Cycle Slip Detection Research Articles

A cycle slip detection and repair method based on generalized-cross-validation regularization for BDS-3 quad/pent-frequency data

Abstract Multi-frequency (quad/pent-frequency) observations improve the success rate for BeiDou Navigation Satellite System (BDS-3) cycle slip detection and repair. Three factors are comprehensively considered: the combination of observation wavelength, the amplification factor of ionospheric delay, and the insensitivity, to select the optimal combination coefficients for BDS-3 multi-frequency cycle slip detection. Due to the ill-conditioned equation in multi-frequency cycle slip repair, the generalized-cross-validation regularization auxiliary LAMBDA method is proposed. To validate the effectiveness of the proposed detection and repair method under different observation environments, two stations are selected for the test. Using real data, the effectiveness of the selected optimal combination coefficients and the proposed method are tested. The conclusions are as follows: (1) for quad-frequency, one geometry-free and ionosphere-free (GFIF) combination [−1, 2, −4, 3] and three linearly independent geometry free carrier phase (GF) combinations [−1, 1, 0, 0], [−1, 1, 1, −1], and [−1, 2, −1, 0] are employed to detect cycle slips. For pent-frequency, one GFIF combination [−2, 2, 1, −2, 1] and four linearly independent GF combinations [−1, 1, 0, 0, 0], [0, 0, −1, 1, 0], [0, 0, −1, 0, 1], and [0, −1, 1, 1, −1] are adopted for cycle slip detection. (2) The algorithm proposed in this paper has been demonstrated to achieve a quad/pent-frequency cycle slip detection success rate of 99.99% and 100% in the coastal environment, and both 100% for quad/pent-frequency detection success in the urban environment. (3) The success rate of repair were 99.27% and 99.94% for the coastal stations, and 99.83% and 100% for the urban stations, respectively. The proposed algorithm offers a dependable approach for the identification and rectification of multi-frequency cycle slips, while also providing a point of reference for the future advancement of multi-frequency cycle slip repair techniques.

CEEMDAN combined wavelet denoising improved the MW cycle slip detection algorithm

In the preprocessing of high-precision navigation and positioning data, the most widely used MW combination cycle slip detection method is greatly affected by pseudorange noise. It has issues such as missing small cycle slips and failing to promptly reset the recursive averaging process after cycle slip detection failure, which leads to subsequent threshold divergence. This paper proposes an improved MW combination cycle slip detection method based on Complete Ensemble Empirical Mode Decomposition (CEEMDAN), permutation entropy, and wavelet denoising, which uses CEEMDAN to decompose the cycle slip signal into a series of intrinsic modal functions (IMFs) and then selects the IMFs that require denoising through the permutation entropy algorithm, and the wavelet denoising technique is combined to eliminate the residual noise further, so that the noise can be removed more accurately. Experimental results show that compared with the original MW algorithm, the proposed improved method can effectively reduce the influence of pseudo-range noise, and reduce the false detection rate of cycle slip from 1.6% and 6–0%. All small period slips can be successfully detected in complex noise environments, avoiding the missed detection of the original MW algorithm and the related threshold divergence problems.

Improving cycle slip detection in ambiguity-fixed precise point positioning for kinematic LEO orbit determination

Improving cycle slip detection in ambiguity-fixed precise point positioning for kinematic LEO orbit determination

Initial Study of Adaptive Threshold Cycle Slip Detection on BDS/GPS Kinematic Precise Point Positioning during Geomagnetic Storms

Global navigation satellite system (GNSS) provides users with all-weather, continuous, high-precision positioning, navigation, and timing (PNT) services. In the operation and use of GNSS, the influence of the space environment is a factor that must be considered. For example, during geomagnetic storms, a series of changes in the Earth’s magnetosphere, ionosphere, and upper atmosphere affect GNSS’s positioning performance. To investigate the positioning performance of global satellite navigation systems during geomagnetic storms, this study selected three geomagnetic storm events that occurred from September to December 2023. Utilizing the global positioning system (GPS)/Beidou navigation satellite system (BDS) dual-system, kinematic precise point positioning (PPP) experiments were conducted, and the raw observational data from 100 stations worldwide was analyzed. The experimental results show that the positioning accuracy of some stations in high-latitude areas decreases significantly when using the conventional Geometry Free (GF) cycle-slip detection threshold during geomagnetic storms, which means that the GF is no longer applicable to high-precision positioning services. Meanwhile, there is no significant change in the satellite signal strengths received at the stations during the period of the decrease in positioning accuracy. Analyzing the cycle-slip rates for stations where abnormal accuracy occurred, it was observed that stations experiencing a significant decline in positioning accuracy exhibited serious cycle-slip misjudgments. To improve the kinematic PPP accuracy during magnetic storms, this paper proposes an adaptive threshold for cycle-slip detection and designs five experimental strategies. After using the GF adaptive threshold, the station positioning accuracy improved significantly. It achieved the accuracy level of the quiet period, while the cycle-slip incidence reached the average level. During magnetic storms, the ionosphere changes rapidly, and the use of the traditional GF constant threshold will cause serious cycle-slip misjudgments, which makes the dynamic accuracy in high latitude areas and some mid-latitude areas uncommon, while the use of the GF adaptive threshold can alleviate this phenomenon and improve the positioning accuracy in the high-latitude regions and some of the affected mid-latitude areas during the magnetic storms.

