Pseudorange Observations Research Articles

Simulation Analysis of LEO Constellation Augmented GNSS (LeGNSS) Zenith Troposphere Delay and Gradients Estimation

Compared with current GNSS, which consists of medium- and high-altitude orbit satellites, Low Earth Orbit (LEO) satellites move faster and can greatly improve the observing geometry. In this contribution, LEO constellation augmented GNSS (LeGNSS) troposphere estimation is investigated, and the impacts of relevant factors are analyzed in detail. When the temporal resolutions of zenith troposphere delay (ZTD) and horizontal gradients are 1 h and 2 h, while standard deviations (STDs) of phase and pseudorange observations at the zenith direction are 0.005 m and 0.5 m, the accuracies of ZTD, north gradient, and east gradient augmented by LEO constellation improve by 15.7%, 29.6%, and 16.4%, respectively, compared with GNSS solution. The results of troposphere estimation under obstructed environment and using low-cost dual frequency receivers also become more robust after adding LEO observations. Most importantly, analysis results during periods with rapid varying troposphere parameters suggest that the contribution of LEO constellation becomes even bigger with increasing temporal resolutions of ZTD and horizontal gradients, indicating that LeGNSS can be used to extract tropospheric parameters with improved accuracies at high temporal resolution. Thus, the capability in rapidly capturing severe weather events can be improved by LeGNSS observations, and the performance can become even better with increasing number of LEO satellites. All these results suggest that LeGNSS might be an important tool in improving the performance of troposphere estimation, and would promote GNSS application in water vapor monitoring.

Targetless Extrinsic Calibration of LiDAR–IMU System Using Raw GNSS Observations for Vehicle Applications

Nowadays, the low-cost MEMS-based Inertial Measurement Units (IMU) and LiDARs are commercially available in vehicle systems and are usually integrated to achieve robust ego-motion estimation due to their excellent complementary properties. In this case, accurate inter-sensor spatial transformation, i.e. extrinsic parameters, is a fundamental prerequisite for the combined application of LiDAR and IMU. However, current LiDAR-IMU calibration methods usually rely on specially-designed artificial targets or facilities, which greatly limits the flexibility and usability of calibration. Fortunately, modern intelligent vehicles are generally equipped with portable global navigation satellite system (GNSS) devices, which are able to provide precise positioning services and could be used to improve the performance of extrinsic calibration. To this end, we innovatively introduce raw GNSS observations to enhance in-vehicle LiDAR-IMU calibration performance without predefined target support. Based on the centralized Extended Kalman Filter (EKF), the estimator tightly fuses the double-differenced pseudorange and carrier phase observations, IMU data, and extracted plane features to obtain the optimal extrinsic parameters. The results of simulated tests and real-world experiments indicate that the introduction of GNSS can significantly improve the calibration performance. The GNSS-aided LiDAR-IMU calibration results also show better odometry accuracy and mapping consistency than those without GNSS aiding.

Time-differenced double difference method for measurement of Navigation with Indian Constellation (NavIC) receiver differential phase bias

The pseudo-range (PR) and carrier phase (CP) observations of Global Navigation Satellite System (GNSS)/Navigation with Indian Constellation (NavIC) receivers are influenced due to various errors like ionosphere delay, troposphere delay, receiver and satellite clock error, multipath, integer ambiguity, receiver hardware noise etc. However, the real-time positioning and navigation applications are in quest of high-quality carrier phase measurements with zero bias. The GNSS/NavIC receiver hardware noise is one of the critical error sources that degrade the quality of carrier phase measurements. And it can be measured by computing the differential phase bias or carrier phase bias employing the double-difference method. This research article proposes a novel approach called Time Differenced Double Difference Carrier Phase (TDDDCP) for estimating differential phase bias or carrier phase bias of NavIC receiver. Moreover, the proposed TDDDCP technique has the advantage over the Double Difference Carrier Phase (DDCP) because it requires data from only one satellite with two zero base length receivers for which the differential phase bias is to be measured. The experimental results show that the differential phase bias value differs for different satellites, ranging from −0.3904 m to 0.3168 m. The bias-free carrier phase observations based on position coordinates (X, Y, Z) found improved precision of standard deviation of 0.4176 m, 0.645 m, and 0.328 m, respectively.

