned aerial vehicle (UAV) swarm under different scenarios, a two-case navigation scheme is proposed and simulated. First, when the Global Navigation Satellite System (GNSS) is available, the inertial navigation system (INS)/GNSS-integrated system based on the Kalman Filter (KF) plays a key role for each UAV in accurate navigation. Considering that Kalman filter’s process noise covariance matrix Q and observation noise covariance matrix R affect the navigation accuracy, this paper proposes a dynamic adaptive Kalman filter (DAKF) which introduces ensemble empirical mode decomposition (EEMD) to determine R and adjust Q adaptively, avoiding the degradation and divergence caused by an unknown or inaccurate noise model. Second, a network navigation algorithm (NNA) is employed when GNSS outages happen and the INS/GNSS-integrated system is not available. Distance information among all UAVs in the swarm is adopted to compensate the INS position errors. Finally, simulations are conducted to validate the effectiveness of the proposed method, results showing that DAKF improves the positioning accuracy of a single UAV by 30–50%, and NNA increases the positioning accuracy of a swarm by 93%. Full article

In this paper a new mathematical algorithm is proposed to improve the accuracy of DGPS (Differential GPS) positioning using several GNSS (Global Navigation Satellites System) reference stations. The new mathematical algorithm is based on a weighting scheme for the following three criteria: weighting in function of baseline (vector) length, weighting in function of vector length error and weighting in function of the number of tracked GPS (Global Positioning System) satellites for a single baseline. The algorithm of the test method takes into account the linear combination of the weighting coefficients and relates the position errors determined for single baselines. The calculation uses a weighting scheme for three independent baselines denoted as $\left(1A,2A,3A\right)$. The proposed research method makes it possible to determine the resultant position errors for ellipsoidal BLh coordinates of the aircraft and significantly improves the accuracy of DGPS positioning. The analysis and evaluation of the new research methodology was checked for data from two flight experiments carried out in Mielec and Dęblin. Based on the calculations performed, it was found that in the flight experiment in Mielec, due to the application of the new research methodology, DGPS positioning accuracy improved from 55 to 94% for all the BLh components. In turn, in the flight experiment in Dęblin, the accuracy of DGPS positioning improved by 63–91%. The study shows that the highest DGPS positioning accuracy is seen when using weighting criterion II, the inverse of the square of the vector length error. Full article

Compared to the BeiDou regional navigation satellite system (BDS-2), the BeiDou global navigation satellite system (BDS-3) carried out a brand new integrity concept design and construction work, which defines and achieves the integrity functions for major civil open services (OS) signals such as B1C, B2a, and B1I. The integrity definition and calculation method of BDS-3 are introduced. The fault tree model for satellite signal-in-space (SIS) is used, to decompose and obtain the integrity risk bottom events. In response to the weakness in the space and ground segments of the system, a variety of integrity monitoring measures have been taken. On this basis, the design values for the new B1C/B2a signal and the original B1I signal are proposed, which are 0.9 × 10⁻⁵ and 0.8 × 10⁻⁵, respectively. The hybrid alarming mechanism of BDS-3, which has both the ground alarming approach and the satellite alarming approach, is explained. At last, an integrity risk analysis and verification work were carried out using the operating data of the system in 2019. The results show that the actual operation of the system is consistent with the conceptual design, which satisfies the integrity performance promised by BDS-3 in the ICAO SAPRs. Full article

There are two problems with using global navigation satellite system-interferometric reflectometry (GNSS-IR) to retrieve the soil moisture content (SMC) from single-satellite data: the difference between the reflection regions, and the difficulty in circumventing the impact of seasonal vegetation growth on reflected microwave signals. This study presents a multivariate adaptive regression spline (MARS) SMC retrieval model based on integrated multi-satellite data on the impact of the vegetation moisture content (VMC). The normalized microwave reflection index (NMRI) calculated with the multipath effect is mapped to the normalized difference vegetation index (NDVI) to estimate and eliminate the impact of VMC. A MARS model for retrieving the SMC from multi-satellite data is established based on the phase shift. To examine its reliability, the MARS model was compared with a multiple linear regression (MLR) model, a backpropagation neural network (BPNN) model, and a support vector regression (SVR) model in terms of the retrieval accuracy with time-series observation data collected at a typical station. The MARS model proposed in this study effectively retrieved the SMC, with a correlation coefficient (R²) of 0.916 and a root-mean-square error (RMSE) of 0.021 cm³/cm³. The elimination of the vegetation impact led to 3.7%, 13.9%, 11.7%, and 16.6% increases in R² and 31.3%, 79.7%, 49.0%, and 90.5% decreases in the RMSE for the SMC retrieved by the MLR, BPNN, SVR, and MARS model, respectively. The results demonstrated the feasibility of correcting the vegetation changes based on the multipath effect and the reliability of the MARS model in retrieving the SMC. Full article

