Cycle Slip Detection Method Research Articles

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.

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.

Position and Attitude Determination in Urban Canyon with Tightly Coupled Sensor Fusion and a Prediction-Based GNSS Cycle Slip Detection Using Low-Cost Instruments.

We present a position and attitude estimation algorithm of moving platforms based on the tightly coupled sensor fusion of low-cost multi baseline GNSS, inertial, magnetic and barometric observations obtained by low-cost sensors and affordable dual-frequency GNSS receivers. The sensor fusion algorithm is realized by an Extended Kalman Filter and estimates the states including GNSS receiver inter-channel biases, integer ambiguities and non-GNSS receiver biases. Tightly coupled sensor fusion increases the reliability of the position and attitude solution in challenging environments such as urban canyons by utilizing the inertial observations in case of GNSS outage. Moreover, GNSS observations can be efficiently used to mitigate IMU sensor drifts. Standard GNSS cycle slips detection methods, such as the application of triple differences or linear combinations such as Melbourne-Wübbena combination and the phase ionospheric residual extended TurboEdit method. However, these techniques are not well suited for the localization in quickly changing environments such as urban canyons. We present a new method of tightly coupled sensor fusion supported by a prediction based cycle slip detection technique, applied to a GNSS setup using three antennas leading to multiple moving baselines on the platform. Thus, not only the GNSS signal properties but also the dynamics of the moving platform are considered in the cycle slip detection. The developed algorithm is tested in an open-sky validation measurement and two sets of measurement in an urban canyon area. The sensor fusion algorithm processes the data sets using the proposed prediction-based cycle slip method, the loss-of-lock indicator-based, and for comparison, the Melbourne-Wübbena and the TurboEdit cycle slip detection methods are also included. The obtained position and attitude estimation results are compared to the internal solution of raw data source GNSS receivers and to the observations of a high-accuracy GNSS/INS unit including a fiber optic gyro. The validation test confirms the proper cycle slip detection in an ideal environment. The more challenging urban canyon test results show the reliability and the accuracy of the proposed method. In the case of the second urban canyon test, the proposed method improved the integer ambiguity resolution success rate by 19% and these results show the lowest horizontal and vertical coordinate distortion in comparison of the linear combination and the loss-of-lock-based cycle slip methods.

Reconstructed doppler cycle slip detection method based on inter satellite difference

Aiming at the problem of single frequency cycle slip detection in GNSS location, a new cycle slip detection method is proposed. This method uses the position and speed of the satellite and the position and speed of the receiver to calculate the Doppler frequency shift, then uses the integral value of the Doppler frequency shift to make a difference with the station satellite distance, and uses the inter satellite difference method to eliminate the receiver clock error, which can accurately detect the small cycle slip of one cycle. This method is not affected by the coordinates of the receiver, and can be realized only by the pseudo range single point positioning result.

Cycle-slip Detection Method Considering Clock Jump for GNSS Raw Observation of Smartphones

Using low-cost sensors to achieve high-precision positioning has been a hot research topic in autonomous driving technology, and smartphones not only have the advantages of low cost and easy installation, but also can provide high-precision navigation and positioning services. In this paper, we focus on the cycle-slip detection method based on the original Global Navigation Satellite System (GNSS) observations of smartphones. In response to the problem that the phase value of smartphone GNSS has serious cycle slip and the existence of frequent clock jumps will affect the cycle slip detection, a cycle slip detection method that integrates clock jumps and single and dual frequency observations is proposed. The experiments show that the method can effectively detect the continuous and as small as 0.5 week of cycle slip for the phase observations with the sampling rate of 1 Hz. The root mean square error (RMSE) in the L1 and L5 phase residuals after the cycle slip repair is 7.0 mm and 8.3 mm, respectively, with an accuracy improvement of 18.16% and 9.62%, which indicates that this method is effective and feasible.