A Novel Cycle Slips Detection and Repair Method with AR Model of BDS-3 Dual-Frequency Signal in Severe Multipath Environments

High-level applications of geo-processing services generally lack accurate temporal and spatial information. BDS-3 provides high precision temporal and spatial reference for geoprocessing services, but their signal is prone to cycle slips in a severe multipath environment. Aiming at the problem of the reliable detection and repair of cycle slips in BDS-3 (B1c + B2a) dual-frequency positioning in a severe multipath environment, an AR (autoregressive) model-assisted MW + GF BDS dual-frequency combined detection method (AMG method) is proposed in this research. A sliding-window autoregressive prediction strategy is introduced to correct the pseudorange observations interfered by a multipath, then an AR + MW + GF cycle slips detection model is constructed, and a cycle slips statistical completeness test index is established to verify the effectiveness of the algorithm. Six groups of cycle slips are artificially added into the different constellations and dual-frequency point phase observations of BDS-3 (B1c and B2a) in a multipath environment to demonstrate the cycle slips’ detection performance. The experimental results show that the traditional MW + GF method fails, but the proposed AMG method still maintains accurate cycle slip detection and repair capabilities. The detection success rate and repair success rate obtained by using the new method are significantly improved by 63.4%, and the cycle slips’ false detection rate and missed detection rate are reduced by 64.5% and 42.0%, respectively, even in harsh environments.

Research on Blunder Detection Methods of Pseudorange Observation in GNSS Observation Domain

Global Navigation Satellite System (GNSS) signal quality, type of receiver equipment, and external environment can cause GNSS observations to be anomalous, and these anomalies are sometimes reflected in GNSS pseudorange observations rather than phase observations. To better detect blunders in pseudorange observations, this paper proposes three pseudorange blunder detection methods under the same frequency and different code types (case1), and the same code type and different frequencies (case2), of pseudorange observations, which are the Code Observation Difference Method (CODM), the Inter-satellite Code Observation Difference Method (ICODM), and the Inter-epoch and Inter-satellite Code Observation Difference Method (IICODM). The corresponding thresholds for the constructed test statistics of the three detection methods were derived based on the Bessel formula. Performance analysis of the three detection methods was performed under case1 based on C2 and P2 code observation data of Global Positioning System (GPS) at 137 Multi-GNSS Experiment (MGEX) stations, and case2 based on BDS B1I and B3I frequency observation data of BeiDou Navigation Satellite System (BDS) at 232 MGEX stations, on 29 July 2022. The results show that the statistical information value of the three methods in case1 was significantly smaller than that in case2. In the first case, the maximum values of test statistics, RMSE and threshold mean values were 0.526, 0.752 and 2.243 m, respectively, while the corresponding values in case2 were 7.066, 4.490 and 13.480 m respectively. The reason for this is that the data quality of global GPS is higher than that of BDS and the differential observation equation eliminates or weakens more errors with the same frequency and different types of code pseudorange observations. Under the same conditions, compared with ICODM and IICODM, CODM has high computational efficiency and a simple mathematical model. It is recommended to use CODM first for pseudorange blunder detection in the GNSS observation domain. According to the RMSE of 3 times as the limit, it is recommended that the threshold be set to 5 m under case1 for GPS and 15 m under case2 for BDS, which is half the existing reference value. Finally, the blunder detection methods proposed can improve positioning performance through actual data verification.

