A new evil waveforms evaluating method for new BDS navigation signals

With the advent of new global navigation satellite systems (GNSSs) and new signals, GNSS users will rely more on them to obtain higher-accuracy positioning. Evil waveform monitoring and assessment are of great importance for GNSS to achieve its positioning, velocity, and timing service with high accuracy. However, the advent of new navigation signals introduces the necessity to extend the traditional analyzing techniques already accepted for binary phase-shift keying modulation to new techniques. First, the well-known second-order step thread model adopted by the International Civil Aviation Organization is introduced. Then the extended new general thread models are developed for the new binary offset carrier modulated signals. However, no research has been done on navigation signal waveform symmetry yet. Simulation results showed that, waveform asymmetry may also cause tracking errors, range biases, and position errors in GNSS receivers. It is thus imperative that the asymmetry be quantified to enable the design of appropriate error budgets and mitigation strategies for various application fields. A novel evil waveform analysis method, called waveform rising and falling edge symmetry (WRaFES) method, is proposed. Based on this WRaFES method, the correlation metrics are provided to detect asymmetric correlation peaks distorted by received signal asymmetry. Then the statistical properties of the proposed methods are analyzed, and a proper deformation detection threshold is calculated. Finally, both simulation results and experimentally measured results of Beidou navigation satellite system (BDS) M1-S B1Cd signal are given, which show the effectiveness and robustness of the proposed thread models.     

Position-domain integrity risk-based ambiguity validation for the integer bootstrap estimator

Integrity monitoring for ambiguity resolution is of significance for utilizing the high-precision carrier phase differential positioning for safety–critical navigational applications. The integer bootstrap estimator can provide an analytical probability density function, which enables the precise evaluation of the integrity risk for ambiguity validation. In order to monitor the effect of unknown ambiguity bias on the integer bootstrap estimator, the position-domain integrity risk of the integer bootstrapped baseline is evaluated under the complete failure modes by using the worst-case protection principle. Furthermore, a partial ambiguity resolution method is developed in order to satisfy the predefined integrity risk requirement. Static and kinematic experiments are carried out to test the proposed method by comparing with the traditional ratio test method and the protection level-based method. The static experimental result has shown that the proposed method can achieve a significant global availability improvement by 51% at most. The kinematic result reveals that the proposed method obtains the best balance between the positioning accuracy and the continuity performance.     

Beidou satellite maneuver thrust force estimation for precise orbit determination

Beidou satellites, especially geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites, need to be frequently maneuvered to keep them in position due to various perturbations. The satellite ephemerides are not available during such maneuver periods. Precise estimation of thrust forces acting on satellites would provide continuous ephemerides during maneuver periods and could significantly improve orbit accuracy immediately after the maneuver. This would increase satellite usability for both real-time and post-processing applications. Using 1 year of observations from the Multi-GNSS Experiment network (MGEX), we estimate the precise maneuver periods for all Beidou satellites and the thrust forces. On average, GEO and IGSO satellites in the Beidou constellation are maneuvered 12 and 2 times, respectively, each year. For GEO satellites, the maneuvers are mainly in-plane, while out-of-plane maneuvers are observed for IGSO satellites and a small number of GEO satellites. In most cases, the Beidou satellite maneuver periods last 15–25 min, but can be as much as 2 h for the few out-of-plane maneuvers of GEO satellites. The thrust forces acting on Beidou satellites are normally in the order of 0.1–0.7 mm/s². This can cause changes in velocity of GEO/IGSO satellites in the order of several decimeters per second. In the extreme cases of GEO out-of-plane maneuvers, very large cross-track velocity changes are observed, namely 28 m/s, induced by 5.4 mm/s² thrust forces. Also, we demonstrate that by applying the estimated thrust forces in orbit integration, the orbit errors can be estimated at decimeter level in along- and cross-track directions during normal maneuver periods, and 1–2 m in all the orbital directions for the enormous GEO out-of-plane maneuver.     

