Small Cycle Slips Research Articles

Cycle‐slip detection and correction of GPS single‐frequency carrier phase based on wavelet transform and LS‐SVM

The high-precision positioning of GPS requires to detect and correct the cycle-slips in carrier phase more accurately and efficiently. In order to improve the ability of GPS single-frequency receivers to detect and correct small cycle-slips, the reason for the occurrence of cycle-slips and the principle of their detection and correction are analysed; then, a method of GPS single-frequency receivers' cycle-slip detection and correction based on wavelet transformation and LS-SVM is proposed. Here, WT is used to locate the cycle-slip and the LS-SVM is used to determine the value of it and correct it. The simulation results show that this method can detect and correct up to one cycle-slip accurately but in contrast, the traditional polynomial fitting method can only detect and correct at least two cycle-slips in the same condition. The feasibility of this method and its ability to accurately correct small cycle-slips are demonstrated.

Reliable real-time triple-frequency cycle slip detection and recovery with adaptive detection thresholds

Fast and reliable cycle slip detection is a prerequisite for successive ambiguity resolution and precise positioning. For dual-frequency signals, sometimes small cycle slips or particular cycle slips cannot be detected. Benefiting from the triple-frequency signals of global navigation satellite systems, more useful linear combinations can be selected to reduce or avoid the cycle slips otherwise difficult to detect. We propose an improved algorithm with three independent geometry-free combinations to detect and recover potential cycle slips. To improve the reliability of cycle slip detection, adaptive thresholds determined using the posterior total noise of the approximately normal-distributed time-differenced combinations are used, rather than fixed thresholds by a priori information such as the measurement noise and ionosphere residual. After the detection procedure, four different types of detection results are obtained, and the corresponding recovery strategies are applied. In this way, we can reliably detect and recover potential integer cycle slips. To demonstrate the performance of the proposed algorithm, numerical analysis is carried out using observation data of the BeiDou Navigation Satellite System with real cycle slips. Different types of cycle slips are also discussed. The results show that the proposed algorithm can reliably avoid false-acceptance or false-rejection caused by the fixed thresholds, and correctly detect and recover different kinds of integer cycle slips for the experimental data with a 1 s sampling rate.

An improved algorithm based on combination observations for real time cycle slip processing in triple frequency BDS measurements

This research presents a new algorithm to resolve real-time cycle slip for undifferenced triple frequency observations of BeiDou navigation satellite system (BDS). The method of cycle slip (CS) detection is based on three linearly independent combinations: GIF (geometry free and ionosphere free) combination, GF (geometry free) phase combination and code-phase combination. First order differenced ionospheric delay is predicted by a back moving window filter. The difference between predicted and calculate first order differenced ionospheric delay is adopted to detect the insensitive cycle slips and to judge whether the detected cycle slips are repaired correctly. With respect to cycle slip determination, modified LAMBDA (MLAMBDA) method is adopted. The proposed method has been verified by real BDS observations adding various artificial cycle slips at every ten epochs. The results show that the proposed algorithm is reliable to detect and repair small and large cycle slips even under low sampling interval (30 s). The fix rate of CS can reach 100% for all the selected satellites. For the most insensitive cycle slip group (1, 1, 1), the fixing rate can reach 99.82% without considering the first order differenced ionospheric delay condition. The fixing rate can also reach 100% when ionospheric delay condition is considered. In terms of the comparative method, the fixing rate is about 91% in according to the IGSO satellites. These results demonstrate that the proposed algorithm can detect and repair all added cycle slips even under low sampling rate at 30 s.

A New Cycle Slip Detection and Repair Method for Single-Frequency GNSS Data

Cycle slip detection for single frequency Global Navigation Satellite System (GNSS) data is currently mainly based on measurement modelling or prediction, which cannot be effectively performed for kinematic applications and it is difficult to detect or repair small cycle slips such as half-cycle slips. In this paper, a new method that is based on the total differential of ambiguity and Least-Squares Adjustment (LSA) for cycle slip detection and repair is introduced and validated. This method utilises only carrier-phase observations to build an ambiguity function. LSA is then conducted for detecting and repairing cycle slips, where the coordinate and cycle slips are obtained successively. The performance of this method is assessed through processing short and long baselines in static and kinematic modes and the impact of linearization and atmospheric errors are analysed at the same time under a controlled variable method. The results indicate this method is very effective and reliable in detecting and repairing multiple cycle slips, especially small cycle slips.