A BDGIM-Based Phase-Smoothed Pseudorange Algorithm for BDS-3 High-Precision Time Transfer

Single point positioning (SPP) can meet the requirements of the majority of real-time time transfer applications. Meanwhile, a single-frequency (SF) receiver is cheaper than a dual-frequency receiver. However, SPP performance can be greatly affected by large pseudorange observation noise. Phase smoothing the pseudorange is an effective approach to reduce pseudorange noise. Since the classical phase-smoothed pseudorange algorithm does not account for the effect of ionosphere delay, we propose a BDGIM-based phase-smoothed pseudorange algorithm to eliminate the ionospheric delay and apply it to BeiDou Navigation Satellite System (BDS-3) SPP time transfer. In this paper, we first evaluate the performance of the BeiDou global ionospheric delay correction model (BDGIM) and compare it with that of the BeiDou Klobuchar model to determine if it is practical to incorporate the BDGIM into our suggested method. The performance of the BDGIM is better than that of the Klobuchar model. The mean RMS value of the BDGIM is 2.6 Total Electron Content Unit (TECU). The average ionospheric correction rate of the BDGIM is 75.5%. Then, we investigate the performance of the improved SF SPP time transfer. The performance of the improved SPP time transfer is much better than that of the traditional SPP time transfer. Compared with the traditional time transfer, the average Type A uncertainty of the improved time transfer is 2.08 ns, which is reduced by about 11.1% from the time transfer without it. Regarding frequency stability, the modified Allan deviations of the improved time transfer are 1.43E-12 and 1.68E-13 at 960 s and 61,440 s, with improvements of 51.2% and 59.9%, respectively.

Performance Evaluation of Multi-Epoch Double-Differenced Pseudorange Observation Method Using GNSS Ground Stations

Multi-epoch double-differenced pseudorange observation (MDPO) is a dual-satellite lunar navigation algorithm specially designed for a precursor mission, using a minimum number of lunar orbiting small satellites to realize a GNSS-like radio navigation system for the Moon. In this study, we evaluated the performance of the MDPO algorithm by using real pseudorange measurements obtained from a pair of GNSS ground stations, one of which represented a lander, and the other a rover on the Moon. It was natural that the resulting positioning accuracy varied largely by satellite geometry, but the estimated error distributions of the double-differenced pseudorange observations were consistent and agreed with the predicted value. The results showed that the MDPO algorithm worked properly with the real GNSS observables and was capable of providing the expected navigation performance for future lunar exploration missions.

Assessment of Galileo FOC + IOV Signals and Geometry-Based Single-Epoch Resolution of Quad-Frequency Carrier Ambiguities

Galileo can independently provide navigation and positioning services globally. Galileo satellites transmit quad-frequency E1, E5a, E5b, and E5 signals, which can benefit the integer ambiguity rapid resolution. Firstly, the qualities of Galileo signals from Carrier-to-Noise (C/N0), Multipath Combination (MPC), and pseudo-range and phase noise using the ultra-short baseline were evaluated. The experimental results indicated that the Galileo E5 signal has the highest C/N0, while the C/N0 of other signals is lower and almost equal. In terms of MPC, the Galileo E1 was the most severe followed by E5a and E5b, and the MPC of E5 is less severe. As for the precision of un-differenced observations, the carrier phase and pseudo-range observations of Galileo E5 had higher accuracy than those of Galileo E5a, E5b, and E1. Secondly, the quad-frequency observations allowed for various linear combinations of different frequencies, which provides some feasibility for improving the performance of ambiguity resolution. Assuming that the phase noise σ∇ΔΦ = 0.01 m and the first-order ionosphere σ∇ΔI1 = 1 m, the total noise of the Extra-Wide-Lane (EWL) combination observation ((0, 0, 1, −1) and (0, −1, 1, 0)) and Very-Wide-Lane (VWL) combination observation ((0, −2, 1, 1), (0, −3, 2, 1)) are still less than 0.5 cycles. Finally, a geometry-based quad-frequency carrier ambiguities (GB-QCAR) method was developed, and all different options of linear combinations were investigated systematically from the ambiguity-fixed rate with two baselines. Experimental results demonstrated that, the ambiguity fixed rate of combination observation (0, −1, 1, 0), (0, −3, 5, −2), (1, −1, 0, 0) and (0, 0, 0, 1) is the highest and the positioning accuracy of VWL combination observation (0, −3, 5, −2) is equivalent to that of the EWL combination observation (0, −1, 1, 0). The positioning accuracies of WL combination observation (1, −1, 0, 0) are preferable to 3 cm and 10 cm in the horizontal and vertical, respectively. The positioning accuracy of NL combination observation E5 in the horizontal direction is about 1 cm, and is better than 4 cm in the vertical direction. Therefore, we can use Galileo observations to realize high-precise navigation services utilizing the proposed GB-QCAR method.