A new multipath mitigation method based on adaptive thresholding wavelet denoising and double reference shift strategy

Multipath disturbance is one of the major error sources in high-accuracy positioning for global navigation satellite system (GNSS). Although various methods based on software and hardware strategies have been developed to mitigate this error, they are still limited by different kinds of factors and the effect is not ideal. After analyzing the existing methods, a new single-difference sidereal filtering method, based on adaptive thresholding wavelet denoising and double reference shift strategy (ATDR), is proposed to mitigate multipath effects for static short-baseline GNSS applications. The key idea of the proposed method is the use of both the adaptive thresholding wavelet denoising to extract an accurate multipath correction model from the reference Day and the double reference shift strategy to mitigate multipath for subsequent Day 2 more accurately and efficiently. By applying the introduced adaptive thresholding method, the average improvement rate of the RMS values of the single-difference residuals can reach about 15.82% compared with the constant thresholding method. Moreover, after applying the proposed ATDR method, the 3D positioning precision is improved by about 37.73% for the single epoch mode with 30 s data sampling rate and about 31.22% for the continuous mode with 1 s high sampling rate compared with the original results. Even compared with the constant thresholding single orbital reference (CTSR) method, the improvement percentage is about 33.94% in single epoch mode and about 25.40% in continuous mode for 3D positioning precision, respectively. In conclusion, the results of the two experiments indicate that the proposed ATDR method performs much better than the CTSR method in mitigating multipath for different sampling rates and different processing modes in the measurement domain for GNSS static short-baseline postprocessing applications.     

Accurate ionospheric delay model for real-time GPS-based positioning of LEO satellites using horizontal VTEC gradient estimation

Ionospheric delays compensation is a mandatory step for precise absolute and relative positioning of Low Earth Orbit Satellites (LEO) by GPS measurements. The most frequently used ionosphere model for real-time GPS-based navigation in LEO is an isotropic model proposed by Lear, which uses the Vertical Total Electron Content (VTEC) above the receiver and a mapping function for TEC evaluation along a given ray path. Based on significant assessed results available for ground-based GPS receivers, we propose the use of a different model relying on the thin shell assumption and a bilinear horizontal variation of the VTEC as a function of latitude and longitude in the shell. It is expected that this model is capable of better describing horizontal gradients in the ionosphere, thus improving ionospheric delay estimation, especially in intense ionospheric conditions. This model is referred to as Linear Thin Shell (LTS). LTS performance in estimating undifferenced and double-differenced ionospheric delays is checked by comparing measured and predicted delays computed using flight data from the GRACE mission. Results show that the LTS always outperforms the isotropic model, especially in case of high solar activity. Moreover, the LTS model provides a higher performance uniformity over a wide range of ionospheric delays, thus ensuring good performance in different conditions. The results obtained demonstrate that the LTS model improves the ionosphere delays estimation accuracy by 20 and 40% for undifferenced and double-differenced delays, respectively. This suggests the LTS model can effectively contribute to improving precision in LEO positioning applications.     

Carrier phase bias estimation of geometry-free linear combination of GNSS signals for ionospheric TEC modeling

The ionosphere can be modeled and studied using multi-frequency GNSS signals and their geometry-free linear combination. Therefore, a number of GNSS-derived ionospheric models have been developed and applied in a broad range of applications. However, due to the complexity of estimating the carrier phase ambiguities, most of these models are based on low-accuracy carrier phase smoothed pseudorange data. This, in turn, critically limits their accuracy and applicability. Therefore, we present a new methodology of estimating the phase bias of the scaled L1 and L2 carrier phase difference which is a function of the ambiguities, the ionospheric delay, and hardware delays. This methodology is suitable for ionospheric modeling at regional and continental scales. In addition, we present its evaluation under varying ionospheric conditions. The test results show that the carrier phase bias of geometry-free linear combination can be estimated with a very high accuracy, which consequently allows for calculating ionospheric TEC with the uncertainty lower than 1.0 TECU. This high accuracy makes the resulting ionosphere model suitable for improving GNSS positioning for high-precision applications in geosciences.     

A new GPS/BDS tropospheric delay resolution approach for monitoring deformation in super high-rise buildings

A new approach for deformation monitoring of super high-rise building using GPS/BDS technology is proposed for the case when prior coordinates are known and the baseline is short but has a large height difference. The approach is based on the ambiguity function method (AFM). Considering that the double-differenced (DD) troposphere delay residual error cannot be ignored, the relative zenith tropospheric delay (RZTD) parameter is introduced into the original AFM equation. Thus, the RZTD and 3D coordinate parameters are together obtained through the modified AFM (MAFM). Due to the low computational efficiency of conventional AFM, an improved particle swarm optimization (IPSO) algorithm is used to search the four optimal parameters X/Y/Z/RZTD and replaces the grid search method. In this study, GPS/BDS deformation monitoring data for buildings with approximately 290 m height difference were used to verify the feasibility of the proposed MAFM. Numerical results show a single-epoch average computation time of approximately 0.3 s, which meets the requirements of near-real-time dynamic monitoring. The average accuracy of the GPS single-epoch RZTD solution is better than 1 cm, the combined GPS/BDS MAFM performance outperforms the GPS-only system, and using multi-epoch observations can further improve the accuracy of the RZTD solution. After RZTD correction, GPS/BDS monitoring precision can be improved, particularly the height dimension, whose precision is improved by approximately 6 cm.     

