GPS Cycle Slip Detection and Correction at Measurement Level

This paper presents a new cycle slip detection and repair method using Total Electron Content Rate (TECR) information derived from individual satellite dual-frequency data of a single Global Positioning System (GPS) receiver while pseudorange measurements are subject to arbitrarily large range errors. Sudden Increase of Pseudorange Error (SIPE), similar to cycle slips in nature, is quite common in various data acquisition scenarios. The basic principle of this method is to take advantage of the fact that the ionospheric TECR does not exceed certain threshold, which is set as 0.35 TECU/s in this study. Analytic expressions to evaluate the effect of SIPE on cycle slip detections have been developed. The search spaces for cycle slip candidate pairs are defined, given a predefined (sufficiently large) SIPE value. Two cycle slip validation rules are proposed to validate the cycle slip candidates. Over 99.9% of candidates can be rejected with the application of two validation rules. The theoretically maximal number of remaining cycle slip candidate pairs (NRCP) can be exactly calculated based on the magnitude of SIPE, TECR threshold, and the data sampling interval. After applying validation rules, the correct cycle slip pairs can be identified using a modified low-order polynomial fitting method. This method is tested on 13 high rate (1-Hz) dual-frequency datasets recorded by both ground-based static and satellite-borne high dynamic GPS receivers under various levels of ionospheric activities. Simulated cycle slips in 12 different possible cases and varying SIPE magnitudes are introduced into the data sets. In each test scheme, averagely 600–750 pairs of cycle slips are simulated. The SIPE magnitudes are set to vary from 50.0 m to 1000.0 m. Test results show that all the cycle slips in all the test schemes and all the datasets have been successfully detected and fixed even with a maximum SIPE of 1000.0 m in pseudoranges. A distinct advantage of this method is that it works in real-time with individual satellite’s data from a single dual-frequency receiver, even if the carrier phases have virtually any size of cycle slips and the pseudoranges have virtually arbitrarily large errors.

Cycle slip detection and correction is an important part of GPS data processing. In the past research, geometry-free and non-geometry-free testing quantities have been proposed. Both of them can be used for static cases. Each of them has their own advantages and disadvantages. This research is aiming to compare these two kinds of testing quantities for static cycle slip detection and correction in different situations, such as in low and high elevation angles, especially in cases of strong atmospheric variations. The performance of geometry-free and non-geometry-free testing quantities is compared with observations of different situations. The numerical results show that the effect of the rapid change of relative humidity on cycle slip detection and correction with these two kinds of testing quantity is not obvious. However, the results clearly show that in the case of a low elevation angle (<10°), non-geometry-free is obviously a better choice. In the case of ionospheric scintillation, geometry-free testing quantity can no longer be used. With non-geometry-free testing quantity, cycle slips can be detected and corrected successfully, if the number of continuous cycle slips is small for example, less than 5.

Cycle slips are a common error source in Global Navigation Satellite System (GNSS) carrier phase measurements. In this paper, the cycle slip problem is approached using Receiver Autonomous Integrity Monitoring (RAIM) methodology. Carrier phase measurements are used here in a single-receiver time-differential positioning method where integer ambiguities are canceled, but any cycle slips remain. The performance of the method was assessed by comparing the detection results to a Real-Time Kinematic (RTK) solution and by manual data examination. Postprocessing results obtained using authentic Global Positioning System (GPS) measurements logged by low-cost single-frequency receivers show that the method is able to reliably detect and identify single errors but fails in an exemplary multiple outlier scenario. As no reference receiver is needed, the method is a potential means to produce cycle-slip-corrected data usable in any postprocessing application.

Accurately detecting and repairing cycle slips is an important pre-processing step in high precision GPS carrier phase positioning and applications. Carrier phase measurements can be divided into high and low frequency components by wavelet transform which wavelet coefficients of local extremum point can be detected phase of the cycle slips. In this paper, wavelet transform is used to detect cycle slip detection which is based on the principle of singularity. Through modulus maxima detection to determine the location of cycle slips, GPS double difference observations used to detect cycle slips is better than single-difference observations. When the cycle slips is larger, the effect of double difference is better. The results show that the method of wavelet transform can be accurately used to detect cycle slips.