GNSS precise positioning for smartphones based on the integration of factor graph optimization and solution separation

Currently, the global navigation satellite system on smartphones suffers from frequent outliers (faults) in the measurements, limiting their precise positioning applications. To mitigate, the factor-graph optimization (FGO) method is used, where the Doppler and time-differenced carrier-phase (TDCP) measurements determine the velocities. However, their estimations are vulnerable since the Doppler measurements are inaccurate, while the TDCP measurements suffer from frequent cycle slips. Statistical testing methods can be used to exclude measurement outliers, but they have high volumes of false alarms and missed detections. In this study, we propose an improved scheme of FGO with a solution separation (SS) test to improve smartphone precise positioning. After excluding measurement outliers with the SS test for TDCP and time-differenced pseudorange observation models, we apply an improved FGO scheme for positioning. We conducted an experiment with Xiaomi Mi 8 and Google Pixel 5, showing that our method outperforms the conventional FGO and Kalman filtering methods.

A resilient adjustment method to weigh pseudorange observation in precise point positioning

The accurate weighting of pseudorange observations is important to improve the convergence time and positioning quality of Precise Point Positioning (PPP). Currently, the weight of a pseudorange observation is mainly determined with empirical stochastic models. However, in a complex environment, due to the inability to adapt for the dynamic changes of the user environment, the empirical stochastic models usually cannot reflect the real error level of pseudorange observations. To address this problem, a resilient adjustment method to weigh pseudorange observations is proposed, which constructs the real-time estimation and inflation model for the variance of pseudorange multipath error and measurement noise to replace the empirical stochastic model to determine the weights of pseudorange observations. A set of static and dynamic Global Positioning System (GPS) test data are used to verify the effectiveness of the proposed method. The test results indicate that the proposed real-time estimation model can provide a better representation of the pseudorange accuracy, and the positioning performance of PPP using the real-time estimation model is better than that with the empirical stochastic model. Compared with the optimal empirical stochastic model, the positioning accuracy of PPP with the real-time estimation model is improved by at least 20%, and the convergence time is reduced by at least 50%.

Research on Linear Combination Models of BDS Multi-Frequency Observations and Their Characteristics

The linear combination of multi-frequency carrier-phase and pseudorange observations can form the combined observations with special properties. The type and number of combined frequencies will directly affect the characteristics of the combined observations. BDS-2 and BDS-3 broadcast three and five signals, respectively, and the study of their linear combination is of great significance for precision positioning. In this contribution, the linear combination form of multi-frequency carrier-phase observations in cycles and meters is sorted out. Seven frequency combination modes are formed, and some special combinations for positioning are searched. Then, based on the principle of minimum combined noise, a simpler search method for the optimal real coefficients of ionosphere-free (IF) combination based on the least squares (LS) principle is proposed. The general analytical expressions of optimal real coefficients for multi-frequency geometry-based and ionosphere-free (GBIF), geometry-free and ionosphere-free (GFIF), and pseudorange multipath (PMP) combinations with the first-order ionosphere delay taken into account are derived. And the expression derivation process is given when both the first-order and second-order ionospheric delays are eliminated. Based on this, the characteristics of the optimal real coefficient combination in various modes are compared and discussed. The various combinations reflect that the accuracy of the combined observations from dual-frequency (DF) to five-frequency (FF) is gradually improving. The combination coefficient becomes significantly larger after taking the second-order ionospheric delay into account. In addition, the combined accuracy of BDS-3 is better than that of BDS-2. When only the first-order ionosphere is considered, the combination attribute of (B1C, B1I, B2a) is the best among the triple-frequency (TF) combinations of BDS-3. When both the first-order and second-order ionospheric delays are considered, the (B1C, B3I, B2a) combination is recommended.