Carrier Phase-Based Precise Heading and Pitch Estimation Using a Low-Cost GNSS Receiver

Attitude and heading estimation methods using the global navigation satellite system (GNSS) are generally based on multi-antenna deployment, where the installation space and system cost increase with the increase in the number of antennas. Since the single-antenna receiver is still the major choice of the mass market, we focus on precise and reliable heading and pitch estimation using a low-cost GNSS receiver. Carrier phase observations are precise but have an ambiguity problem. A single difference between consecutive epochs can eliminate ambiguity and reduce the measurement errors. In this work, a measurement model based on the time-differenced carrier phases (TDCPs) is utilized to estimate the precise delta position of the antenna between two consecutive epochs. Then, considering the motion constraint, the heading and pitch angles of a moving land vehicle can be determined by the components of the estimated receiver delta position. A threshold on the length of the delta position is selected to avoid large errors in static periods. To improve the reliability of the algorithm, the Doppler-aided cycle slip detection method is applied to exclude carrier phases with possible cycle slips. A real vehicular dynamic experiment using a low-cost, single-frequency GNSS receiver is conducted to evaluate the proposed algorithm. The experimental results show that the proposed algorithm is capable of providing precise vehicular heading and pitch estimates, with both the root mean square errors being better than 1.5°. This also indicates that the cycle slip exclusion is indispensable to avoid unexpected large errors.

A real-time inertial-aided cycle slip detection method based on ARIMA-GARCH model for inaccurate lever arm conditions

The processing of cycle slip is one of the key techniques of carrier-phase-based high-precision positioning. As for the poor performance of the single-station inertial-aided cycle slip detection based on the tightly coupled integration system using pseudorange and Doppler measurements under inaccurate lever arm conditions, an improved real-time method based on ARIMA-GARCH (autoregressive integrated moving average-generalized autoregressive conditional heteroscedastic) model is proposed. The ARIMA (1, 1, 0) model is used to detrend the fundamental test statistics, and then, the GARCH (1,1) model is used to estimate the conditional variance of the residuals with the characteristics of volatility clustering. Considering the needs for real-time applications, two algorithms with model parameters varied at every epoch and periodically, respectively, are proposed. Two kinds of numerical experiments based on the real data collected from vehicular and flight tests are carried out. The results show that the proposed method can not only greatly reduce the false alarm rate but also can detect simulated 1-cycle slips for all frequencies of all satellites of BDS (BeiDou System) and the period-varied algorithm is recommended due to its good performance of cycle slip detection and low computation cost online.

A Cycle Slip Repair Method Against Ionospheric Effects and Observational Noises for BDS Triple-Frequency Undifferenced Phases.

The cycle slip detection (CSD) and cycle slip repair (CSR) are easily affected by ionospheric delay and observational noise. Aiming at mitigating the above disadvantage, a new BeiDou navigation satellite system (BDS) triple-frequency CSR method (BTCSR) is proposed for the undifferenced phase. BTCSR learns from the classic triple-frequency CSR (CTCSR), with combinations of phases and pseudoranges in correcting ionospheric delay and optimizing observational noise. Different from CTCSR, though, BTCSR has made the following improvements: (1) An optimal model of calculating cycle slip combination is established, which further takes into account the minimization of the effect of residual ionospheric error after the correction. The calculation of cycle slip combination is obtained with the root mean squared errors (0.0646, 0.1261, 0.1069) of cycles, resulting in CSR success rate of 99.9927%, and the wavelengths (4.8842,3.5738,8.1403) of m. (2) A discriminant function is added to guarantee the CSR correctness. This function utilizes epoch-difference value of the ionosphere-free and geometry-free phase to select the correct cycle slip value, which eliminates the interference of large pseudorange errors in determining the final cycle slip. Consequently, the performances of BTCSR and CTCSR have been compared. For the real BDS pseudorange observation with additional 1.5 m errors, which can cover situations of 99.96% pseudorange noise, results of CTCSR show failure, but results of BTCSR keep correct. Moreover, BTCSR has made the following improvements relative to the geometry-free cycle slip detection method (GFCSD) and Melboune–Wubbena cycle slip combination detection method (MWCSD): (1) During a moderate magnetic storm of level 6, CSR testing, with the BDS monitoring station in a low latitude region, showed that some failures occur in GFCSD because of severe ionospheric variation, but BTCSR could correctly identify and fix cycle slips. (2) For the BDS observation data with an additional 1.5 m error on the actual pseudoranges, MWCSD exhibited failures, but the repair results of BTCSR were correct and reliable. (3) For the special slips of (0,59,62) cycles, and equal slips of (1,1,1) cycles on (B1,B2,B3), that are hard to detect by GFCSD and MWCSD, respectively, BTCSR could repair these correctly. Finally, BTCSR obtains reliable repair results under large pseudorange errors and severe ionospheric variations, and the cut-off elevation larger than 10 degrees is the suggested background.