An innovative algorithm is introduced for cycle slip detection and correction in communication systems that employ APSK modulation. The algorithm is well suited for carrier phase synchronizers that are based on phase locked loops, and it achieves significant improvement in BER performance without compromising spectral efficiency. A systematic approach for the selection of all main algorithm parameters is detailed. In particular, the 16-APSK scheme, (recommended in the DVB-S2 standard) is analyzed by assuming an AWGN channel, and simulation results in the presence of various channel impairments are presented. The results establish the superiority of the proposed algorithm over other known cycle slip handling techniques for PLL synchronization. Integration with state-of-the-art iterative synchronization is also considered.

To ensure high accuracy results from an integrated GPS/INS system, the carrier phase observables have to be used to update the filter's states. As a prerequisite the integer ambiguities must be resolved before using carrier phase measurements. However, a cycle slip that remains undetected (and uncorrected) will significantly degrade the filter's performance. In this paper, an algorithm that can effectively detect and identify any type of cycle slip is presented. The algorithm uses additional information provided by the INS, and applies a statistical technique known as the cumulative-sum (CUSUM) test. In this approach, cycle slip decision values can be computed from the INS-predicted position (due to the fact that its short-term accuracy is very high), and the CUSUM test used to detect cycle slips (as it is very sensitive to abrupt changes of mean values). Test results are presented to demonstrate the effectiveness of the proposed algorithm.

Integer ambiguity resolution (AR) is the key to the attitude determination with global navigation satellite system (GNSS) differential carrier phases. Traditional applications in surveying field are generally performed in open areas with geodeticgrade receivers, and solve the AR problem in ambiguity domain. However, for some applications such as urban vehicle/unmanned air vehicle (UAV) attitude determination with single-frequency low-cost receivers, the AR success rate is not as satisfactory as the one in surveying field. Due to the reasons such as low-cost receivers’ inferior pseudorange quality, multipath interference and frequent cycle slips in complicated urban environment, it is difficult to give an accurate estimation for the float ambiguities which is used as the search center of the traditional AR methods in ambiguity domain, thus leading to the failure of finding the correct ambiguities. Here, we propose a single-epoch AR method in position domain to improve the AR success rate of urban attitude determination for ultra-short baselines. To get rid of the effect of the large pseudorange noise, our proposed algorithm abandons both the pseudorange measurements and the traditional idea of estimating the float ambiguities. With the known baseline length, the 3-D position search space can be compressed to a spherical surface, and by a 2-D traversal in angle domain, we can get a set of candidate position points. With the use of the integer property of the ambiguities and the geometric relationship between the position search space and carrier phase measurements, we establish an objective function whose performance relies on the carrier phases and geometric distribution only, and thus, the algorithm can provide a higher AR success rate. The corresponding 2-D traversal method and acceptance test method for validity judgment are also addressed in the paper. The results of both the simulation and the experiment under actual multipath environment are presented at the end of the paper.

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.

Global Satellite Navigation System (GNSS) has become one of the most important infrastructural facilities for major countries in the world. GPS carrier phase observations are often used for high precision positioning, but are susceptible to the influence of cycle slips. The EWL (extra-wide-lane) combination, for longer combination wavelengths, is frequently used for detecting and repairing cycle slips. The EWL combination adopts carrier phase and pseudorange observations; but in some cases, pseudorange observations have proven to be imprecise or inapplicable. Based on the traditional EWL model, a Doppler-aided EWL cycle slip detection and repair model is proposed herein. The model is applicable to situations where the ionosphere is stable and the sampling rate is high. Analyzing the static experimental data with 1s sampling interval, it could be observed that combining the proposed new method with traditional EWL method before adding any cycle slip will lower the first-order difference of integer ambiguity down to less than 0.5 cycles. This implies that the new method is also applicable to cycle slips detectable and reparable by traditional EWL methods. However, the ionospheric delay term reintroduced by the new method still requires further research.