Verification and Validation of the COSMIC-2 Excess Phase and Bending Angle Algorithms for Data Quality Assurance at STAR

In recent years, Global Navigation Satellite System (GNSS) radio occultation (RO) has become a critical observation system for global operational numerical weather prediction. Constellation Observing System for Meteorology, Ionosphere, Climate (COSMIC) 2 (COSMIC-2) has been a backbone RO mission for NOAA. NOAA also began to purchase RO data from commercial sources in 2020. To ensure the consistent quality of RO data from different sources, NOAA Center for Satellite Applications and Research (STAR) has developed capabilities to process all available RO data from different missions. This paper describes the STAR RO processing systems which convert the pseudo-range and carrier phase observations to excess phases and bending angles (BAs). We compared our COSMIC-2 data products with those processed by the University Corporation for Atmospheric Research (UCAR) COSMIC Data Analysis and Archive Center (CDAAC). We processed more than twelve thousand COSMIC-2 occultation profiles. Our results show that the excess phase difference between UCAR and STAR is within a few centimeters at high altitudes, although the difference increases towards the lower atmosphere. The BA profiles derived from the excess phase are consistent with UCAR. The mean relative BA differences at impact height from 10 to 30 km are less than 0.1% for GLObal NAvigation Satellite System (GLONASS) L2C signals and Global Positioning System (GPS) L2C and L2P signals. The standard deviations are 1.15%, 1.15%, and 1.32% for GLONASS L2C signal and for GPS L2C and L2P signals, respectively. The BA profiles agree with those derived from European Center for Medium-range Weather Forecast (ECMWF) reanalysis version 5 (ERA5). The Signal-to-Noise-Ratio (SNR) plays an essential role in the processing. The STAR BA profiles with higher L1 SNRs (L1 at 80 km) tend to yield more consistent results than those from UCAR, with a negligible difference and a smaller deviation than lower SNR profiles. Profiles with lower SNR values tend to show a more significant standard deviation towards the surface during the open-loop stage in the lower troposphere than those of higher SNR. We also found that the different COSMIC-2 clock solutions could contribute to the significant relative BA difference at high altitudes; however, it has little effect on the lower troposphere comparisons given larger BA values.

Performance evaluation of BDS-3 ionospheric delay correction models (BDSK and BDGIM): First year for full operational capability of global service

The BeiDou global navigation satellite system (BDS-3) has been providing full operational capability of global service since July 31, 2020. There are two kinds of broadcast ionospheric delay correction models for the BDS-3, i.e., the BDS Klobuchar model (BDSK) and the BeiDou global ionospheric delay correction model (BDGIM). We first assessed the performance of the BDS-3 ionospheric models during the first year from August 1, 2020, to July 31, 2021. The assessment was conducted in both the ionospheric total electron content (TEC) domain and the BDS single-frequency standard point positioning domain. A consistency experiment shows that the BDSK and BDGIM can correct the ionospheric delay by approximately 64% and 75%, respectively, when compared with the global ionospheric map (GIM) provided by the international global navigation satellite system service (IGS). The model precision and accuracy were also computed by comparing these models with the internal GPS-derived slant TEC (STEC) and the external Jason-3-derived vertical TEC (VTEC), respectively. A precision experiment shows that the root mean square (RMS) of the BDSK and the BDGIM are 5.0 and 3.0 total electron content unit (TECU), respectively, in the continental region. There exists systematic bias (6.4 TECU for the BDSK and 2.9 TECU for the BDGIM) between the global navigation satellite system (GNSS) VTEC and the Jason-3 VTEC. The standard deviation (STD) in the accuracy experiment for the BDSK and the BDGIM are 4.2 and 3.4 TECU, respectively, in the oceanic region. When applying the BDSK model or the BDGIM model in the BDS standard point positioning using B1I frequency pseudorange observations, the 3D RMS positioning error is better than 3 m for most stations under different solar activity conditions, and the positioning accuracy of the BDGIM outperforms that of the BDSK by approximately 10%. The GPS Klobuchar model and the Galileo NeQuickG model were also included for comparison. All the results in our experiment demonstrate that the newly designed BDGIM has the best performance among the GNSS broadcast ionospheric models.