Cycle slip detection and repair for BeiDou-3 triple-frequency signals

When carrier phase observations are applied to high-precision positioning, how to handle the cycle slip is an unavoidable problem. For cycle slip correction, detection combination noise and the ionospheric delay are two crucial factors. Specifically, the drastic changes in the ionosphere and the increased noise of code observations will increase the failure probability of cycle slip detection. To reduce the influence of code observation noise and ionospheric bias, a novel cycle slip detection method for BDS-3 satellites is proposed. Considering that code measurement noise is closely related to the satellite elevation angle, an elevation-based model is built to evaluate the code measurement noise. Firstly, two modified code-phase combinations are selected optimally based on 1% missed detection rate and 99% success detection rate to minimize the effects of code measurement noise. However, the second modified code-phase combination is more affected by ionospheric delay bias, so ionospheric bias of current epoch needs to be corrected. To reduce the influence of ionospheric bias, two moving windows of time-differenced ionospheric delay are introduced to correct the ionospheric bias of the second code-phase combination. Experiments with BeiDou-3 data are implemented in three different scenarios. To verify the effectiveness of the algorithm in the environment of high code observations noise, Gaussian noise is added to the code observations in the first scenario, and the results demonstrate that the success rate of cycle slip detection and repair is still greater than 95% when the standard deviation of Gaussian noise is 0.8 m. The second scenario is carried out under low ionospheric activity, and results indicate that the proposed method significantly reduces the times of failed detection and repair. Moreover, in the third scenario, BeiDou-3 data with cycle slips of different types under high ionospheric activity are tested, and all cycle slips can be correctly detected and corrected.

A New Cycle Slip Detection and Repair Method Using a Single Receiver's Single Station B1 and L1 Frequencies in Ground-Based Positioning Systems.

The detection and repair of the cycle slip is a key step for high precision navigation and positioning in indoor environments. Different methods have been developed to detect and repair cycle slips for carrier phase processing. However, most approaches are designed to eliminate the effects of the ionosphere in an outdoor environment, and many of them use pseudorange (code) information that is no longer suitable for indoor multipath environments. In this paper, a method based on the geometry-free combination without the pseudorange data is proposed to detect and fix cycle slips. A ground-based navigation system is built for data collection. Unlike the traditional dual-frequency cycle slip detection method, the Beidou B1, GPS L1 carrier phase combination is used instead of the B1, B2, or L1, L2 carrier phase combination, Ublox is used for data collecting. For fixing the cycle slips quickly, an improved adaptive Particle Swarm Optimization (PSO) algorithm is employed. We compared the performance of the new method with the existing two methods using simulated data in different conditions. The results show that the proposed method has better performance than other methods.

Doppler Differential Positioning Technology Using the BDS/GPS Indoor Array Pseudolite System.

A Global Satellite Navigation System (GNSS) cannot provide normal location services in an indoor environment because the signals are blocked by buildings. The Beidou satellite navigation system (BDS)/GPS indoor array pseudolite system is proposed to overcome the problems of indoor positioning with conventional pseudolite, such as time synchronization, ambiguity resolution and base stations. At the same time, an algorithm for Doppler differential positioning is proposed to improve the indoor positioning accuracy and the positioning coverage of the system, which uses the Doppler difference equation and Known Point Initialization (KPI) to determinate the velocity and position of the receiver. Experiments were conducted to verify the proposed system under different conditions; the average positioning error of the Doppler differential positioning algorithm was 7.86 mm in the kinematic test and 2.9 mm in the static test. The results show that BDS/GPS indoor array pseudolite system has the potential to make indoor positioning achieve sub-centimeter precision. Finally, the positioning error of the proposed algorithm is also analyzed, and the data tests show that the dilution of precision (DOP) and cycle- slips have a significant impact on the indoor positioning accuracy; a cycle-slip of a half-wavelength can cause positioning errors of tens of millimeters. Therefore, the Doppler-aided cycle-slip detection method (DACS) is proposed to detect cycle-slips of one cycle or greater than one, and the carrier phase double difference cycle-slip detection method (CPDD) is used to detect cycle slips of a half-wavelength.