An improved robust Kalman filtering strategy for GNSS kinematic positioning considering small cycle slips

In GNSS (Global Navigation Satellite Systems) kinematic positioning, observations will be inevitably contaminated by cycle slips and gross errors, as the complex observation environment changes rapidly. These outliers will degrade the performance of classic Kalman filtering applied in GNSS kinematic resolution and eventually, the filtering may converge slowly or even diverge and thus the precision will be degraded. Therefore, a robust Kalman filter should be applied to resist the influence of these outliers that cannot be identified in the data preprocessing stage. Based on the conventional IGG (Institute of Geodesy and Geophysics) III equivalent weight method which addresses the outliers of the zero-weight segment with the same strategy, this paper proposes an improved robust Kalman filtering strategy that detects outliers by both posterior phase residuals and standardized residuals and handles the carrier-phase observation of zero-weight segment as cycle slips. In addition, to avoid unnecessary ambiguity reinitialization caused by the detected cycle slips, only when the carrier-phase observation of the same satellite is classified in the zero-weight segment over two consecutive epochs should the ambiguity be reinitialized. Experimental results of relative positioning show that the improved method can not only mitigate the influence of unexpected outliers in the Kalman filter but also improve the fixing rate of ambiguity resolution as well as the accuracy and reliability of positioning.

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.

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.

Bayesian methods for outliers detection in GNSS time series

This article is concerned with the problem of detecting outliers in GNSS time series based on Bayesian statistical theory. Firstly, a new model is proposed to simultaneously detect different types of outliers based on the conception of introducing different types of classification variables corresponding to the different types of outliers; the problem of outlier detection is converted into the computation of the corresponding posterior probabilities, and the algorithm for computing the posterior probabilities based on standard Gibbs sampler is designed. Secondly, we analyze the reasons of masking and swamping about detecting patches of additive outliers intensively; an unmasking Bayesian method for detecting additive outlier patches is proposed based on an adaptive Gibbs sampler. Thirdly, the correctness of the theories and methods proposed above is illustrated by simulated data and then by analyzing real GNSS observations, such as cycle slips detection in carrier phase data. Examples illustrate that the Bayesian methods for outliers detection in GNSS time series proposed by this paper are not only capable of detecting isolated outliers but also capable of detecting additive outlier patches. Furthermore, it can be successfully used to process cycle slips in phase data, which solves the problem of small cycle slips.

A new automated cycle slip detection and repair method for a single dual-frequency GPS receiver

This paper develops a new automated cycle slip detection and repair method that is based on only one single dual-frequency GPS receiver. This method jointly uses the ionospheric total electron contents (TEC) rate (TECR) and Melbourne–Wubbena wide lane (MWWL) linear combination to uniquely determine the cycle slip on both L1 and L2 frequencies. The cycle slips are inferred from the information of ionospheric physical TECR and MWWL ambiguity at the current epoch and that at the previous epoch. The principle of this method is that when there are cycle slips, the MWWL ambiguity will change and the ionospheric TECR will usually be significantly amplified, the part of artificial TECR (caused by cycle slips) being significantly larger than the normal physical TECR. The TECR is calculated based on the dual-frequency carrier phase measurements, and it is highly accurate. We calculate the ionospheric change information (including TECR and TEC acceleration) using the previous epochs (30 epochs in this study) and use the previous data to predict the TECR for the epoch needing cycle slip detection. If the discrepancy is larger than our defined threshold 0.15 TECU/s, cycle slips are regarded to exist at that epoch. The key rational of method is that during a short period (1.0 s in this study) the TECR of physical ionospheric phenomenon will not exceed the threshold. This new algorithm is tested with eight different datasets (including one spaceborne GPS dataset), and the results show that the method can detect and correctly repair almost any cycle slips even under very high level of ionospheric activities (with an average Kp index 7.6 on 31 March 2001). The only exception of a few detected but incorrectly repaired cycle slip is due to a sudden increased pseudorange error on a single satellite (PRN7) under very active ionosphere on 31 March 2001. This method requires dual-frequency carrier phase and pseudorange data from only one single GPS receiver. The other requirement is that the GPS data rate ideally is 1 Hz or higher in order to detect small cycle slips. It is suitable for many applications where one single receiver is used, e.g. real-time kinematic rover station and precise point positioning. An important feature of this method is that it performs cycle slip detection and repair on a satellite-by-satellite basis; thus, the cycle slip detection and repair for each satellite are completely independent and not affected by the data of other satellites.

Cycle slip detection using multi-frequency GPS carrier phase observations: A simulation study

The detection and repair of the cycle slip or gross error is a key step for high precision global positioning system (GPS) carrier phase navigation and positioning due to interruption or unlocking of GPS signal. A number of methods have been developed to detect and repair cycle slips in the last two decades through cycle slip linear combinations of available GPS observations, but such approaches are subject to the changing GPS sampling and complex algorithms. Furthermore, the small cycle slip and gross error cannot be completely repaired or detected if the sampling is quite longer under some special observation conditions, such as Real Time Kinematic (RTK) positioning. With the development of the GPS modernization or Galileo system with three frequencies signals, it may be able to better detect and repair the cycle slip and gross error in the future. In this paper, the cycle slip and gross error of GPS carrier phase data are detected and repaired by using a new combination of the simulated multi-frequency GPS carrier phase data in different conditions. Results show that various real-time cycle slips are completely repaired with a gross error of up to 0.2 cycles.