Roll Rate Estimation for Cylindrical Spinning Vehicle Based on Pseudorange Observations

Roll rate estimation is essential to attitude measurement. During the processing of baseband signals, it is complicated to measure the vehicle rolling attitude, based on the energy features of existing satellite signals. To measure the energy of received signals in real time, the data communication interface and storage unit of the receiving device must be customized. However, the customization will push up the cost of attitude sensors, and result in processing delays. To solve the problem, this paper measures the vehicle roll rate by the variation features of pseudorange observations, which are easy to acquire and highly applicable. Specifically, the roll rate of a cylindrical spinning vehicle was estimated, using Global Navigation Satellite System (GNSS) receiver with single side-mounted antenna. After analyzing the variation of pseudorange observations, the authors calculated the roll rate of the cylindrical spinning vehicle based on the variation rules. The proposed approach was verified through experiments with simulated GNSS signals. The accuracy of our approach was measured at different rotation speeds and translational speeds. The results show that our approach can accurately estimate the roll rate when the standard deviations of noise is less than 1m for pseudorange measurement.

A Cycle Slip Detection and Repair Method Using BDS Triple-Frequency Optimization Combination with Wavelet Denoising

The traditional triple-frequency geometry-free pseudorange minus phase (GFPMP) method is very susceptible to the influence of pseudorange observation noise, and it is difficult to detect insensitive small cycle slips. The dual-frequency phase ionospheric residual (PIR) method has the ability to detect sensitive small cycle slips, but its detection results have multivalue problems. In view of this, a GFPMP-PIR combination model method with wavelet denoising (GPW) is proposed here. The idea of this method is as follows: firstly, wavelet transform is used to denoise the pseudorange observations; then, by optimizing and selecting the combination coefficients with the minimum condition, an optimized GFPMP-PIR combination model is constructed. Hence, the source data quality is assured through wavelet denoising. And the accuracy of cycle slip detection and repair is improved by using the dual-frequency PIR combination. Moreover, the multivalue problem of the dual-frequency PIR method is solved by triple-frequency GFPMP combination; finally, the BeiDou navigation satellite system (BDS) triple-frequency measurement data is used for experimental verification. The experiment results show that the GFPMP-PIR optimization combination model with wavelet denoising can detect and repair various cycle slips, especially for insensitive small cycle slips.

Evaluation and mitigation of the influence of pseudorange biases on GNSS satellite clock offset estimation

The pseudorange bias inconsistencies are notably originating primarily from the individual chip shape distortions in the ranging signals, these distortions cause different shifts of the correlator’s tracking point for receivers, as a result giving rise to a different pseudorange bias for each pseudorange observation. The different bias should be properly dealt with in the process of satellite clock offset estimation when receivers of mixed types are used. In this work, using observations from 140 international global navigation satellite system (GNSS) service stations, the pseudorange bias was calculated, and the effect of inconsistent biases on satellite clock offset estimation from different receiver networks was investigated. The inconsistencies between the GPS satellites were ranging from −6 ns to 4 ns. For GALILEO and BDS, the biases are significant, ranging from −20 ns to 40 ns and −60 ns to 40 ns, respectively. The biases of the individual satellites are receiver-related and statistically stable from day to day. The influence of pseudorange bias was strikingly noticeable, and can improve the accuracy of the estimated clock offset by several ps for GPS; and by more than 15 ps for GALILEO and BDS after considering bias inconsistencies. Furthermore, owing to the pseudorange bias correction, the convergence and positioning performance have improved significantly, with an improvement of more than 12 % for the static precise point position (PPP), and more than 10 % for the kinematic PPP.