Cycle Slip Detection during High Ionospheric Activities Based on Combined Triple-Frequency GNSS Signals

The current cycle slip detection methods of Global Navigation Satellite System (GNSS) were mostly proposed on the basis of assuming the ionospheric delay varying smoothly over time. However, these methods can be invalid during active ionospheric periods, e.g., high Kp index value and scintillations, due to the significant increase of the ionospheric delay. In order to detect cycle slips during high ionospheric activities successfully, this paper proposes a method based on two modified Hatch–Melbourne–Wübbena combinations. The measurement noise in the Hatch–Melbourne–Wübbena combination is minimized by employing the optimally selected combined signals, while the ionospheric delay is detrended using a smoothing technique. The difference between the time-differenced ambiguity of the combined signal and this estimated ionospheric trend is adopted as the detection value, which can be free from ionospheric effect and hold the high precision of the combined signal. Five threshold determination methods are proposed and compared to decide the cycle slip from the magnitude aspect. This proposed method is tested with triple-frequency Global Navigation Satellite System observations collected under high ionospheric activities. Results show that the proposed method can correctly detect and fix cycle slips under disturbed ionosphere.

Comparison between cycle slip detection methods based on dual-frequency observation data

Comparison between cycle slip detection methods based on dual-frequency observation data

Improved time-differenced cycle slip detect and repair for GNSS undifferenced observations

GNSS undifferenced signal processing, in which the individual signal of each frequency is treated as independent observable, has drawn increasing interest in GNSS community. However, undifferenced signal processing brings new challenges for cycle slip detection and repair. One important feature is the carrier frequency identification of cycle slips since observations are processed separately. An analysis of real cycle slips in a BDS triple-frequency baseline dataset illustrates the deficiencies in the cycle slip detection process commonly implemented, in the case when cycle slips occur in just one specific carrier frequency. Hence, we propose an improved cycle slip detection and repair approach based on a time-differenced model. Two major advantages characterize this proposed approach. The first one is a significant reduction in false alarms due to carrier frequency identification of cycle slips. Having access to a reliable cycle slip detection method significantly reduces the number of ambiguity parameters to be estimated. The second advantage is the benefit of separating the OSS (Observation at the other frequency of Same Satellite without cycle slip) and OSE (Observation at the Same Epoch from other satellites without cycle slip) from the OCS (Observation with Cycle Slip). The simulation results indicate that separation of the OSS and OSE can significantly improve the model strength of cycle slip estimation, especially OSS. The proposed approach is validated by cycle slip estimation with a real data set. Smaller biases and larger ratio values jointly demonstrate that a much stronger model strength can be achieved. Finally, the cycle slip repair procedure is applied to triple-frequency PPP. The stable and fast convergence, as well as the reduction in standard deviations, proves the efficiency of the proposed approach.

Enhanced cycle slip detection method for dual-frequency BeiDou GEO carrier phase observations

Cycle slip detection is one of the essential steps for high-precision GNSS data processing when carrier phase observations are involved, such as in precise point positioning (PPP) and precise orbit determination (POD). A number of algorithms have been developed since the 1980s and are effective for processing dual-frequency GPS. However, the emerging BeiDou navigation satellite system in China brings some new challenges for these existing algorithms, especially when small cycle slips occur more frequently. In this study, a large number of 1-cycle slips have been found in low-elevation BeiDou GEO carrier phase observations, which are collected by receivers of the IGS multi-GNSS experiment. Such small cycle slips should be identified and repaired, if possible, before PPP and POD processing. We propose an enhanced cycle slip detection method based on the series of dual-frequency phase geometry-free combinations. A robust polynomial fit algorithm and a general autoregressive conditional heteroskedastic modeling technique is employed to provide an adaptive detection threshold, which allows identification of such small cycle slips with high reliability. Simulated and real data tests reveal that the proposed method has both high sensitivity and low false-alarm rate even in the case of ionospheric scintillation.