Revisit the calibration errors on experimental slant total electron content (TEC) determined with GPS

The calibration errors on experimental slant total electron content (TEC) determined with global positioning system (GPS) observations is revisited. Instead of the analysis of the calibration errors on the carrier phase leveled to code ionospheric observable, we focus on the accuracy analysis of the undifferenced ambiguity-fixed carrier phase ionospheric observable determined from a global distribution of permanent receivers. The results achieved are: (1) using data from an entire month within the last solar cycle maximum, the undifferenced ambiguity-fixed carrier phase ionospheric observable is found to be over one order of magnitude more accurate than the carrier phase leveled to code ionospheric observable and the raw code ionospheric observable. The observation error of the undifferenced ambiguity-fixed carrier phase ionospheric observable ranges from 0.05 to 0.11 total electron content unit (TECU) while that of the carrier phase leveled to code and the raw code ionospheric observable is from 0.65 to 1.65 and 3.14 to 7.48 TECU, respectively. (2) The time-varying receiver differential code bias (DCB), which presents clear day boundary discontinuity and intra-day variability pattern, contributes the most part of the observation error. This contribution is assessed by the short-term stability of the between-receiver DCB, which ranges from 0.06 to 0.17 TECU in a single day. (3) The remaining part of the observation errors presents a sidereal time cycle pattern, indicating the effects of the multipath. Further, the magnitude of the remaining part implies that the code multipath effects are much reduced. (4) The intra-day variation of the between-receiver DCB of the collocated stations suggests that estimating DCBs as a daily constant can have a mis-modeling error of at least several tenths of 1 TECU.     

Image-aided platform orientation determination with a GNSS/low-cost IMU system using robust-adaptive Kalman filter

The availability of miniaturized sensors with enhanced capabilities, new methods for image processing, and easy access to small and low-weight airborne platforms for data acquisition, including unmanned vehicles, opens new possibilities for geodetic navigation applications and developing new developments in sensor fusion. In this context, the development of efficient methods, based on low-cost sensors, to extract precise georeferenced information from digital cameras is of utmost interest. We present a method to improve the performance of the integration of GNSS/low-cost IMU by exploiting the orientation changes retrieved from digital images. In this work, a robust-adaptive Kalman filter is also introduced to further improve the performance of the method deployed. The adaptive factor and the robust factor accomplished are determined by innovation information and the threshold value of orientation changes between consecutive images. Results from airborne tests used to assess the performance of the method are presented. The results show that using a non-metric camera, the Euler angle estimation accuracy of the GNSS/low-cost IMU integration can be improved to be close to 0.5 degree and an additional improvement, which can reach 59%, can be achieved after using the robust-adaptive Kalman filter.     

Analysis of estimated satellite clock biases and their effects on precise point positioning

This study provides a systemic analysis to identify the biases in estimated satellite clocks and illustrates their effects in precise point positioning (PPP). First, the precise satellite clock estimation method considering pseudorange and carrier phase hardware delays is derived. Two methods for satellite clock estimation are compared, and their equivalency is discussed. The results show that apart from the well-known constant code hardware biases, the time-variant phase hardware biases are also absorbed by the estimated clocks. Also, the satellite clocks contain biases caused by modeling errors. To analyze the effects of these biases, they are grouped into initial clock biases (ICBs) and time-dependent biases (TDBs). Then, a detailed analysis of the impact of the biases on PPP-based troposphere and coordinate estimates is conducted. The experimental analysis demonstrates that TDBs affect positioning and tropospheric estimates, and their impacts are more significant in the static mode. The ICBs affect coordinate accuracy, zenith total delay mean bias, and its standard deviations only at the millimeter level for kinematic and static PPP, which is negligible. However, the ICBs affect the convergence period for both static and real kinematic PPP, and the magnitude of their impact largely depends on data quality. Note that satellites clocks are generally estimated with the P1/P2 and L1/L2 ionospheric-free combinations, and that hardware-specific parts of ICBs and TDBs cancel if users employ the same type of observables as the clock providers. Otherwise, the effects of biases cannot be ignored, especially for triple-frequency applications. Also, modeling-specific parts of ICBs and TDBs are significant in real-time clocks, which also affect user applications. Our conclusion is applicable for understanding the effects of these biases.