An Enhanced Cycle Slip Detection Approach Based on Inter-Frequency Cross-Validation for Multi-Constellation and Multi-Frequency GNSS Systems

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 slips are discontinuity events in a receiver’s phase lock on a Global Navigation Satellite System (GNSS) signal. If cycle-slip events are not detected and repaired, the quality of positioning using carrier phase processing suffers. In this paper, we present an algorithm for flagging cycle slips during data preprocessing. This new algorithm is part of a new GNSS software that replaces a legacy software at the National Geodetic Survey (NGS). It uses the Hatch–Melbourne–Wübbena (HMW), ionosphere-free and geometry-free linear combinations to detect cycle slips. The use of the three observables in parallel helps improve sensitivity to cycle slips and overcome the challenge of detecting cycle slips of equal size and same sign on both/multiple frequencies. Different detection threshold values were evaluated in a well-controlled environment using GNSS data acquired from continuously operating reference stations (CORS) networks and artificially simulated cycle slips that were introduced into the datasets. The goal of evaluation was to determine the optimal values for cycle-slip detection parameters. In the absence of formal confidence limits, the results of the study show that, in a worst-case scenario involving small slips of magnitudes ranging from 1 to 3 cycles, there is a range of parameter values that resulted in at least 97% success rate without any false detections. Based on these and other findings, we provide a set of optimal values from which the results are an improvement of at least 34% in cycle-slip detection, compared to results from the legacy algorithm’s settings. The results of the study will support the National Oceanic and Atmospheric Administration’s (NOAA) GNSS services and tools for the public, such as the Online Positioning User Service (OPUS).

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

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.

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.

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.

Global navigation satellite systems (GNSS) products are integral to a wide array of scientific and commercial applications such as pecise orbit determination of low Earth orbit satellites, earthquake monitoring, GNSS reflectomrety, tropospheric and ionospheric research, surveying and much more. These products consisting of GNSS orbit, clock, phase biases and more are generated by the analysis centres of the International GNSS Service (IGS) by processing observations from a global network of ground stations to one or more GNSS constellations. The processing consists of a combined station position and GNSS satellite orbit determination through a least squares approach donated as global multi-GNSS processing.Within global multi-GNSS processing it is assumed that the observation noise is elevation-dependent and any spatial and temporal correlations are disregarded. Within numerous studies it has been shown that this assumption is incorrect while several studies additional pointed out that a sophisticated stochastic modelling has a positiv impact on GNSS processing and resulting products. In past reseach we have shown to exploit the post-fit residuals to derive temporal correlations for a sophisticated stochastic modeling. However, there have not been any large-scale investigations regarding the impact of stochastic modelling of observation noise on global GNSS processing products. Furthermore, to guarantee the quality of the GNSS products global multi-GNSS processing requires a sophisticated cycle slip detection and repairing algorithm. Cycle slips are discontinuities in the phase observations and if not corrected can lead to degrading quality of GNSS products.   We present our advancements in global multi-GNSS processing by exploiting post-fit residuals for stochastic modeling and cycle slip detection. We used several years of observations and a selected IGS network of ground stations to generate GNSS products. Based on this data we analysed the impact our newly integrated approaches have on GNSS products such as orbits, clocks, phase biases and station coordinate time series.  

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

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.

Carrier phase measurements are much more precise than pseudorange measurements and can be used to achieve very accurate positioning solutions. However, carrier phase measurements require resolution of integer ambiguities before precise positioning can be achieved. The GPS receiver can keep track of the integer number of cycles as long as the receiver maintains lock to the satellite signal. However, in reality, the GPS signal could be interrupted momentary by some disturbing factors leading to a discontinuity of an integer number of cycles in the measured carrier phase. This interruption in the counting of cycles in the carrier phase measurements is known as a cycle slip. When a cycle slip occurs, the Doppler counter would restart causing a jump in the instantaneous accumulated phase by an integer number of cycles. Thus, the integer counter is reinitialized meaning that ambiguities are unknown again. In this event, either the ambiguities need to be resolved again or cycle slips need to be corrected to resume the precise positioning/navigation process. These cycle slips can, to some extent, be detected and fixed to avoid delay and computation complexity attributed to integer ambiguity resolution. Researchers have been addressing the problem of cycle slip detection and correction for the last two decades. This paper provides a detailed survey for available techniques to tackle the problem showing their pros and cons.

For the current problem of cycle slips in the observation data of the BDS-2 and BDS-3 (Bei Dou Navigation Satellite System), in this paper, BDS B1I and B3I signals are used as research objects to study the detection of cycle slips, and their repair algorithm. The Geometry-free (GF) and Melbourne–Wübeena (MW) combination algorithm are used for the detection of cycle slips. A new method of arc partition is proposed in this work to detect cycle slips as the boundary to delimit two different observation arcs. In this way, the different values of cycle slips can be divided and marked. Moreover, the gross errors can be removed. Finally, the detection of cycle slips and the analysis of all epochs can be completed and repaired. This work also analyzes the dual-frequency data effect of cycle slips on code multipath observation. The results showed that this method greatly improved the speed of detection of cycle slips.

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.

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%.

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.

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.