DGVINS: Tightly Coupled Differential GNSS/Visual/Inertial for Robust Positioning Based on Optimization Approach

Abstract Due to the fragility of single-sensor positioning technology in complex scenarios, especially in complex urban areas, multi-sensor positioning technology is becoming increasingly popular. To further improve the robustness of the positioning system by fully utilizing the information from various sensors, this article proposes a differential-GNSS-visual-inertial navigation system (DGVINS) that tightly fuses differential global navigation satellite system (GNSS), vision and inertial information to provide accurate, robust and seamless position information for intelligent navigation applications. DGVINS effectively utilizes all sensor measurements within the factor graph optimization (FGO) framework. When using the carrier phase of GNSS, single-epoch ambiguity optimization is employed to prevent cycle slip detection and adapted to complex environments. We conducted experiments on public datasets with various features and compared the performance of simple differential-GNSS (DGNSS), DGNSS+Inertial, and the state-of-the-art GNSS-visual-inertial navigation systems (GVINS). We also compared the performance of different combinations of GNSS differential factors in various environments. Due to the superiority of differential GNSS and its appropriate integration with visual and inertial measurements, the experimental results demonstrate that DGVINS exhibits significant improvements in accuracy, stability, and continuity in both GNSS-challenged and vision-challenged environments.

A novel method for cycle slip detection and restoration of BDS carrier phase

The chief purpose of this present study is to develop a new approach to cycle slip detection and restoration of the BeiDou Navigation Satellite System (BDS) carrier phase. Based on the RAIM algorithm in the application of aviation safety, we extend the application to ensure the precision of the carrier phase. To stand-alone receivers of a low-cost single frequency, carrier phase data is made different between adjacent epochs. Then least-square residuals were to design a RAIM scheme with differential carrier phase data to find out the epoch with cycle slip, and finally repair cycle slip by Chebyshev polynomial. Results indicate that the approach can detect cycle slip effectively and both big cycle slip and small cycle slip could be repaired.

Detection and repair of BDS six-frequency cycle slips based on recursive filtering and integer constraint method

The multi-frequency signals of the Beidou system are very helpful for positioning, but in data processing, the detection and repair of multi-frequency cycle slips also face certain challenges. A recursive filtering and integer constraint cycle slip detection and repair method for the Beidou six-frequency is proposed in this paper. This method utilises five sets of combination coefficients of six-frequency and three sets of dual-frequency combinations, and detects and repairs cycle slips through integer constraints of cycle slip estimation. The proposed method has been validated by data with a sampling rate of 1 Hz, and can detect the position and size of cycle slips at various frequencies, whether it is random cycle slips or small cycle slips of equal size less than 2 cycles, with a detection success rate of 100%.

GPS/BDS triple-frequency cycle slip detection and repair based on moving window global search method

Cycle slip detection and repair are crucial steps in achieving high accuracy in Global Navigation Satellite System (GNSS) data processing. The use of Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS) triple frequency observations allows for more accurate detection and repair of cycle slips compared to single or dual frequency. This study presents a moving window global search method by selecting three sets of combined coefficients to construct geometry-free (GF) models to minimize the influence of the ionosphere, using a moving window to update the standard deviation of cycle slip estimation, applying the "3 σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upsigma$$\\end{document}" criterion to constrain the range, and utilizing a global search method to detect and repair triple-frequency cycle slips. Through five sets of 1 Hz GNSS data experiments, the results demonstrate the effectiveness of this method in determining the position and size of triple-frequency cycle slips while avoiding multi-value problems. The detection success rate for GPS ranges from 98.0 to 100.0%, while BDS ranges from 92.0 to 100.0%. On average, GPS achieves a detection rate of 99.2%, and BDS reaches 96.7%, which is 0.8% and 1.8% higher than the direct rounding method, respectively. Compared to existing methods, it is also effective for the vast majority of small cycle slips within 2 cycles.