Successful resolution of cycle ambiguities plays a crucial to high accuracy and high integrity navigation by carrier phase differenced positioning architecture. However, a cycle slip caused by loss-of-lock of signal changes the fixed ambiguity, which will affect the cycle resolution integrity. It is, therefore, necessary for detecting cycle slip and further satisfying its integrity. In general, dual frequency measurements are deployed to construct the carrier phase differenced positioning architecture for satisfying the stringent accuracy and integrity performance for safety-critical applications, such as automatic shipboard landing. Thus, dual-frequency-based cycle slip detection methodologies can be introduced in this positioning architecture. The geometry-free (GF) modeling uses only dual-frequency phase measurements to construct the statistical residuals, which are sensitive to small cycle slips that should be detected in high-integrity applications. At present, the threshold of the GF modeling is generally designed as an empirical constant, such as 5 cm, lacking theoretical derivation to quantify its integrity risk. Therefore, this paper proposes an integrity monitoring method for GF modeling to satisfy the integrity performance. Determining the threshold value of the cycle slip statistical test is designed as a function of a required false alarm probability and the quality of raw phase measurements. A required missed detection probability can be used to construct the minimal detectable error (MDB), which can evaluate the availability of the integrity monitoring method to control the missed detection probability. As noted above, the threshold and the MDB are jointly deployed to provide the high-integrity requirements. This paper collects simulated and real-world dual-frequency GNSS datasets to verify the performance of the proposed method. The results show that this method can dynamically adjust the detection threshold to control the false alarm probability and adjust the MDB to evaluate the availability of the integrity monitoring method to control the missed detection probability. Consequently, the proposed integrity monitoring method of cycle slip detection can effectively satisfy the high integrity requirements of cycle slip detection.

A novel method of ambiguity resolution and cycle slip processing for single-frequency GNSS/INS tightly coupled integration system

Cycle slip detection in the carrier phase is important for achieving precise relative positioning with global navigation satellite systems (GNSSs) in urban environments. The false alarm rate (FAR) and missing detection rate (MDR) of the detection approach will significantly affect the positioning error. This paper proposes a novel cycle slip detection approach based on inter-frequency cross-validation (IFCV), and designs corresponding test statistics and thresholds. In contrast to conventional cycle slip detection methods, the proposed IFCV approach has the advantages of higher accuracy and efficiency, which is validated by the airborne dynamic test. For cycle slips of specific proportions (such as five-cycle and four-cycle slips), the IFCV method significantly reduces the MDR from 3.89% to 0% and decreases the relative positioning error from 4.69 cm to 3.17 cm. In tests involving randomly injected cycle slips, the IFCV method reduces the MDR from 0.02% to 0%, reduces the relative positioning error from 3.83 cm to 3.02 cm, and decreases the average computational time from 1.02 ms to 0.53 ms.

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

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%.

Based on the time series analysis method, this article develops a Bayesian method of detecting and repairing the cycle slips in the GNSS carrier-phase data. Firstly, this article analyses the characteristics of the cycle slips in the GNSS carrier-phase observations and establishes the relationships between the cycle slips and the additive outliers (AOs) in the stationary time series. When the ARMA (autoregressive moving-average) model is used to fit the stationary time series obtained by differencing the GNSS carrier-phase observations, the detection of cycle slips in the GNSS carrier-phase observations can be transformed to the detection of AOs in the ARMA model. Then, this article proposes a Bayesian method of detecting the AOs in the ARMA model, and the implementation of detecting the cycle slips in the GNSS carrier-phase observations is also developed. Finally, the new Bayesian method of detecting the cycle slips is used to the real GNSS carrier-phase data. From the comparison among the Bayesian method, the high-order differences method and ionospheric residual method, we can find that the Bayesian method has a better detection efficiency for several kinds of cycle slips in the GNSS carrier-phase observations than other methods.