The vector tracking loop (VTL) has high tracking accuracy and a superior ability to track weak signals in GNSS. However, traditional VTL architecture is established on continuous Code Division Multiple Access (CDMA) signal and is incompatible with pseudolite positioning systems (PLPS) because PLPS generally adopts a pseudo-random pulsing CDMA signal structure to mitigate the near-far effect. Therefore, this paper proposes an optimized VTL architecture for pseudo-random pulsing CDMA signals. To avoid estimation biases in PLPS, the proposed VTL adopts irregular update periods (IUP) pre-filters which adjust the update cycles according to the active timeslot intervals. Meanwhile, as the active timeslots of different pseudolites do not overlap, the sampling time of the navigation filter inputs is inconsistent and time-varying, causing jitter degradation. Thus, the proposed VTL predicts the measurements so that they can be sampled at the same time, which improves tracking accuracy. Simulation is carried out to evaluate the performance of the proposed VTL. The results suggest that the proposed VTL outperforms the traditional pre-filter-based VTL and IUP pre-filter-based VTL. Full article

Most UAVs rely on GPS for localization in an outdoor environment. However, in GPS-denied environment, other sources of localization are required for UAVs to conduct feedback control and navigation. LiDAR has been used for indoor localization, but the sampling rate is usually too low for feedback control of UAVs. To compensate this drawback, IMU sensors are usually fused to generate high-frequency odometry, with only few extra computation resources. To achieve this goal, a real-time LiDAR inertial odometer system (RTLIO) is developed in this work to generate high-precision and high-frequency odometry for the feedback control of UAVs in an indoor environment, and this is achieved by solving cost functions that consist of the LiDAR and IMU residuals. Compared to the traditional LIO approach, the initialization process of the developed RTLIO can be achieved, even when the device is stationary. To further reduce the accumulated pose errors, loop closure and pose-graph optimization are also developed in RTLIO. To demonstrate the efficacy of the developed RTLIO, experiments with long-range trajectory are conducted, and the results indicate that the RTLIO can outperform LIO with a smaller drift. Experiments with odometry benchmark dataset (i.e., KITTI) are also conducted to compare the performance with other methods, and the results show that the RTLIO can outperform ALOAM and LOAM in terms of exhibiting a smaller time delay and greater position accuracy. Full article

This paper designs a cascading vector tracking loop based on the Unscented Kalman Filter (UKF) for high dynamic environment. Constant improvement in dynamic performance is an enormous challenge to the traditional receiver. Due to the doppler effect, the satellite signals received by these vehicles contain fast changing doppler frequency shifts and the first and second derivatives of doppler frequency, which will directly cause a negative impact on the receiver’s stable tracking of the signals. In order to guarantee the dynamic performance and the tracking accuracy, this paper designs a vector carrier structure to estimate the doppler component of a signal. Firstly, after the coherence integral, the IQ values are reorganized into new observations. Secondly, the phase error and frequency of the carrier are estimated through the pre-filter. Then, the pseudorange and carrier frequency are used as the observations of the main filter to estimate the motion state of the aircraft. Finally, the current state is fed back to the carrier Numerical Controlled Oscillator (NCO) as a complete closed loop. In the whole structure, the cascading vector loop replaces the original carrier tracking loop, and the stable signal tracking of code loop is guaranteed by carrier assisted pseudo-code method. In this paper, with the high dynamic signals generated by the GNSS signal simulator, this designed algorithm is validated by a software receiver. The results show that this loop has a wider dynamic tracking range and lower tracking error than the second-order frequency locked loop assisted third-order phase locked loop in high dynamic circumstances. When the acceleration of carrier is 100 g, the convergence time of vector structure is about 100 ms, and the carrier phase error is lower than 0.6 mm. Full article

It has been proven that to solve the problems that arise in the combinatorial modeling of the prospects for the development of regional renewable energy, an algorithmically simple general combinatorial approach is the most appropriate option. The conceptual express method and corresponding mechanisms of the economic estimation of the efficiency of variants of the formation of regional systems of renewable energy have been suggested. These variants take into account the inflationary factors which serve as a basis of the analysis of investment and innovative projects of renewable energy sources by means of combinatorial modeling methods. To qualitatively analyze the effectiveness of the compared options, the system of existing indicators of the economic efficiency of renewable energy sources at the meso-level has been studied. The system was supplemented by informal and environmental indicators, the need for which is due to the fact that they have a significant impact on renewable energy in the region. Factors that significantly determine the effectiveness of the investment and innovation project for the introduction of renewable energy sources into the regional economy have been substantiated. Full article