Undifferenced Cycle Slip Estimation of Triple-Frequency BeiDou Signals with Ionosphere Prediction

ABSTRACTWith the rapid development of BeiDou satellite navigation system (BDS), high-quality service has been provided in the Asia-Pacific region currently, which will be extended to the whole world very soon. BDS is the first Global Navigation Satellite System that all satellites broadcast the triple-frequency signals. The triple-frequency signals in theory can improve the cycle slip detection that is one of the preconditions in precise positioning by making use of carrier phase. This paper discusses the development of a cycle slip detection method for undifferenced BDS triple-frequency observations in kinematic scenario. In this method, two geometry-free extra-wide-lane combinations and one geometry-free narrow-lane (NL) combinations are employed. The key is to mitigate the between-epoch ionospheric biases in the geometry-free NL combinations. We propose to predict the ionospheric biases of current epoch by using those from its consecutive foregoing epochs. The method is tested with extensive experiments in varying observation scenarios. The results show that in case of sampling interval as small as 5 s, the between-epoch ionospheric biases can be ignored and the correct cycle slips can be determined. Meanwhile in case of lower sampling frequency, one needs to compensate the ionospheric biases of current epoch by using the predicted ionospheric biases. The presented method can correctly detect all cycle slips even if they are as small as 1 cycle.

Inertial Aided Cycle Slip Detection and Repair for PPP/INS Tightly Coupled Navigation

The integration of Precise Point Positioning (PPP) with Inertial Navigation Systems (INS) has been very intensively developed and widely applied in multiple areas. The integrated navigation system is able to provide high accuracy position and attitude with a single receiver. However, the cycle slip caused by high dynamics, signal lock and low satellite elevation will decrease accuracy and degrade the system performance. In this paper, an inertial aided cycle slip detection and repair method is applied in PPP/INS tightly coupled navigation to obtain higher accuracy navigation information. The inertial information is introduced to the wide-lane combination observation to avoid the noise and multipath from pseudorange. Detail error analysis is given to determine the critical value of INS position accuracy which makes inertial aided wide-lane combination have better performance and a new decision variable is constructed. The inertial aided cycle slip detection and repair scheme that replaces the ambiguity re-initialisation is applied in PPP. An experiment was performed to validate the new algorithm. The results indicate that the inertial aided decision variable has higher accuracy than the traditional Melbourne-Wübbena decision variable. The inertial aided scheme can efficiently detect and repair the small cycle slip (from 1 to 6) and large cycle slip (from 10 to 20). The inertial-aided cycle slip detection method introduced in PPP resolution will remove the error by ambiguity re-initialisation.

Study on cycle-slip detection and repair methods for a single dual-frequency global positioning system (GPS) receiver

In this work, we assessed the performance of the cycle-slip detection methods: Turbo Edit (TE), Melbourne-Wübbena wide-lane ambiguity (MWWL) and forward and backward moving window averaging (FBMWA). The TE and MWWL methods were combined with ionospheric total electron content rate (TECR), and the FBMWA with second-order time-difference phase ionosphere residual (STPIR) and TECR. Under different scenarios, 10 Global Positioning System (GPS) datasets were used to assess the performance of the methods for cycle-slip detection. The MWWL-TECR delivered the best performance in detecting cycle-slips for 1 s data. The relative comparisons show that the FBMWA-TECR method performed slightly better than its original version, FBMWA-STPIR, detecting 100% and 73%, respectively. For data with a sample rate of 5 s, the FBMWA-TECR performed better than MWWL-TECR. However, the FBMWA is suitable only for post-processing, which refers to applications where the data are processed after the fact.

A Practical Algorithm for LEO Orbit Determination

: The primary objective of this paper is to present a practical, fast, and effective triple-difference algorithm for precision orbit determination (POD) of low earth orbiters (LEOs). This technique was developed for near-real-time POD to support occultation data processing, as well as atmospheric data retrieval from the land-based GPS network. In particular, the paper focuses on the GPS/LEO POD, with special emphasis on the triple-difference–based kinematic approach to LEO POD. The paper provides the theoretical foundation of the method, and presents the results of a performance analysis for the CHAMP (CHAllenging Minisatellite Payload) satellite POD. In addition, data screening and quality control procedures applied to CHAMP and ground station GPS data are presented, with preliminary statistics related to the number and distribution of cycle-slip events. A comparison of the results from two cycle-slip detection methods is also included.