Doppler-aided EWL Cycle Slip Detection and Repair Method

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 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.

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

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 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.

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.

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.

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.

The Global Navigation Satellite System (GNSS) positioning technology using smartphones can be applied to many aspects of mass life, and the world’s first dual-frequency GNSS smartphone Xiaomi MI 8 represents a new trend in the development of GNSS positioning technology with mobile phones. The main purpose of this work is to explore the best real-time positioning performance that can be achieved on a smartphone without reference stations. By analyzing the GNSS raw measurements, it is found that all the three mobile phones tested have the phenomenon that the differences between pseudorange observations and carrier phase observations are not fixed, thus a PPP (precise point positioning) method is modified accordingly. Using a Xiaomi MI 8 smartphone, the modified real-time PPP positioning strategy which estimates two clock biases of smartphone was applied. The results show that using multi-GNSS systems data can effectively improve positioning performance; the average horizontal and vertical RMS positioning error are 0.81 and 1.65 m respectively (using GPS, BDS, and Galileo data); and the time required for each time period positioning errors in N and E directions to be under 1 m is less than 30s.

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%.

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.