Real-time Cycle Slip Detection Research Articles

A hierarchical combination algorithm for real-time cycle slip detection and repair in low satellite elevation and high ionospheric activity conditions

To enhance the accuracy and robustness of cycle slip detection and repair for triple-frequency data while minimizing the adverse effects of low satellite elevation and high ionospheric activity, a hierarchical combination algorithm for real-time cycle slip detection and repair is proposed. This algorithm begins by prioritizing the reduction of noise and ionospheric delay coefficients. It determines the optimal coefficients for the combination of observations from the BeiDou Navigation Satellite System’s (BDS) Extra-Wide Lane (EWL), Wide Lane (WL), and Narrow Lane (NL). Leveraging the longer wavelength characteristics of the EWL combination, it simultaneously conducts cycle slip detection on the EWL combination alongside the pseudorange combination. Following this, based on the detection outcomes from the EWL combination, cycle slip detection is carried out on the WL combination. Finally, using the detection findings from the WL combination, cycle slip detection is executed on the NL combination. Given the NL combination’s shorter wavelength and higher susceptibility to ionospheric delay, a dynamic ionospheric prediction model is applied to the NL combination to further mitigate the impact of ionospheric disturbances. After completing the cycle slip detection process, the results from the EWL, WL, and NL combinations are integrated and solved. Experimental results clearly demonstrate that, even in scenarios characterized by low satellite elevation and active ionospheric conditions, this algorithm consistently delivers outstanding detection performance for cycle slip instances, particularly for small cycle slip (less then two cycles). Remarkably, this performance is achieved without the need for intricate searches during cycle slip repair.

Improved real-time cycle-slip detection for Low Earth Orbit satellites based on the dynamic force model

Cycle-slip detection is crucial in achieving high-accuracy Global Navigation Satellite System (GNSS) data processing for Low Earth Orbit (LEO) satellites. The detector based on the dynamic force model has emerged as a promising approach to cycle-slip detection, as it is insensitive to the number of visible tracked satellites and insufficient accuracy of a prior orbit. However, the ionospheric delay limits the applications of the method for high-speed LEO satellites under different scenarios. To complete the method, we propose a new combination of two test parameters: the phase ionosphere-free (IF) combinations in the second-order time-difference model and the Melbourne–Wübbena (MW) combinations. Meanwhile, we highlight the identification of whether the fake-positive cycle slips are derived from the flicker noises and jumps in the receiver quartz-based clock. Considering highly, moderately active and quiet ionospheric activities, comparisons are performed among our proposed two test parameters and the phase second-order time-difference wide-lane (WL) combinations. The results indicate that the detector based on the IF combinations performs optimally under the three levels of ionospheric activities. The time-difference ionospheric delays vary dramatically even under moderately active and quiet ionospheric activities, which leads to the inferiority of the detector based on the WL combinations to one based on the MW combinations. The performances of detectors based on the IF and MW combinations are further evaluated through real-time kinematic orbital determinations comparisons with the Jet Propulsion Laboratory (JPL) precise science orbits (PSO). After using the IF detector, the mean 3-Dimensional (3D) root-mean-squares (RMS) of the orbit differences have slightly decreased by 12% and 6% for the Gravity Recovery and Climate Experiment (GRACE) A and B satellites, respectively. In the case of the GRACE follow-on (GRACE-FO) satellites, the IF detector has achieved a more than 40% improvement over the MW detector. Further, the use of both detectors simultaneously results in a slight improvement in orbit accuracy.

A new real‐time cycle slip detection and repair approach based on BDS dual‐frequency carrier phase and Doppler observations

The Global Navigation Satellite System (GNSS) traditional dual-frequency cycle slip detection and repair methods such as the TurboEdit algorithm are restricted by the availability and accuracy of pseudorange observations. Doppler observations represent the instantaneous variation of the carrier phase during the integration time, which are immune to cycle slips. They are less affected by multipath effects compared with the pseudorange observations. Hence, a real-time cycle slip detection and repair approach for the BeiDou Navigation Satellite System (BDS) dual-frequency signals is proposed by combining the carrier phase and Doppler observations. The proposed method adopts the phase-Doppler combination and the geometry-free combination to detect cycle slips, and uses the simple rounding method or the dual-frequency least-square ambiguity decorrelation adjustment (LAMBDA) method to repair cycle slips. The validity of the proposed method is verified by the static and kinematic observation data under 1 s sampling interval and steady ionosphere. The results show that the new method can successfully detect all the small, insensitive, and large cycle slips. Moreover, the fixing rates of the simple rounding method under static and kinematic conditions are above 94% and 83%, respectively, while those of the dual-frequency LAMBDA method are both 100%.