An investigation of PPP degradations over Asia-Pacific region during Tonga volcanic eruption on 15 January 2022

On 15 January 2022, a significant volcanic eruption occurred at Hunga Tonga-Hunga Ha’apai (HTHH), causing global ionospheric disturbances. To investigate ionospheric anomalies and the kinematic GNSS PPP responses to this volcanic eruption over the Asia-Pacific region, the rate of the total electron content index (ROTI) map derived from about 1100 GNSS stations data and ionospheric scintillation indices S4 and σφ are used. We first selected data from six stations for kinematic PPP experiments. Multi-constellation and multi-frequency Precision Positioning (GAMP) software and GNSS analysis software are employed in the process. We then found that the positioning errors of three directions (east, north, up) during disturbance time are larger than those on an ionospheric quiet day (3 January 2022). To explore the reasons for PPP degradation, we conduct a quality analysis of GNSS data on these two days, including carrier-to-noise power-density ratio (C/N0) and the number of cycle slips. The number of satellites affected by cycle slips increased obviously in the disturbance time. The statistics of cycle slip occurrence rate at low latitudes is 12.35 % while that on ionospheric quiet day is only 6.05 %. The strategy of expanding the cycle slip detection thresholds from 0.15 m to 1.5 m for phase geometry free (PGF) combination and 5 cycles to 12 cycles for Hatch–Melbourne-Wübbena (HMW) combination failed to significantly improve the PPP solutions based on data from 357 stations. It was found that only increasing the detection thresholds could not mitigate the PPP degradations. Our investigations contribute to the study of space weather and kinematic GNSS PPP responses to volcanic eruptions.

A hierarchical combination algorithm for real-time cycle slip detection and repair in low satellite elevation and high ionospheric activity conditions

To enhance the accuracy and robustness of cycle slip detection and repair for triple-frequency data while minimizing the adverse effects of low satellite elevation and high ionospheric activity, a hierarchical combination algorithm for real-time cycle slip detection and repair is proposed. This algorithm begins by prioritizing the reduction of noise and ionospheric delay coefficients. It determines the optimal coefficients for the combination of observations from the BeiDou Navigation Satellite System’s (BDS) Extra-Wide Lane (EWL), Wide Lane (WL), and Narrow Lane (NL). Leveraging the longer wavelength characteristics of the EWL combination, it simultaneously conducts cycle slip detection on the EWL combination alongside the pseudorange combination. Following this, based on the detection outcomes from the EWL combination, cycle slip detection is carried out on the WL combination. Finally, using the detection findings from the WL combination, cycle slip detection is executed on the NL combination. Given the NL combination’s shorter wavelength and higher susceptibility to ionospheric delay, a dynamic ionospheric prediction model is applied to the NL combination to further mitigate the impact of ionospheric disturbances. After completing the cycle slip detection process, the results from the EWL, WL, and NL combinations are integrated and solved. Experimental results clearly demonstrate that, even in scenarios characterized by low satellite elevation and active ionospheric conditions, this algorithm consistently delivers outstanding detection performance for cycle slip instances, particularly for small cycle slip (less then two cycles). Remarkably, this performance is achieved without the need for intricate searches during cycle slip repair.

QUALITY ANALYSIS OF SMARTPHONE GNSS OBSERVATIONS AND IMPACT ON PRECISE POSITIONING

Abstract. The use of low-cost and ultra-low-cost receivers such as smartphones and wearables has been raising these days due to their affordability and widespread availability. Along with the release of Android Version 7 in 2016, the raw GNSS measurements became accessible through the location API, which includes the GNSSMeasurement class and GNSSClock class. However, the users are required to extract the typical GNSS observations, such as pseudorange, carrier-phase, and Doppler observations, from the raw data coming from these two classes. It should be mentioned some quality concerns may arise during the conversion process from the raw GNSS measurements to the typical GNSS measurements. These quality concerns would subsequently affect GNSS data processing such as cycle slip detection, code smoothing and ultimately positioning performance. In this paper, we first analyse the quality of GNSS observations logged from smartphones. Furthermore, we address potential issues that can arise during the generation of GNSS observations. We also introduce our developed in-house software, UofC CSV2RINEX, which is designed to convert CSV files into RINEX files.