A Novel Two-Stage Adaptive Filtering Model-Based GNSS/INS Tightly Coupled Precise Relative Navigation Algorithm for Autonomous Aerial Refueling

Autonomous aerial refueling (AAR) has generated great interest in recent years. However, much research has focused on the vision-based close docking stage; few studies have been conducted on the navigation algorithm for the rendezvous and following stages. High-precision relative navigation in following stage can provide favourable conditions for successful docking. Aiming at precise relative navigation in the complex high dynamic environment of aerial refueling rendezvous and following stages, a two-stage adaptive filtering architecture is exploited in this paper. An adaptive main Kalman filter (AKF) is realized for ambiguity eliminated GNSS/INS tightly coupled integrated system, and a robust adaptive subfilter is developed for GNSS individually. Particularly, aiming at the influence of pseudorange observation multipath outliers and state abnormal disturbances in unmanned air vehicle- (UAV-) tanker proximity, an INS-aided bifactor robust and classified factor adaptive filtering (IBRCAF) algorithm for single-frequency ambiguity resolution is proposed. Finally, the effectiveness of the algorithm is verified by the simulation experiments for UAV-tanker. The results indicate that the IBRCAF algorithm can efficiently suppress the influence of pseudorange multipath gross errors and abnormal state disturbances and greatly raise the success rate of ambiguity resolution, and the two-stage adaptive filtering algorithm of IBRCAF-AKF can significantly improve relative navigation performance and achieve centimeter-level accuracy.

Navigation in GEO, HEO, and Lunar Trajectory Using Multi-GNSS Sidelobe Signals

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.

Water Level Retrieval Using a posteriori Residual of GNSS Pseudorange and Carrier-Phase Observations

In global navigation satellite system reflectometry (GNSS-R) applications, water level variations could be determined by analyzing one of three types of data: signal-to-noise ratios (SNRs), combinations of carrier-phase observations and combinations of pseudorange and carrier-phase observations. In this study, a new GNSS-R method based on the analysis of a posteriori residual of undifferenced and uncombined (UC) Precise Point Positioning (PPP) and ionosphere free (IF) PPP was proposed. Double peaks were found in the Lomb-Scargle periodogram (LSP) estimates of dual-frequency carrier-phase residuals generated with UC PPP, the pseudorange and carrier-phase residuals generated with IF PPP and the detrended S2 time series. To solve this problem, we present a strict quality control strategy to screen the correct retrievals. Two experimental datasets from a dam and a bridge-deformation monitoring system, respectively, were used to evaluate the performance of this new method in water-level retrieval. The results show that the water level retrievals from the pseudorange and carrier-phase residuals generated by the UC PPP and IF PPP positioning method show a good agreement with the in-situ references, with correlation coefficient exceeding 0.95 and 0.97 in the two experiments, which is comparable to the SNR method. The retrievals showed a root mean square error (RMSE) of 6-7cm in the reservoir experiment and 13-16cm in the Ganjiang river experiment. Meanwhile, the inter-frequency bias for about 0.2m was found in the Xilongchi reservoir water level retrieval experiment, however, it is not the case for the Ganjiang River water level retrieval experiment. The new method enables the simultaneous determination of displacements and water-level variation and is thus applicable for in-situ displacement monitoring of civil engineering structures, such as dam, bridge etc.

INS/GNSS Integrated Rover Navigation Designed With MDPO-Based Dual-Satellite Lunar Global Navigation Systems

Aiming to provide navigational framework to upcoming early lunar exploration missions by lunar rovers, interests in robust and low-cost global satellite navigation systems (GNSS) around the Moon are growing more than ever before. In response, dual-satellite lunar global navigation systems (LGNS) based on Multi-epoch Double-differenced Pseudorange Observation (MDPO) algorithm was proposed in our earlier work. While the MDPO-based dual-satellite LGNS can provide reasonably high positioning accuracy at an order of several tens of meters within a one-minute observation, the positioning calculation is only available when the two navigational satellites are in user’s view. This limitation can be overcome by integrating other navigational sensors such as inertial navigation system (INS) and compensating for user’s positions in the absence of GNSS signals. The main objective of this research is to provide an integration model of INS and MDPO-based dual-satellite LGNS measurements and quantitatively show the benefits of the proposed integration by numerical simulations. More specifically, the major contributions of this paper are three-fold: 1) proposed a mathematical model of INS/GNSS integration adopted for the MDPO algorithm, 2) developed a numerical simulation that combines INS measurements and dual-satellite LGNS measurements, and 3) performed a quantitative comparison between the proposed INS/GNSS integration and raw dual-satellite LGNS measurements.