Real-time cycle slip detection and repair for BDS-3 triple-frequency and quad-frequency B1C/B1I/B3I/B2a signals

This paper presents a real-time cycle slip detection and repair strategy for the BDS-3 triple-frequency and quad-frequency phase observations. For the triple-frequency phase observations, two EWL code-phase combinations and one GF-phase combination are jointly employed to detect and repair cycle slips. Based on the different performances in the success of cycle slip detection and repair, this paper uses GF-phase combinations to detect and repair cycle slip individually. Specifically, the GF-phase combination with a large MTIV value is applied to detect cycle slip possessing the stronger ability to resist ionospheric delay. Besides, the GF-phase combination with a higher success rate of cycle slip repair is selected to repair cycle slip, and the classic LAMBDA method and Ratio test are implemented to fix the cycle slip solution and evaluate reliability separately. For the quad-frequency phase observations, we employ a supernumerary EWL combination based on the triple-frequency, which can directly determine the cycle slip value of the 4th frequency. The results show that the cycle slip estimation value still can detect and repair all real and artificially added cycle slips even under harsh conditions. Moreover, the overall cycle slip repair success rate is greater than 99.99 %.

Algorithm for Real-Time Cycle Slip Detection and Repair for Low Elevation GPS Undifferenced Data in Different Environments

Real-time cycle slip detection and repair is one of the key issues in global positioning system (GPS) high precision data processing and application. In particular, when GPS stations are in special environments, such as strong ionospheric disturbance, sea, and high-voltage transmission line interference, cycle slip detection and repair in low elevation GPS observation data are more complicated than those in normal environments. For low elevation GPS undifferenced carrier phase data in different environments, a combined cycle slip detection algorithm is proposed. This method uses the first-order Gauss–Markov stochastic process to model the pseudorange multipath in the wide-lane phase minus narrow-lane pseudorange observation equation, and establishes the state equation of the wide-lane ambiguity with the pseudorange multipath as a parameter, and it uses the Kalman filter for real-time estimation and detects cycle slips based on statistical hypothesis testing with a predicted residual sequence. Meanwhile, considering there are certain correlations among low elevation, observation epoch interval, and ionospheric delay error, a second-order difference geometry-free combination cycle slip test is constructed that takes into account the elevation. By combining the two methods, real-time cycle slip detection for GPS low elevation satellite undifferenced data is achieved. A cycle slip repair method based on spatial search and objective function minimization criterion is further proposed to determine the correct solution of the cycle slips after they are detected. The whole algorithm is experimentally verified using the static and kinematic measured data of low elevation satellites under four different environments: normal condition, high-voltage transmission lines, dynamic condition in the sea, and ionospheric disturbances. The experimental results show that the algorithm can detect and repair cycle slips accurately for low elevation GPS undifferenced data, the difference between the float solution and the true value for the cycle slip does not exceed 0.5 cycle, and the differences obey the normal distribution overall. At the same time, the wide-lane ambiguity and second-order difference GF combination sequence calculated by the algorithm is smoother, which give further evidence that the algorithm for cycle slip detection and repair is feasible and effective, and has the advantage of being immune to the special observation environments.

A Real-Time Cycle Slip Detection and Repair Method Based on Ionospheric Delay Prediction for Undifferenced Triple-Frequency BDS Signals

The detection and repair of cycle slips are key steps in high-accuracy GNSS (Global Navigation Satellite System) data processing using carrier phase observations. BDS (BeiDou Navigation Satellite System) triple-frequency observations provide better combinations for cycle slip detections and repairs compared to dual-frequency observations. Although a number of algorithms have been developed and may correctly detect cycle slips most of the time, the reliability of empirical thresholds methods cannot be guaranteed. In this study, an adaptive threshold is proposed for three sets of triple-frequency Geometry-Free (GF) pseudorange minus phase combinations to improve the cycle slip detection performance and reduce the false alarm rate of the cycle slip detection by combining the predicted epoch-differenced ionospheric delays under active ionospheric conditions. Moreover, in the cycle slip repair, the integral combined cycle slips are determined by directly rounding the estimated float-combined cycle slips, which will lead to a repair error if the between-epoch ionospheric variation is large. In this study, a new rounding method considering the predicted epoch-differenced ionospheric delays is proposed, and it is proven that the new method has a higher success rate for estimating the integer value of a cycle slip than the traditional method. The performance of the newly proposed method is validated by using static BDS triple-frequency observations that contain simulated cycle slips. BDS triple-frequency observations were collected at 30-s sampling intervals under active ionospheric conditions. The results show that this method can successfully detect and repair all slips of more than one cycle. In addition, dynamic BDS data collected with a vehicle-based receiver at a 1-s sampling intervals are processed, and the results show that the proposed method is also effective in the detection and repair of cycle slips in dynamic data.