Dual-frequency GPS Cycle Slip Detection and Repair Based on Dynamic Test

How to solve the multi-values and accurately detect the cycle slip of each frequency was particularly critical of dual-frequency GPS. This paper used the geometry-free phase combinations, proposed a dynamic test method to detect cycle slip outliers, which determined the cycle slip by constraining the value range of the cycle slip sequences of the dual-frequency GPS through the constantly updated its standard deviation. The dynamic test of cycle slip detection and repair method has been tested by using GPS data with sampling interval of 1s, 5s, 10 s and 15s. The method can not only solve the problem of multi-values, but also accurately detect the cycle slip values at various frequencies, whether the fixed cycle slip is added to the random position or the random cycle slip is added to the random position. Experiments with four different sampling intervals, the results showed that the proposed method of cycle slip detection and repair calculation success rate reaches 98.75%.

A Modified Cycle Slip Detection Method with GNSS Doppler Assistance and Optimizing by Adaptive Threshold and Sliding Polynomial Fitting

Cycle slip determination plays an important role in high-precision data processing and application of global navigation satellite systems (GNSS). The TurboEdit method consists of the Melbourne-Wubbena (MW) and the geometry-free phase (GF) combination. It can correctly detect and repair cycle slip in most cases. Cycle slip detection (CSD) with GF is disturbed by severe ionospheric delay variations; moreover, CSD or cycle slip repair (CSR) with the MW faces the risk of the disturbance from large pseudorange errors. Hence, cycle slip determination would be difficult under some extreme conditions, e.g., cycle slips occur in low altitude satellite, low sampling rate of dual-frequency observations. To overcome the limitations, a new dual-frequency CSD and CSR method is proposed. The main contents are as follows: (1) compared with the MW method, the Doppler-assisted phase subtraction pseudorange (DAPSP) method that we proposed has no detection blind spot and can effectively reduce the influence of pseudorange noise at high sampling rates; thus, we replace MW by the DAPSP method to improve the detection accuracy. (2) An adaptive threshold model with root mean square (RMS) is established to effectively reduce the missing and false range detection of cycle slip. (3) The sliding polynomial fitting-assisted GF (SPFAGF) is carried out according to the satellite altitude angle. The trend of ionospheric delay and residual multipath effect error between adjacent epochs is extracted and suppressed by SPFAGF. The method combined with DAPSP and SPFAGF (DAPSP-SPFAGF) overcomes the situation that the TurboEdit method cannot effectively detect under extreme conditions. The experimental results of Beidou dual-frequency observation data show that the TurboEdit method and the DAPSP-SPFAGF method can perform CSD and CSR in most cases. At the sampling rate of 1 s, the detection speed of DAPSP-SPFAGF method is significantly faster than TurboEdit method. The number of false positives about CSD is reduced from 68 to 0. At the sampling rate of 30 s and under the condition of the observed satellite altitude angle below 30°, the false alarm rate of the DAPSP-SPFAGF method is 0, but the TurboEdit method’s false alarm rate is 71.2%. So DAPSP-SPFAGF method is prior to the TurboEdit method at the high sampling rates or under extreme conditions, especially it can accurately detect and repair cycle slip and reduce the false positives and false alarm rate.

Dual-Frequency GNSS Observations Cycle Slip Detection and Repair Method Using the Ensemble Hatch–Melbourne–Wübbena (HMW) Combination—Prophet Model

Dual-Frequency GNSS Observations Cycle Slip Detection and Repair Method Using the Ensemble Hatch–Melbourne–Wübbena (HMW) Combination—Prophet Model

Cycle Slip Detection By Combining TECR And Reconstructed Doppler Integral Method

Poor observation environment and other factors lead to the whole cycle slips of carrier phase observation value, which affects the positioning accuracy. There are detection loopholes in the traditional cycle slips detection methods, especially the small value cycle slips, equivalent cycle slips and special value cycle slips are difficult to detect. A method combining Total Electron Contents Rate (TECR) and Doppler Value Reconstruction is proposed to solve the deficiency of cycle slip detection. Based on Doppler observations and Doppler detection method, the Doppler observations are reconstructed. This method improves the accuracy of Doppler observations. The proposed method has been verified that the reconstructed Doppler observations can improve the detection accuracy of small cycle slips, and can accurately detect any large value, small value of 1 cycle, Both frequency equivalent cycle slips and special value cycle slips can be accurately detected.