Real-Time Cycle Slip Detection and Repair Method for BDS-3 Five-Frequency Data

Theoretically, five-frequency observations can form combined observations with longer wavelength, smaller ionospheric delay and smaller noise, which may improve the performance of cycle slip detection and repair. Four geometry-free phase combinations and one geometry-free phase and pseudorange combination are formed to detect and repair the cycle slips in real time. Firstly, the high-quality geometry-free phase combinations of three, four and five frequencies are discussed, then the optimal five-frequency geometry-free phase combinations are selected to detect the cycle slips. Secondly, one geometry-free phase and pseudorange combination which is linearly independent with the above four phase combinations is added to ensure that all the cycle slips can be detected. Thirdly, a real-time cycle slip repair algorithm based on the LAMBDA search method is deduced. The five-frequency real-time cycle slip detection and repair method has been tested by using BDS-3 undifferenced data, even under the condition of active ionospheric and low sampling interval. The results showed that the proposed method is capable of detecting and repairing all the simulated cycle slips on the five carriers in real time.

A Solution for Real-Time Ionospheric Delay Using an Adaptive Kalman Filter Based on Estimating the Variance Component

Real-time solution of Global Navigation Satellite System (GNSS) epoch-differenced ionospheric delay (DID) is of great significance for real-time cycle slip detection and repair of multi-GNSS dual-frequency or trifrequency undifferenced measurements under high ionospheric activity. We construct a dynamic model of DID and perform a real-time estimate of the noise level of DID based on estimating the variance component. The estimated and predicted values of DID are obtained by designing a new adaptive Kalman filter algorithm with colored noise. Combining the predicted value and the detection method for cycle slips for Melbourne-Wübbena (MW) and Geometry-Free (GF) combination and taking into account the correlation between the predicted value and the carrier signal, we estimate the cycle slip, N2, on the second frequency of the carrier signal. The prediction and estimate of DID and detection and repair of dual-frequency cycle slip of multisystem undifferenced phase observations are measured with the GNSS multisystem observational data at different sampling rates (30 s, 15 s, 10 s, and 1 s). The results show that the DID model constructed in this paper is correct. The predicted value of DID has a high accuracy, which can effectively assist in dual-frequency cycle slip detection and repair. (1) The obtained predicted values, the estimated value, and the difference value between the two values of DID are less than 1.2 cm (STD), 1.2 cm (STD), and 0.6 cm (STD), respectively; (2) the precisions of the detection of cycle slip for MW, GF, and N2 are less than 0.083 cycles (STD), 0.4 cm (STD), and 0.071 cycles (STD), respectively; (3) with the obtained predicted value of DID to aid the detection and repair of cycle slip in GNSS double-frequency signals, a success rate of 100% can be reached.

Real-time triple-frequency cycle slip detection and repair method under ionospheric disturbance validated with BDS data

In order to resolve the real-time cycle slip detection and repair problem with the data under ionospheric disturbance and low sample rate, a new method is proposed by using triple-frequency combinations. First, the geometry-free and ionospheric-free (GFIF) carrier phase combination and then the GFIF pseudorange minus phase linear combination are derived for cycle slip detection. The special slip groups which cannot be discovered by the two GFIF combinations are divided into two types, and each of them is designed to be detected by using three additional geometry-free (GF) linear combinations. In the estimation step, the two GFIF combinations and the pseudorange minus phase linear combination with B3 carrier phase observations are used together to determinate the cycle slip on the original three carriers. The strategy is first to search B3 for cycle slips and then find the B1 and B2 cycles using the two GFIF combinations by integer bootstrapping method. The ionospheric delay variations between two consecutive epochs are estimated using the carrier phase data of the previous epochs and used for compensating time-differenced linear combinations that contain residual ionospheric variations. Then, in the validation step, both the criterions of threshold judgment and minimum one norm are used to validate the cycle slip candidates and finally get the correct one. The real-data tests with simulated and real cycle slips reveal that the new method can repair all cycle slips with high reliability even under ionospheric disturbance. Several failed repairs may occur with the most insensitive slip combinations ± (1, 1, 1) under bad observation conditions, but these cycle slips can be detected.

A New Real-Time Cycle Slip Detection and Repair Method under High Ionospheric Activity for a Triple-Frequency GPS/BDS Receiver.

Cycle slip detection and repair is a prerequisite for high-precision global navigation satellite system (GNSS)-based positioning. With the modernization and development of GNSS systems, more satellites are available to transmit triple-frequency signals, which allows the introduction of additional linear combinations and provides new opportunities for cycle slip detection and repair. In this paper, we present a new real-time cycle slip detection and repair method under high ionospheric activity for undifferenced Global Positioning System (GPS)/BeiDou Navigation Satellite System (BDS) triple-frequency observations collected with a single receiver. First, three optimal linearly independent geometry-free pseudorange minus phase combinations are selected to correctly and uniquely determine the cycle slips on the original triple-frequency carrier phase observations. Then, a second-order time-difference algorithm is employed for the pseudorange minus phase combinations to mitigate the impact of between-epoch ionospheric residuals on cycle slip detection, which is especially beneficial under high ionospheric activity. The performance of the approach is verified with static GPS/BDS triple-frequency observations that are collected with a 30 s sampling interval under active ionospheric conditions, and observations are manually inserted with simulated cycle slips. The results show that the method can correctly detect and repair cycle slips at a resolution as small as 1 cycle. Moreover, kinematic data collected from car-driven and airborne experiments are also processed to verify the performance of the method. The experimental results also demonstrate that the method is effective in processing kinematic data.

Real-time cycle-slip detection and repair for BeiDou triple-frequency undifferenced observations

A new method of real-time cycle-slip detection and repair for BeiDou navigation satellite system (BDS) triple-frequency undifferenced observations is proposed. The method, which is based on code–phase and geometry-free phase combinations, composes linearly independent combination observations to uniquely determine the cycle-slip of original frequency phase observations in two independent steps. First, two extra-wide lane (EWL) code–phase combinations are utilised to determine the EWL combination cycle-slips. The sum of the carrier phase combination coefficients is zero. Second, the geometry-free phase combination with a non-zero sum of combination coefficients composes linearly independent combination observations with two code–phase combinations. Ionospheric delay variance systematic deviation is corrected with several previous carrier-phase observations without cycle-slip, which seriously affect the accuracy of the geometry-free phase combination observations. The BDS triple-frequency carrier-phase and code observations of different satellite types at 30 s sampling interval, which involve increased active ionospheric conditions in 1 day, are utilised to test the method. Results show that the proposed method can efficiently detect and accurately repair any cycle-slip combinations in real-time for different satellite types under active ionospheric conditions. No erroneous and leakage judgments are observed in the test.

Real-time detection and repair of cycle slips in triple-frequency GNSS measurements

Cycle slip detection and repair are prerequisites to the use of the global navigation satellite system (GNSS) carrier phases for precise positioning. Modern GNSS techniques introduce triple- or multi-frequency signals that are beneficial for cycle slip detection and repair. We present a new real-time cycle slip detection and repair method based on the independent linear combinations of undifferenced triple-frequency GNSS observations. The proposed method forms three types of linear combinations based on the original observations. These combinations are called extra-wide lane (EWL), wide lane (WL), and narrow lane (NL). Cycle slips on the combinations are determined sequentially in three cascaded steps. The first step employs the geometry-free and ionosphere-free Hatch–Melbourne–Wübbena combination to determine and repair the EWL cycle slips. The second step subtracts the cycle-slip-repaired EWL combination from the WL combination to eliminate the geometry part of the WL combination. This subtraction results in a new function that contains the WL ambiguity and residual ionospheric delay. This function is differenced at two consecutive epochs to determine the WL cycle slips. The residual ionospheric delay difference is ignored because of its small magnitude relative to WL wavelength. The third step determines the NL cycle slips in the same manner as in the second step. The difference is that the cycle-slip-repaired EWL combination is replaced with the more accurate cycle-slip-repaired WL combination. Moreover, the residual ionospheric delay difference is compensated by the ionospheric delay rate derived from the original carrier phase observations. When the EWL, WL, and NL cycle slips are determined, cycle slips on the original carrier phase observations can be uniquely identified. The proposed approach has been tested on 30-s triple-frequency BeiDou navigation satellite system data under different levels of ionospheric variations, and on 30-s triple-frequency global positioning system and quasi-zenith satellite system data. Results indicate that the approach can effectively detect and correct cycle slips even for one cycle under low sampling rate or active ionospheric conditions on each frequency in real time.

Real Time Cycle Slip Detection and Correction for APSK Modulation

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.

Real-time cycle slip detection in triple-frequency GNSS

The modernization of the global positioning system and the advent of the European project Galileo will lead to a multifrequency global navigation satellite system (GNSS). The presence of new frequencies introduces more degrees of freedom in the GNSS data combination. We define linear combinations of GNSS observations with the aim to detect and correct cycle slips in real time. In particular, the detection is based on five geometry-free linear combinations used in three cascading steps. Most of the jumps are detected in the first step using three minimum-noise combinations of phase and code observations. The remaining jumps with very small amplitude are detected in the other two steps by means of two-tailored linear combinations of phase observations. Once the epoch of the slip has been detected, its amplitude is estimated using other linear combinations of phase observations. These combinations are defined with the aim of discriminating between the possible combinations of jump amplitudes in the three carriers. The method has been tested on simulated data and 1-second triple-frequency undifferenced GPS data coming from a friendly multipath environment. Results show that the proposed method is able to detect and repair all combinations of cycle slips in the three carriers.