A Cycle Slip Detection and Repair Method Based on Inertial Aiding for BDS Triple-Frequency Signals

Cycle slip detection and repair is a prerequisite to obtain high-precision positioning based on a carrier phase. Traditional triple-frequency pseudorange and phase combination algorithm are highly sensitive to the pseudorange observation accuracy. To solve the problem, a cycle slip detection and repair algorithm based on inertial aiding for a BeiDou navigation satellite system (BDS) triple-frequency signal is proposed. To enhance the robustness, the INS-aided cycle slip detection model with double-differenced observations is derived. Then, the geometry-free phase combination is united to detect the insensitive cycle slip, and the optimal coefficient combination is selected. Furthermore, the L2-norm minimum principle is used to search and confirm the cycle slip repair value. To correct the INS error accumulated over time, the extended Kalman filter based on the BDS/INS tightly coupled system is established. The vehicular experiment is conducted to evaluate the performance of the proposed algorithm from a few aspects. The results indicate that the proposed algorithm can reliably detect and repair all cycle slips that occur in one cycle, including the small and insensitive cycle slips as well as the intensive and continuous cycle slips. Additionally, in signal-challenged environments, the cycle slips occurring 14 s after a satellite signal outage can be correctly detected and repaired.

Improved real-time cycle-slip detection for Low Earth Orbit satellites based on the dynamic force model

Cycle-slip detection is crucial in achieving high-accuracy Global Navigation Satellite System (GNSS) data processing for Low Earth Orbit (LEO) satellites. The detector based on the dynamic force model has emerged as a promising approach to cycle-slip detection, as it is insensitive to the number of visible tracked satellites and insufficient accuracy of a prior orbit. However, the ionospheric delay limits the applications of the method for high-speed LEO satellites under different scenarios. To complete the method, we propose a new combination of two test parameters: the phase ionosphere-free (IF) combinations in the second-order time-difference model and the Melbourne–Wübbena (MW) combinations. Meanwhile, we highlight the identification of whether the fake-positive cycle slips are derived from the flicker noises and jumps in the receiver quartz-based clock. Considering highly, moderately active and quiet ionospheric activities, comparisons are performed among our proposed two test parameters and the phase second-order time-difference wide-lane (WL) combinations. The results indicate that the detector based on the IF combinations performs optimally under the three levels of ionospheric activities. The time-difference ionospheric delays vary dramatically even under moderately active and quiet ionospheric activities, which leads to the inferiority of the detector based on the WL combinations to one based on the MW combinations. The performances of detectors based on the IF and MW combinations are further evaluated through real-time kinematic orbital determinations comparisons with the Jet Propulsion Laboratory (JPL) precise science orbits (PSO). After using the IF detector, the mean 3-Dimensional (3D) root-mean-squares (RMS) of the orbit differences have slightly decreased by 12% and 6% for the Gravity Recovery and Climate Experiment (GRACE) A and B satellites, respectively. In the case of the GRACE follow-on (GRACE-FO) satellites, the IF detector has achieved a more than 40% improvement over the MW detector. Further, the use of both detectors simultaneously results in a slight improvement in orbit accuracy.

Real-time GNSS triple-frequency cycle slip detection using three optimal linear combinations

Real-time GNSS triple-frequency cycle slip detection using three optimal linear combinations

Cycle slip detection and repair based on the unmodeled-error-constrained geometry-free combining geometry-based models for a single-frequency receiver

Accurate cycle slip detection and repair is the prerequisite of high-precision and high-reliability Global Navigation Satellite System (GNSS) positioning and navigation. The cycle slips are widely existent in a challenging environment or a low-cost receiver, where the unmodeled errors are usually significant. Therefore, it is highly urgent to enhance the performance of cycle slip detection and repair for a single-frequency receiver under complex conditions. In this paper, a new cycle slip processing method based on the unmodeled-error-constrained geometry-free (GF) combining geometry-based (GB) models is proposed. Specifically, first, the short-term GF and GB unmodeled errors are predicted based on their temporal behaviours. Second, the predicted GF and GB unmodeled errors are applied to correct the potentially biased GF and GB models. Finally, the cycle slips are detected and repaired by combing the unmodeled-error-constrained GF and GB models. By using the real dataset with multipath effects and ionospheric delays, the proposed short-term prediction of unmodeled errors is effective both in GF and GB models, where the centimetre-level accuracy can be obtained, respectively. Based on this, three different typical situations, i.e., large, small, and mixed cycle slips, are all analysed. The results show that compared with the traditional methods, the proposed method considering the unmodeled errors is the most effective. Precisely, it can process the cycle slips with a detection percentage of 100% and a mean repair percentage of 93% even under challenging environments.

Cycle Slip Detection in Multi Frequency GPS Monitoring under High Sampling Rate Based on P-code Constraint

Cycle Slip Detection in Multi Frequency GPS Monitoring under High Sampling Rate Based on P-code Constraint